Search for an optimal solution to vague traffic problems using the psk method

Handbook of Research
on Investigations in
Artificial Life Research
and Development
Maki Habib
The American University in Cairo, Egypt
A volume in the Advances in Computational
Intelligence and Robotics (ACIR) Book Series

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Subjects: LCSH: Intelligent personal assistants (Computer software) |
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ISSN:2327-0411
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• Computational Logic
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Titles in this Series
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Critical Developments and Applications of Swarm Intelligence
Yuhui Shi (Southern University of Science and Technology, China)
Engineering Science Reference • copyright 2018 • 478pp • H/C (ISBN: 9781522551348) • US $235.00 (our price)
Handbook of Research on Biomimetics and Biomedical Robotics
Maki Habib (The American University in Cairo, Egypt)
Androids, Cyborgs, and Robots in Contemporary Culture and Society
Steven John Thompson (University of Maryland University College, USA)
Developments and Trends in Intelligent Technologies and Smart Systems
Vijayan Sugumaran (Oakland University, USA)
Handbook of Research on Modeling, Analysis, and Application of Nature-Inspired Metaheuristic Algorithms
Sujata Dash (North Orissa University, India) B.K. Tripathy (VIT University, India) and Atta ur Rahman (University
of Dammam, Saudi Arabia)
Concept Parsing Algorithms (CPA) for Textual Analysis and Discovery Emerging Research and Opportunities
Uri Shafrir (University of Toronto, Canada) and Masha Etkind (Ryerson University, Canada)
Information Science Reference • copyright 2018 • 139pp • H/C (ISBN: 9781522521761) • US $130.00 (our price)
Handbook of Research on Applied Cybernetics and Systems Science
Snehanshu Saha (PESIT South Campus, India) Abhyuday Mandal (University of Georgia, USA) Anand Narasim-
hamurthy (BITS Hyderabad, India) Sarasvathi V (PESIT- Bangalore South Campus, India) and Shivappa Sangam
(UGC, India)
Information Science Reference • copyright 2017 • 463pp • H/C (ISBN: 9781522524984) • US $245.00 (our price)
Handbook of Research on Machine Learning Innovations and Trends
Aboul Ella Hassanien (Cairo University, Egypt) and Tarek Gaber (Suez Canal University, Egypt)
InformationScienceReference•copyright2017•1093pp•H/C(ISBN:9781522522294)•US$465.00(ourprice)
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Preface

INTRODUCTION
The evolution of nature and biological systems is helping to create new reality with great potential to
resolve many research and development challenges. Hence, there is a need to study and examine nature,
itsmodels,elements,processes,systems,structures,mechanisms,etc.totakeinspirationfrom,oremulate,
nature’s best biological ideas and products in order to solve modern science and engineering problems.
Artificial Life is featured as an emerging, interdisciplinary and unifying field of research to study
phenomena or abilities of living systems in nature including human and analyze research findings to
integrate effectively scientific information for the purpose to develop life like artificial systems and
machines that exhibit the autonomous behavioral and characteristics of natural living systems. These
systemsarenormallybasedoncomputersimulationsandhardwaredesignsofstate-of-the-arttechnologies
that span brain and cognitive sciences, the origin of life and living systems, self-assembly and develop-
ment of evolutionary and ecological dynamics, animal and machine behaviors including robots, social
organization, and cultural evolution to improve and comprehend real-world problems.
ORGANIZATION OF THE BOOK
This handbook includes 19 chapters that contribute with the state-of-art and up-to-date knowledge on
research advancement in the field of Artificial Life research and development. The chapters provide
theoretical knowledge, practices, algorithms, technological evolution and new findings. Furthermore,
the handbook helps to prepare engineers and scientists who are looking to develop innovative, challeng-
ing, intelligent, bioinspired systems and value added ideas for autonomous and smart interdisciplinary
software, hardware and systems to meet today’s and future most pressing challenges.
Chapter 1: An Electric Wheelchair Controlled by
Head Movements and Facial Expressions
A bio-signal based human machine interface is proposed for hands-free control of a wheelchair. An
Emotiv EPOC sensor is used to detect facial expressions and head movements of users. Nine facial
expressions and up-down head movements can be chosen to form five commands: move-forward and
xviii

Preface
backward, turn-left and right, and stop. Four unimodal modes, three bi-modal modes and three fuzzy
bi-modal modes are created to control a wheelchair. Fuzzy modes use the users’ strength in making
the head movement and facial expression to adjust the wheelchair speed via a fuzzy logic system. The
developed system was tested and evaluated.
Chapter 2: Innovative Features and Applications
Provided by a Large-Area Sensor Floor
This chapter describes new functions, features and applications of the developed capacitive sensor system
SensFloor®. The chapter focuses on applications for health care and Ambient Assisted Living (AAL).
In addition, the chapter presents applications in other domains as well, such as medical assessments,
retail, security and multimedia.
Chapter 3: Reassessing Underlying Spatial Relations in Pedestrian
Navigation – A Comparison Between Sketch Maps and Verbal Descriptions
The chapter assesses underlying spatial relations for pedestrian wayfinding by examining and experi-
menting navigational directions given in both forms of sketch maps and verbal descriptions. The authors
were specifically interested in the landmarks and spatial relationships such as route topology, linear order
relation and relative orientation extracted from the navigational directions. A new ontological approach
to sketch and verbal interpretations was adopted for spatial analysis.
Chapter 4: What Is It Like to Be a Cyborg?
This chapter describes the personal experience of the author experimenting a Cyborg (part biology/part
technology) by having technology implanted in his body, which he lived with over a period of time. A
look is also taken at the author’s experiments into creating Cyborgs by growing biological brains which
are subsequently given a robot body. In each case the nature of the experiment is briefly described along
with the results obtained and this is followed by an indication of the experience, including personal
feelings and emotions felt in and around the time of the experiments and subsequently as a result of the
experiments.
Chapter 5: Artificial-Intelligence-Based Service-Oriented
Architectures (SOAs) for Crisis Management
This chapter deals with the complexity of crisis-related situations that requires the use of advanced tech-
nologicalinfrastructures.Inordertodevelopsuchinfrastructures,specificarchitecturesneedtobeapplied
such as the Service-Oriented Architectures (SOAs). The purpose of this chapter is to indicate how SOAs
can be used in modern Crisis Management systems, such as the ATHENA system. It also underlines the
need for a detailed study of specific biological systems, such as the human brain’s hippocampus which
follows the current, intense attempts of improvement of the current Artificial Intelligence-based systems
and the development of a new area in Artificial Intelligence.
xix

Preface
Chapter 6: A Tour of Lattice-Based Skyline Algorithms
There exist many Skyline algorithms which can be classified into generic, index-based, and lattice-based
algorithms. The work in this chapter takes a tour through lattice-based Skyline algorithms summarizing
itsbasicconceptsandproperties,presentshigh-performanceparallelapproaches.Inaddition,itintroduces
how to overcome the low-cardinality restriction of lattice structures. Experimental results on synthetic
and real datasets show that lattice-based algorithms outperform state-of-the-art Skyline techniques.
Chapter 7: Swarm Optimization Application to
Molding Sand System in Foundries
In this chapter optimization of resin-bonded molding sand system is discussed. Six different case studies
are considered by assigning different combination of weight fractions for multiple objective functions
and corresponding desirability (Do) values are determined for DFA, GA, PSO and MOPSO-CD. The
highest desirability value is considered as the optimum solution.
Chapter 8: Application of Computational Intelligence
in Network Intrusion Detection – A Review
Network Intrusion detection (NID) suffers from several problems, such as false positives, operational
issues in high dimensional data, and the difficulty of detecting unknown threats. Most of the problems
withintrusiondetectionarecausedbyimproperimplementationofthenetworkintrusiondetectionsystem
(NIDS). The scope of this chapter encompasses the concept of NID and presents the core methods that
use computational intelligence and cover Support vector machine, Hidden Naïve Bayes, Particle Swarm
Optimization, Genetic Algorithm and Fuzzy logic techniques. The findings of this studyhighlight current
research challenges and progress with focus on the promising new research directions.
Chapter 9: Performance Comparison of PSO and Hybrid PSO-
GA in Hiding Fuzzy Sensitive Association Rules
It is possible to infer sensitive information from the published non sensitive data using association rule
mining. An association rule is characterized as sensitive if its confidence is above disclosure threshold.
This chapter proposes a system with aim to hide a set of sensitive association rules by perturbing the
quantitative data that contains sensitive knowledge using PSO and Hybrid PSO-GA with minimum side
effects like lost rules, ghost rules. The performance of PSO and Hybrid PSO-GA approach in effectively
hiding Fuzzy association rule is also compared.
Chapter 10: Modeling Fish Population Dynamics
for Sustainability and Resilience
Conservation of any living creature is very vital to maintain the balance of ecosystem. Fish is one of the
most regularly consumed living creatures, and hence its conservation is essential for sustainable fish
population to help maintain a balanced ecosystem. Developing a model on fish population dynamics is
neededtoachievethisobjective.Thischapterpresentsasystemdynamicsmodelthatprovidesthescientific
xx

Preface
tools for determining fish population, its growth, and harvesting. The model’s sensitivity to changes in
key parameters and initial values resulting from the changes in basic scenarios and boundary conditions
were tested under different real-world changing conditions to maintain a sustainable fish population.
Chapter 11: Search for an Optimal Solution to Vague
Traffic Problems Using the PSK Method
This chapter tries to categorize the transportation problem (TP) under four different environments and
formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal
fuzzy numbers (TrFNs) to solve the TP. A new method, namely, PSK (P. Senthil Kumar) method for find-
ing a fuzzy optimal solution to fuzzy transportation problem (FTP) is proposed I this chapter. Practical
usefulness of the PSK method over other existing methods is demonstrated and discussed.
Chapter 12: Design Patterns for Social Intelligent
Agent Architectures Implementation
Multi-Agent Systems (MAS) architectures are popular for building open, distributed, and evolving soft-
ware required by today’s business IT applications such as eBusiness systems, web services or enterprise
knowledge bases. Since the fundamental concepts of MAS are social and intentional rather than object,
functional, or implementation-oriented, the design of MAS architectures can be eased by using social
patterns. This chapter presents social patterns and focuses on a framework aimed to gain insight into
these patterns.
Chapter 13: Agent-Based Software Engineering,
Paradigm Shift, or Research Program Evolution
Information systems are deeply linked to human activities. Unfortunately, development methodologies
have been traditionally inspired by programming concepts and not by organizational and human ones.
This leads to ontological and semantic gaps between the systems and their environments. This chapter
presents the adoption of agent orientation and Multi-Agent Systems (MAS) to reduce these gaps by of-
feringmodelingtoolsbasedonorganizationalconcepts(actors,agents,goals,objectives,responsibilities,
social dependencies, etc.) as fundamentals to conceive systems through all the development process.
Chapter 14: Application of Fuzzy Sets and Shadowed
Sets in Predicting Time Series Data
In all existing works on fuzzy time series model, cluster with highest membership is used to form fuzzy
logical relationships. However, the position of the element within the cluster is not considered. This
chapter incorporates the idea of fuzzy discretization and shadowed set theory in defining intervals and
uses the positional information of elements within a cluster in selection of rules for decision making.
The objective is to show the effect of the elements, lying outside the core area on forecast.
xxi

Preface
Chapter 15: Fuzzy-DSS Human Health Risk
Assessment Under Uncertain Environment
It is noticed that often model parameters, data, information are fouled with uncertainty due to lack of
precision, deficiency in data, diminutive sample sizes, etc. In such environments, fuzzy set theory or
Dempster-Shafer theory (DST) can be explored to represent this type of uncertainty. This chapter pres-
ents two algorithms to combine Dempster-Shafer structure (DSS) with generalized/normal fuzzy focal
elements, generalized/normal fuzzy numbers within the same framework. Finally, human health risk
assessment is carried out under these setting.
Chapter 16: Enhanced Complex Event Processing
Framework for Geriatric Remote Healthcare
Geriatric Remote Health Monitoring System (GRHMS) uses WBAN (Wireless Body Area Network)
which provides flexibility and mobility for the patients. GRHMS uses Complex Event Processing (CEP)
to detect the abnormality in patient’s health condition, formulate contexts based on spatiotemporal rela-
tions between vital parameters, learn rules dynamically and generate alerts in real time. Though, CEP is
powerful in detecting abnormal events, its capability is limited due to uncertain incoming events, static
rule base and scalability problem. Hence, this chapter addresses these challenges and proposes an en-
hanced CEP (eCEP) which encompasses augmented CEP (a-CEP), a statistical event refinement model
to minimize the error due to uncertainty, Dynamic CEP (DCEP) to add and delete rules dynamically
into the rule base and Scalable CEP (SCEP) to address scalability problem. Experimental results show
that the proposed framework has better accuracy in decision making.
Chapter 17: CASPL – A Coevolution Analysis
Platform for Software Product Lines
It is important to recognize that the change impact analysis and the evolution understanding in software
product lines require greater focus than in single software. This chapter presents CASPL platform for
co-evolution analysis in software product lines. The platform uses evolutionary trees that are mainly used
in biology to analyze the co-evolution between applications. The major goal is to enhance the change
understanding and to compare the history of changes in the applications of the family, at the aim of cor-
recting divergences between them.
Chapter 18: Hybrid Term-Similarity-Based Clustering
Approach and Its Applications
This chapter presents a method that first adopts ontology learning to generate ontologies via the hidden
semantic patterns existing within complex terms. Then, it proposes service recommendation and selec-
tion approaches based on the proposed clustering approach. Experimental results show that developed
term-similarity approach outperforms comparable existing clustering approaches. Further, empirical
study of the prototyping recommendation and selection approaches have proved the effectiveness of
proposed novel two approaches.
xxii

Preface
Chapter 19: Deep Model Framework for Ontology-Based Document Clustering
Although there is enormous amount of information available online, most of the documents are uncat-
egorized. It is time consuming task for the users to browse through a large number of documents and
search for information about specific topics. The ability of automatic clustering from uncategorized
documents is important and has great potential to improve the efficiency of information seeking behav-
iors. To address this issue this chapter proposes a deep ontology based approach to document clustering.
The obtained results are used to implement annotation rules and the information extraction capabilities
of annotated framework are compared with and without using ontology.
Maki K. Habib
The American University in Cairo, Egypt
xxiii

Table of Contents

Preface................................................................................................................................................xviii
Chapter 1
An Electric Wheelchair Controlled by Head Movements and Facial Expressions: Uni-Modal, Bi-
Modal, and Fuzzy Bi-Modal Modes........................................................................................................ 1
Ericka Janet Rechy-Ramirez, Universidad Veracruzana, Mexico
Huosheng Hu, University of Essex, UK
Chapter 2
Innovative Features and Applications Provided by a Large-Area Sensor Floor.................................... 31
Axel Steinhage, Future-Shape GmbH, Germany
Christl Lauterbach, Future-Shape GmbH, Germany
Axel Techmer, Future-Shape GmbH, Germany
Raoul Hoffmann, Future-Shape GmbH, Germany
Miguel Sousa, Future-Shape GmbH, Germany
Chapter 3
Reassessing Underlying Spatial Relations in Pedestrian Navigation: A Comparison Between
Sketch Maps and Verbal Descriptions................................................................................................... 49
Jia Wang, University of Greenwich, UK
Rui Li, University at Albany (SUNY), USA Sichuan Fine Arts Institute, China
Chapter 4
What Is It Like to Be a Cyborg?............................................................................................................ 68
Kevin Warwick, Coventry University, UK
Chapter 5
Artificial-Intelligence-Based Service-Oriented Architectures (SOAs) for Crisis Management............ 79
Konstantinos Domdouzis, Sheffield Hallam University, UK
Chapter 6
A Tour of Lattice-Based Skyline Algorithms........................................................................................ 96
Markus Endres, University of Augsburg, Germany
Lena Rudenko, University of Augsburg, Germany

Chapter 7
Application of Statistical Modelling and Evolutionary Optimization Tools in Resin-Bonded
Molding Sand System.......................................................................................................................... 123
Ganesh R. Chate, K. L. S. Gogte Institute of Technology, India
Manjunath Patel G. C., Sahyadri College of Engineering and Management, India
Mahesh B. Parappagoudar, Padre Conceicao College of Engineering, India
Anand S. Deshpande, K. L. S. Gogte Institute of Technology, India
Chapter 8
Application of Computational Intelligence in Network Intrusion Detection: A Review..................... 153
Heba F. Eid, Al Azhar University, Egypt
Chapter 9
Performance Comparison of PSO and Hybrid PSO-GA in Hiding Fuzzy Sensitive Association
Rules.................................................................................................................................................... 175
Sathiyapriya Krishnamoorthy, PSG College of Technology, India
Sudha Sadasivam G., PSG College of Technology, India
Rajalakshmi M., Coimbatore Institute of Technology, India
Chapter 10
Modeling Fish Population Dynamics for Sustainability and Resilience.............................................. 199
Nayem Rahman, Portland State University, USA
Mahmud Ullah, University of Dhaka, Bangladesh
Chapter 11
Search for an Optimal Solution to Vague Traffic Problems Using the PSK Method........................... 219
P. Senthil Kumar, Jamal Mohamed College (Autonomous), India
Chapter 12
Design Patterns for Social Intelligent Agent Architectures Implementation....................................... 258
Manuel Kolp, Université catholique de Louvain, Belgium
Yves Wautelet, KU Leuven, Belgium
Samedi Heng, Université catholique de Lovuain, Belgium
Chapter 13
Agent-Based Software Engineering, Paradigm Shift, or Research Program Evolution...................... 284
Yves Wautelet, KU Leuven, Belgium
Christophe Schinckus, Royal Melbourne Institute of Technology, Australia
Manuel Kolp, Université catholique de Lovuain, Belgium
Chapter 14
Application of Fuzzy Sets and Shadowed Sets in Predicting Time Series Data.................................. 297
Mahua Bose, University of Kalyani, India
Kalyani Mali, University of Kalyani, India

Chapter 15
Fuzzy-DSS Human Health Risk Assessment Under Uncertain Environment..................................... 316
Palash Dutta, Dibrugarh University, India
Chapter 16
Enhanced Complex Event Processing Framework for Geriatric Remote Healthcare.......................... 348
V. Vaidehi, VIT University, India
Ravi Pathak, Striim Inc., India
Renta Chintala Bhargavi, VIT University Chennai, India
Kirupa Ganapathy, Saveetha University, India
C. Sweetlin Hemalatha, VIT University, India
A. Annis Fathima, VIT University, India
P. T. V. Bhuvaneswari, Madras Institute of Technology, India Anna University, India
Sibi Chakkaravarthy S., Madras Institute of Technology, India Anna University, India
Xavier Fernando, Ryerson University, Canada
Chapter 17
CASPL: A Coevolution Analysis Platform for Software Product Lines............................................. 380
Anissa Benlarabi, Mohamed V University, Morocco
Amal Khtira, Mohammed V University, Morocco
Bouchra El Asri, Mohamed V University, Morocco
Chapter 18
Hybrid Term-Similarity-Based Clustering Approach and Its Applications........................................ 397
Banage T. G. S. Kumara, Sabaragamuwa University of Sri Lanka, Sri Lanka
Incheon Paik, University of Aizu, Japan
Koswatte R. C. Koswatte, Sri Lanka Institute of Information Technology, Sri Lanka
Chapter 19
Deep Model Framework for Ontology-Based Document Clustering.................................................. 424
U. K. Sridevi, Sri Krishna College of Engineering and Technology, India
P. Shanthi, Sri Krishna College of Engineering and Technology, India
N. Nagaveni, Coimbatore Institute of Technology, India
Compilation of References................................................................................................................ 436
About the Contributors..................................................................................................................... 490
Index.................................................................................................................................................... 499

219
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Chapter 11
DOI: 10.4018/978-1-5225-5396-0.ch011
ABSTRACT
There are several algorithms, in literature, for obtaining the fuzzy optimal solution of fuzzy transporta-
tion problems (FTPs). To the best of the author’s knowledge, in the history of mathematics, no one has
been able to solve transportation problem (TP) under four different uncertain environment using single
method in the past years. So, in this chapter, the author tried to categories the TP under four different
environments and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers
(TFNs), and trapezoidal fuzzy numbers (TrFNs) to solve the TP. A new method, namely, PSK (P. Senthil
Kumar) method for finding a fuzzy optimal solution to fuzzy transportation problem (FTP) is proposed.
Practical usefulness of the PSK method over other existing methods is demonstrated with four different
numerical examples. To illustrate the PSK method different types of FTP is solved by using the PSK
method and the obtained results are discussed.
1. INTRODUCTION
Resource allocation is used to assign the available resources in an economic way. When the resources
to be allocated are scarce, a well-planned action is necessary for a decision-maker (DM) to attain the
optimal utility. If the supplying sources and the receiving agents are limited, the best pattern of alloca-
tion to get the maximum return or the best plan with the least cost, whichever may be applicable to the
problem, is to be found out. This class of problems is termed as ‘allocation problems’ and is divided
into ‘transportation problems (TPs)’ and ‘assignment problems (APs)’. The TPs and APs both are also
called optimization problems.
Search for an Optimal Solution
to Vague Traffic Problems
Using the PSK Method
P. Senthil Kumar
Jamal Mohamed College (Autonomous), India

220
Search for an Optimal Solution to Vague Traffic Problems Using the PSK Method

TPs play an important role in logistics and supply chain management for reducing cost and improving
service. In today’s highly competitive market, the pressure on organizations to find better ways to create
and deliver products and services to customers becomes stronger. How and when to send the products to
the customers in the quantities which they want in a cost-effective manner becomes more challenging.
Transportation models provide a powerful framework to meet this challenge. They ensure the efficient
movement and timely availability of raw materials and finished goods.
The TP is a special class of linear programming problem (LPP) which deals with the distribution of
single homogeneous product from various origins (sources) to various destinations (sinks). The objec-
tive of the TP is to determine the optimal amount of a commodity to be transported from various supply
points to various demand points so that the total transportation cost is minimum for a minimization
problem or total transportation profit is maximum for a maximization problem.
The unit costs, that is, the cost of transporting one unit from a particular supply point to a particular
demand point, the amounts available at the supply points and the amounts required at the demand points
are the parameters of the TP. Efficient algorithms have been developed for solving TPs when the cost
coefficients, the demand and supply quantities are known precisely.
In the history of mathematics, Hitchcock (1941) originally developed the basic TP. Charnes and
Cooper (1954) developed the stepping stone method which provides an alternative way of determin-
ing the simplex method information. Appa (1973) discussed several variations of the TP. Arsham et
al. (1989) proposed a simplex type algorithm for general TPs. An Introduction to Operations Research
Taha (2008) deals the TP. Aljanabi and Jasim (2015) presented an approach for solving TP using modi-
fied Kruskal’s algorithm. Ahmed et al. (2016) developed a new approach to solve TPs. Akpan and Iwok
(2017) presented a minimum spanning tree approach of solving a TP.
In today’s real world problems such as in corporate or in industry many of the distribution problems
are imprecise in nature due to variations in the parameters. To deal quantitatively with imprecise infor-
mation in making decision, Zadeh (1965) introduced the fuzzy set theory and has applied it successfully
in various fields. The use of fuzzy set theory becomes very rapid in the field of optimization after the
pioneering work done by Bellman and Zadeh (1970). The fuzzy set deals with the degree of membership
(belongingness) of an element in the set. In a fuzzy set the membership value (level of acceptance or
level of satisfaction) lies between 0 and 1 where as in crisp set the element belongs to the set represent
1 and the element not belongs to the set represent 0.
The occurrence of randomness and imprecision in the real world is inevitable owing to some unex-
pected situations. To deal quantitatively with imprecise information in making decisions, Bellman and
Zadeh (1970) and Zadeh (1978) introduced the notion of fuzziness. There are cases that the cost coef-
ficients (or profit coefficients for the maximization TP) or/and the supply and demand quantities of a
TP may be uncertain due to some uncontrollable factors. Such TPs are known as FTPs. The objective of
the FTP is to determine the shipping schedule that optimizes the total fuzzy transportation cost / fuzzy
transportation profit while satisfying fuzzy supply and fuzzy demand limits. In the history of math-
ematics, various efficient algorithms were developed for solving FTPs using fuzzy linear programming
techniques, crisp conversion techniques, or the parametric programming technique. Some of the studies
provide an optimal solution for FTPs, which is not a fuzzy number, but a crisp value. If the obtained
results are crisp values, then it might lose some helpful information.
Various effective methods were developed for solving TPs with the assumption that the coefficients
of the objective function and the demand and supply values are specified in a precise manner. However,
these conditions may not be satisfied always. For example, the unit transportation costs are rarely con-

P. Senthil Kumar (Jamal Mohamed College (Autonomous), India)
Source Title: Handbook of Research on Investigations in Artificial Life Research and
Development
Copyright: © 2018 |Pages: 39
DOI: 10.4018/978-1-5225-5396-0.ch011
OnDemand PDF $30.00
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Reference to this paper should be made as follows:
MLA
Kumar, P. Senthil. Search for an Optimal Solution to Vague Traffic Problems Using the
PSK Method. Handbook of Research on Investigations in Artificial Life Research and
Development. IGI Global, 2018. 219-257. Web. 8 Jun. 2018. doi:10.4018/978-1-5225-5396-
0.ch011
APA
Kumar, P. S. (2018). Search for an Optimal Solution to Vague Traffic Problems Using the
PSK Method. In M. Habib (Ed.), Handbook of Research on Investigations in Artificial Life
Research and Development (pp. 219-257). Hershey, PA: IGI Global. doi:10.4018/978-1-
5225-5396-0.ch011
Chicago
Kumar, P. Senthil. Search for an Optimal Solution to Vague Traffic Problems Using the
PSK Method. In Handbook of Research on Investigations in Artificial Life Research and
Development, ed. Maki Habib, 219-257 (2018), accessed June 08, 2018. doi:10.4018/978-1-
5225-5396-0.ch011
Harvard
Kumar, P.S., 2018. Search for an Optimal Solution to Vague Traffic Problems Using the PSK
Method. In Handbook of Research on Investigations in Artificial Life Research and
Development (pp. 219-257). IGI Global.
Vancouver
Kumar PS. Search for an Optimal Solution to Vague Traffic Problems Using the PSK
Method. In Handbook of Research on Investigations in Artificial Life Research and
Development 2018 (pp. 219-257). IGI Global.

248

,
,
µZ
c
for c
c
fo
( )=
≤
−
0 104
104
64
rr c
for c
c
for
,
,
104 168
1 168 184
248
64
≤ ≤
≤ ≤
−
1184 248
0 248
≤ ≤
≥



c
for c,



(8)
Advantages of the PSK method
By using the proposed method a DM has the following advantages:
1. The proposed method gives the optimal solution in terms of mixed fuzzy numbers. Moreover, the
proposed method give the opportunity to the DM to solve all the types of FTP.
2. The PSK method is easy to understand and computationally very simple.
3. Both the maximization and minimization FTP can be solved by using PSK method.
4. The PSK method gives the new ideas for solving the variety of optimization problems.
5. The PSK method reduces the computation time of the decision maker.
7. CONCLUSION AND FUTURE WORK
On the basis of the present study, it can be concluded that the type-1, type-2, type-3 or mixed FTP and
type-4 FTP which can be solved by the existing methods (Pandian and Natarajan (2010), Dinagar and
Palanivel (2009), Rani, Gulathi, and Kumar (2014), Basirzadeh (2011), Ahmed et al. (2015), Gani
Figure 2. Graphical representation of type-3 fuzzy transportation cost

249

and Razak (2006)) can also be solved by the proposed method. However, it is much easier to apply the
proposed method as compared to all the existing methods. Also, new method and new multiplication
operation on TrFN is proposed to compute the optimal objective values in terms of TrFNs which are
very simple and easy to understand and it can be easily applied by DM to solve type-1, type-2, type-3
and type-4 FTP. The PSK method gives the optimal solution in terms of mixed fuzzy numbers. Hence
the PSK method give the opportunity to the DM to solve all the types of FTP and computationally very
simple when compared to all the existing methods. Further, the optimal solution and optimal objective
value of the proposed type-2 FTP and its crisp TP have been verified by using both the proposed method
and the LINGO 17.0 software tool. My future research will extend the proposed method here to deal
with the transportation problems under intuitionistic fuzzy environment. In addition, the author would
like to develop the software package for solving fuzzy transportation problems by using PSK method.
ACKNOWLEDGMENT
The author sincerely thanks the anonymous reviewers and Editor-in-Chief Professor Maki Habib for
their careful reading, constructive comments and fruitful suggestions. The author would also like to
acknowledge Dr.S.Ismail Mohideen, Additional Vice Principal, My Guide and Associate Professor
Dr.R.Jahir Hussain, Dr.A.Nagoor Gani, Associate Professor, Dr.K.Ramanaiah, Associate Professor
(retired), Mr.N.Shamsudeen, Associate Professor (retired), Jamal Mohamed College (Autonomous),
Tiruchirappalli, Tamil Nadu, India for their motivation and kind support.
REFERENCES
Agustina, F., Lukman, Puspita, E. (2017, May 30). PMZ method for solving fuzzy transporta-
tion. In AIP Conference Proceedings. Melville, NY: American Institute of Physics (AIP) Publishing.
doi:10.1063/1.4983945
Ahmed, M. M., Khan, A. R., Uddin, M. S., Ahmed, F. (2016). A new approach to solve transportation
problems. Open Journal of Optimization, 5(01), 22–30. doi:10.4236/ojop.2016.51003
Ahmed, N. U., Khan, A. R., Uddin, M. S. (2015). Solution of mixed type transportation problem:
A fuzzy approach. Bul. Ins. Pol. Din Iasi, Romania. Secţia Automatica si Calculatoare, 61(2), 19–32.
Akpan, N. P., Iwok, I. A. (2017). A minimum spanning tree approach of solving a transportation
problem. International Journal of Mathematics and Statistics Invention, 5(3), 8-17.
Ali, A. M., Faraz, D. (2017). Solving fuzzy triangular transportation problem using fuzzy least cost
method with ranking approach. International Journal of Current Research in Science and Technology,
3(7), 15–20.
Aljanabi, K. B., Jasim, A. N. (2015). An approach for solving transportation problem using modified
Kruskal’s algorithm. International Journal of Science and Research, 4(7), 2426–2429.
AnithaKumari, T., Venkateswarlu, B., Murthy, A. S. (2017). Fuzzy transportation problems with new
kind of ranking function. International Journal of Engineering Science, 6(11), 15–19.

250

Anuradha, D., Sobana, V. E. (2017, November). A survey on fuzzy transportation problems. In IOP
Conference Series: Materials Science and Engineering (Vol. 263, No. 4, p. 042105). IOP Publishing.
doi:10.1088/1757-899X/263/4/042105
Appa, G. M. (1973). The transportation problem and its variants. The Journal of the Operational Re-
search Society, 24(1), 79–99. doi:10.1057/jors.1973.10
Arsham, H., Kahn, A. B. (1989). A simplex-type algorithm for general transportation problems:
An alternative to stepping-stone. The Journal of the Operational Research Society, 40(6), 581–590.
doi:10.1057/jors.1989.95
Atanassov, K.T. (1983). Intuitionistic fuzzy sets. Library of Bulg. Acad. of Sci., 1697(84).
Basirzadeh, H. (2011). An approach for solving fuzzy transportation problem. Applied Mathematical
Sciences, 5(32), 1549–1566.
Baykasoğlu, A., Subulan, K. (2017). Constrained fuzzy arithmetic approach to fuzzy transportation
problems with fuzzy decision variables. Expert Systems with Applications, 81, 193–222. doi:10.1016/j.
eswa.2017.03.040
Bellman, R. E., Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science,
17(4), B-141–B-164. doi:10.1287/mnsc.17.4.B141
Biswas, A., Modak, N. (2012). Using fuzzy goal programming technique to solve multiobjective
chance constrained programming problems in a fuzzy environment. International Journal of Fuzzy
System Applications, 2(1), 71–80. doi:10.4018/ijfsa.2012010105
Chanas, S., Delgado, M., Verdegay, J. L., Vila, M. A. (1993). Interval and fuzzy extensions
of classical transportation problems. Transportation Planning and Technology, 17(2), 203–218.
doi:10.1080/03081069308717511
Chanas, S., Kołodziejczyk, W., Machaj, A. (1984). A fuzzy approach to the transportation problem.
Fuzzy Sets and Systems, 13(3), 211–221. doi:10.1016/0165-0114(84)90057-5
Chanas, S., Kuchta, D. (1996). A concept of the optimal solution of the transportation problem with
fuzzy cost coefficients. Fuzzy Sets and Systems, 82(3), 299–305. doi:10.1016/0165-0114(95)00278-2
Chanas, S., Kuchta, D. (1998). Fuzzy integer transportation problem. Fuzzy Sets and Systems, 98(3),
291–298. doi:10.1016/S0165-0114(96)00380-6
Charnes, A., Cooper, W. W. (1954). The stepping stone method of explaining linear programming
calculations in transportation problems. Management Science, 1(1), 49–69. doi:10.1287/mnsc.1.1.49
Chen, M., Ishii, H., Wu, C. (2008). Transportation problems on a fuzzy network. International Journal
of Innovative Computing, Information, Control, 4(5), 1105–1109.
Chen, S. H., Hsieh, C. H. (1999). Graded mean integration representation of generalized fuzzy num-
bers. Journal of the Chinese Fuzzy Systems Association, 5(2), 1–7.
Chiang, J. (2005). The optimal solution of the transportation problem with fuzzy demand and fuzzy
product. Journal of Information Science and Engineering, 21(2), 439–451.

251

Christi, M. S. A., Malini, D. (2016). An approach to solve transportation problems with octagonal
fuzzy numbers using best candidates method and different ranking techniques. International Journal of
Computers and Applications, 6(1), 71–85.
Das, M., Baruah, H. K. (2007). Solution of the transportation problem in fuzzified form. Journal of
Fuzzy Mathematics, 15(1), 79–95.
De, P. K., Yadav, B. (2010). Approach to defuzzify the trapezoidal fuzzy number in transportation
problem. International Journal of Computational Cognition, 8(4), 64–67.
Dinagar, D. S., Palanivel, K. (2009). The transportation problem in fuzzy environment. International
Journal of Algorithms. Computing and Mathematics, 2(3), 65–71.
Ebrahimnejad, A. (2012). Cost efficiency measures with trapezoidal fuzzy numbers in data envelopment
analysis based on ranking functions: Application in insurance organization and hospital. International
Journal of Fuzzy System Applications, 2(3), 51–68. doi:10.4018/ijfsa.2012070104
Ebrahimnejad, A. (2016a). Fuzzy linear programming approach for solving transportation problems with
interval-valued trapezoidal fuzzy numbers. Sadhana, 41(3), 299–316.
Ebrahimnejad, A. (2016b). New method for solving fuzzy transportation problems with LR flat fuzzy
numbers. Information Sciences, 357, 108–124. doi:10.1016/j.ins.2016.04.008
Gani, A. N., Razak, K. A. (2006). Two stage fuzzy transportation problem. The Journal of Physi-
ological Sciences; JPS, 10, 63–69.
Gani, A. N., Samuel, A. E., Anuradha, D. (2011). Simplex type algorithm for solving fuzzy trans-
portation problem. Tamsui Oxford Journal of Information and Mathematical Sciences, 27(1), 89–98.
Hasan, M. K. (2012). Direct methods for finding optimal solution of a transportation problem are not
always reliable. International Refereed Journal of Engineering and Science, 1(2), 46–52.
Hitchcock,F.L.(1941).Thedistributionofaproductfromseveralsourcestonumerouslocalities.Journal
of Mathematics and Physics, 20(2), 224–230. doi:10.1002apm1941201224
Hunwisai, D., Kumam, P. (2017). A method for solving a fuzzy transportation problem via Robust
rankingtechniqueandATM.CogentMathematics,4(1),1283730.doi:10.1080/23311835.2017.1283730
Hussain, R. J., Kumar, P. S. (2012a). The transportation problem with the aid of triangular intuitionistic
fuzzy numbers. In Proceedings in International Conference on Mathematical Modeling and Applied
Soft Computing (MMASC-2012). Coimbatore Institute of Technology.
Hussain, R. J., Kumar, P. S. (2012b). The transportation problem in an intuitionistic fuzzy environ-
ment. International Journal of Mathematics Research, 4(4), 411–420.
Hussain, R. J., Kumar, P. S. (2012c). Algorithmic approach for solving intuitionistic fuzzy transporta-
tion problem. Applied Mathematical Sciences, 6(80), 3981–3989.
Hussain,R.J.,Kumar,P.S.(2013).Anoptimalmore-for-lesssolutionofmixedconstraintsintuitionistic
fuzzy transportation problems. International Journal of Contemporary Mathematical Sciences, 8(12),
565–576. doi:10.12988/ijcms.2013.13056

252

Kikuchi, S. (2000). A method to defuzzify the fuzzy number: Transportation problem application. Fuzzy
Sets and Systems, 116(1), 3–9. doi:10.1016/S0165-0114(99)00033-0
Kumar, A., Kaur, A. (2013). Methods for solving fully fuzzy transportation problems based on clas-
sical transportation methods. In J. Wang (Ed.), Optimizing, Innovating, and Capitalizing on Information
Systems for Operations (pp. 328–347). Hershey, PA: IGI Global. doi:10.4018/978-1-4666-2925-7.ch017
Kumar, A., Kaur, A., Gupta, A. (2011). Fuzzy linear programming approach for solving fuzzy trans-
portation problems with transhipment. Journal of Mathematical Modelling and Algorithms, 10(2),
163–180. doi:10.100710852-010-9147-8
Kumar, P. S. (2016a). PSK method for solving type-1 and type-3 fuzzy transportation problems. Inter-
national Journal of Fuzzy System Applications, 5(4), 121–146. doi:10.4018/IJFSA.2016100106
Kumar,P.S.(2016b).Asimplemethodforsolvingtype-2andtype-4fuzzytransportationproblems.Inter-
nationalJournalofFuzzyLogicandIntelligentSystems,16(4),225–237.doi:10.5391/IJFIS.2016.16.4.225
Kumar, P. S. (2017a). PSK method for solving type-1 and type-3 fuzzy transportation problems. In I.
Management Association (Ed.), Fuzzy Systems: Concepts, Methodologies, Tools, and Applications (pp.
367-392). Hershey, PA: IGI Global. doi:10.4018/978-1-5225-1908-9.ch017
Kumar, P. S. (2017b). Algorithmic approach for solving allocation problems under intuitionistic fuzzy
environment (Unpublished doctoral dissertation). Jamal Mohamed College (Autonomous), Tiruchirap-
palli, India.
Kumar, P. S. (2018a). A note on ‘a new approach for solving intuitionistic fuzzy transportation problem
of type-2’. International Journal of Logistics Systems and Management, 29(1), 102–129. doi:10.1504/
IJLSM.2018.088586
Kumar, P. S. (2018b). Linear programming approach for solving balanced and unbalanced intuitionistic
fuzzy transportation problems. International Journal of Operations Research and Information Systems,
9(2), 73–100. doi:10.4018/IJORIS.2018040104
Kumar, P. S. (2018c). Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy trans-
portation problem. International Journal of Operational Research.
Kumar, P. S. (2018d). PSK method for solving intuitionistic fuzzy solid transportation problems. Inter-
national Journal of Fuzzy System Applications.
Kumar, P. S. (2018e). A simple and efficient algorithm for solving type-1 intuitionistic fuzzy solid
transportation problems International Journal of Operations Research and Information Systems.
Kumar, P. S., Hussain, R. J. (2014a). New algorithm for solving mixed intuitionistic fuzzy assignment
problem. In Elixir Applied Mathematics (pp. 25971–25977). Salem, Tamilnadu, India: Elixir Publishers.
Kumar, P. S., Hussain, R. J. (2014b). A systematic approach for solving mixed intuitionistic fuzzy
transportation problems. International Journal of Pure and Applied Mathematics, 92(2), 181–190.
doi:10.12732/ijpam.v92i2.4

253

Kumar, P. S., Hussain, R. J. (2014c) A method for finding an optimal solution of an assignment
problem under mixed intuitionistic fuzzy environment. In Proceedings in International Conference on
Mathematical Sciences (ICMS-2014). Elsevier.
Kumar, P. S., Hussain, R. J. (2015). A method for solving unbalanced intuitionistic fuzzy transporta-
tion problems. Notes on Intuitionistic Fuzzy Sets, 21(3), 54–65.
Kumar, P. S., Hussain, R. J. (2016a). An algorithm for solving unbalanced intuitionistic fuzzy assign-
ment problem using triangular intuitionistic fuzzy number. The Journal of Fuzzy Mathematics, 24(2),
289–302.
Kumar, P. S., Hussain, R. J. (2016b). Computationally simple approach for solving fully intuitionistic
fuzzy real life transportation problems. International Journal of System Assurance Engineering and
Management, 7(1), 90–101. doi:10.100713198-014-0334-2
Kumar, P. S., Hussain, R. J. (2016c). A simple method for solving fully intuitionistic fuzzy real life
assignment problem. International Journal of Operations Research and Information Systems, 7(2),
39–61. doi:10.4018/IJORIS.2016040103
Li, L., Huang, Z., Da, Q., Hu, J. (2008, May). A new method based on goal programming for solving
transportationproblemwithfuzzycost.InInformationProcessing(ISIP),2008InternationalSymposiums
on (pp. 3-8). IEEE. doi:10.1109/ISIP.2008.9
Liao, X. (2015). Decision method of optimal investment enterprise selection under uncertain infor-
mation environment. International Journal of Fuzzy System Applications, 4(1), 33–42. doi:10.4018/
IJFSA.2015010102
Lin, F. T. (2009, August). Solving the transportation problem with fuzzy coefficients using genetic algo-
rithms. In Fuzzy Systems, 2009. FUZZ-IEEE 2009. IEEE International Conference on (pp. 1468-1473).
IEEE. 10.1109/FUZZY.2009.5277202
Liou, T. S., Wang, M. J. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems,
50(3), 247–255. doi:10.1016/0165-0114(92)90223-Q
Maity, G., Roy, S. K. (2017). Multiobjective transportation problem using fuzzy decision variable
through multi-choice programming. International Journal of Operations Research and Information
Systems, 8(3), 82–96. doi:10.4018/IJORIS.2017070105
Mathur, N., Srivastava, P. K., Paul, A. (2016). Trapezoidal fuzzy model to optimize transportation
problem. International Journal of Modeling, Simulation, and Scientific Computing, 7(3). DOI: 10.1142/
S1793962316500288
Mohideen, S. I., Kumar, P. S. (2010). A comparative study on transportation problem in fuzzy envi-
ronment. International Journal of Mathematics Research, 2(1), 151–158.
Mohideen, S. I., Kumar, P. S. (2010). A comparative study on transportation problem in fuzzy envi-
ronment (Unpublished master’s thesis). Jamal Mohamed College (Autonomous), Tiruchirappalli, India.

254

Nasseri, S. H., Ebrahimnejad, A. (2011). Sensitivity analysis on linear programming problems with
trapezoidal fuzzy variables. International Journal of Operations Research and Information Systems,
2(2), 22–39. doi:10.4018/joris.2011040102
Oheigeartaigh, M. (1982). A fuzzy transportation algorithm. Fuzzy Sets and Systems, 8(3), 235–243.
doi:10.1016/S0165-0114(82)80002-X
Pandian, P., Natarajan, G. (2010). A new algorithm for finding a fuzzy optimal solution for fuzzy
transportation problems. Applied Mathematical Sciences, 4(2), 79–90.
Pattnaik, M. (2015). Decision making approach to fuzzy linear programming (FLP) problems with post
optimal analysis. International Journal of Operations Research and Information Systems, 6(4), 75–90.
doi:10.4018/IJORIS.2015100105
Ping, J. I., Chu, K. F. (2002). A dual-matrix approach to the transportation problem. Asia-Pacific
Journal of Operational Research, 19(1), 35–45.
Purushothkumar, M.K., Ananathanarayanan, M. (2017). Fuzzy transportation problem of trapezoidal
fuzzy numbers with new ranking technique. IOSR Journal of Mathematics, 13(6), 6-12.
Rajarajeswari, P. Sangeetha, M. (2016). New similarity performance measures of fuzzy transporta-
tion and its application. International Journal of Innovative Research in Computer and Communication
Engineering, 4(4), 6353-6360. DOI: .040400910.15680/IJIRCCE.2016
Rani, D., Gulati, T. R., Kumar, A. (2014). A method for unbalanced transportation problems in fuzzy
environment. Indian Academy of Sciences Sadhana, 39(3), 573–581. doi:10.100712046-014-0243-8
Rao, K. R., Mudaliar, R. K., Hasan, M. K., Alam, M. K. (2016, December). A perfect mathematical
formulation of fuzzy transportation problem provides an optimal solution speedily. In Computer Sci-
ence and Engineering (APWC on CSE), 2016 3rd Asia-Pacific World Congress on (pp. 271-278). IEEE.
10.1109/APWC-on-CSE.2016.051
Reddy, M. R., Raman, P. V., Kumar, M. V. (2016). Unclear carrying problem of triangular numbers
with α–slash and position method. International Journal of Mathematical Archive, 7(10), 66–68.
Saad, O. M., Abass, S. A. (2003). A parametric study on transportation problem under fuzzy environ-
ment. Journal of Fuzzy Mathematics, 11(1), 115–124.
Saati, S., Hatami-Marbini, A., Tavana, M., Hajiahkondi, E. (2012). A two-fold linear programming
model with fuzzy data. International Journal of Fuzzy System Applications, 2(3), 1–12. doi:10.4018/
ijfsa.2012070101
Sahoo, P. K., Behera, S. K., Nayak, J. R. (2016). Solution of fuzzy transportation problem by using
ranking function. Advanced Science Letters, 22(2), 564–566. doi:10.1166/asl.2016.6864
Samuel, A. E., Raja, P. (2017a). Algorithmic approach to unbalanced fuzzy transportation problem.
International Journal of Pure and Applied Mathematics, 113(5), 553–561.

255

Samuel, A. E., Raja, P. (2017b). Advanced approximation method for finding an optimal solution of
unbalanced fuzzy transportation problems. Global Journal of Pure and Applied Mathematics, 13(9),
5307–5315.
Shankar, N. R., Saradhi, B. P., Babu, S. S. (2013). Fuzzy critical path method based on a new approach
of ranking fuzzy numbers using centroid of centroids. International Journal of Fuzzy System Applica-
tions, 3(2), 16–31. doi:10.4018/ijfsa.2013040102
Singh, R., Saxena, V. (2017). A new data transfer approach through fuzzy Vogel’s approximation
method. International Journal of Advanced Research in Computer Science, 8(3), 515–519.
Solaiappan, S., Jeyaraman, K. (2014). A new optimal solution method for trapezoidal fuzzy transpor-
tation problem. International Journal of Advanced Research, 2(1), 933–942.
Sudhakar, V. J., Kumar, V. N. (2011). A different approach for solving two stage fuzzy transportation
problems. International Journal of Contemporary Mathematical Sciences, 6(11), 517–526.
Taha, H. A. (2008). Operations Research: An Introduction (8th ed.). Pearson Education.
Vimala,S.,Prabha,S.K.(2016).Fuzzytransportationproblemthroughmonalisha’sapproximationmeth-
od. British Journal of Mathematics Computer Science, 17(2), 1–11. doi:10.9734/BJMCS/2016/26097
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. doi:10.1016/S0019-
9958(65)90241-X
Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(1), 3–28.
doi:10.1016/0165-0114(78)90029-5

256
APPENDIX
Global optimal solution found.
Objective Value: 141.0000
Infeasibilities: 0.000000
Total Solver Iterations: 5
Elapsed Runtime Seconds: 0.49
Model Class: LP
Total Variables: 12
Nonlinear Variables: 0
Integer Variables: 0
Total Constraints: 20
Nonlinear Constraints: 0
Total Nonzeros: 48
Nonlinear Nonzeros: 0
Box 1.
Variable Value Reduced Cost
X11 0.000000 3.000000
X12 0.000000 2.000000
X13 3.000000 0.000000
X14 0.000000 7.000000
X21 0.000000 2.000000
X22 0.000000 3.000000
X23 0.000000 2.000000
X24 5.000000 0.000000
X31 5.000000 0.000000
X32 4.000000 0.000000
X33 0.000000 2.000000
X34 3.000000 0.000000

257
Box 2.
Row Slack or Surplus Dual Price
1 141.0000 -1.000000
2 0.000000 0.000000
3 0.000000 0.000000
4 3.000000 0.000000
5 0.000000 0.000000
6 0.000000 0.000000
7 0.000000 0.000000
8 0.000000 0.000000
9 5.000000 0.000000
10 5.000000 0.000000
11 4.000000 0.000000
12 0.000000 0.000000
13 3.000000 0.000000
14 0.000000 0.000000
15 0.000000 -1.000000
16 0.000000 -5.000000
17 0.000000 0.000000
18 0.000000 -3.000000
19 0.000000 -8.000000
20 0.000000 -5.000000

Index

A
AAL 31-32, 38, 41, 43, 47
AFS 132, 135, 152
Agent-Oriented Software Engineering 258, 280
Alert generation 366
Ambient Assisted Living (AAL) 31-32, 47
ANNOVA 152
Architectures79-81,84,90,117,258-260,280,286,350
Artificial 44, 54, 59, 79, 81, 84, 87, 90, 114, 126, 292,
299, 332
Assistive technology 4, 43
B
BHN 152
Bi-Modal 1, 5, 12-13, 16-18, 21-22, 24-26, 30
Bio-signal 26
C
Capacitive Sensor 31-34, 47
CCD 141, 147, 152
Cells 68, 74, 86, 91, 223, 229, 236
Cladistics 381
Cluster 116, 177, 183, 185, 191, 194, 297-298, 305-
307, 398, 401-402, 409-418, 420, 428
Clustering 83-84, 165, 183-184, 298, 350, 397-399,
401-403, 408-410, 412-414, 416-420, 424-426,
428
Co-evolution 380-383
Cognitiv® Suite of Emotiv 30
Complex Event Processing 348, 351-353, 372
Computational intelligence 153, 156
Control command 2, 8, 11
Core 82, 89, 97, 153, 189, 290, 292, 297, 299-302,
304, 306-307, 350, 364, 412
CP97,100-101,103,109,115-116,125-127,132-133,
137-140, 152
Crisis 79-83, 87-89, 290-291
CS 126-127, 132-133, 137-138, 140, 152
D
Deep Model 424, 426-428
Design of experiments 125, 133, 152
Design Patterns 258, 260-262, 275, 277, 279-280
DFA 123, 126-128, 133, 138, 140-141, 146, 152
di 105, 152
Discretization 163, 166, 176, 297-301, 303, 308, 310
Do 8, 34, 38, 51, 57, 62, 68, 70, 72-74, 76, 83-84, 87,
97, 103, 112, 115, 117, 123, 138, 141, 147, 152,
165-166, 181, 270, 275-276, 280, 286, 349, 360,
382-383, 387, 410, 416, 419
DOE 125-126, 152
Dynamic Rule Addition 350
E
Emotiv EPOC 1-2, 4-6, 26, 30
Emotiv EPOC sensor 1-2, 6, 26, 30
epistemology 289, 292-293
Evolutionary Trees 380-381, 383, 386-387, 394
Expressiv® Suite of Emotiv 30
F
Fall Detection 32-33, 37-39, 47
Fishery 202-203
forecast 297-300, 302, 304, 311
Fuzzification 14, 30, 178, 180, 187, 191, 298, 300
Fuzzy Focal elements 316-319, 323-325, 328, 333-
336, 338-340
Fuzzy Logic 1, 5, 13-15, 26, 30, 153, 156, 159, 168,
176, 299, 318-319
Fuzzy logic system 1, 5, 13-15, 318
Fuzzy Number 220, 223-224, 226, 230, 317, 322-
324, 336
499

Index
Fuzzy Set 176, 178-180, 220-222, 224-225, 299, 304,
306, 316, 318, 320, 324, 340
FuzzyTransportationProblem219,222,227-229,235
G
GA 123, 126-128, 130-131, 133, 138, 140, 142, 146,
152, 159, 165, 167, 179, 187, 192, 194
Gait Pattern 40-41, 47
GE 126-127, 132-134, 137-141, 152
Generalized 44, 223, 316-319, 323-325, 334, 336,
338-339
Genetic algorithm 126, 130, 142, 146, 152-153, 156,
159, 165, 167, 177-179, 221, 299
Geriatric Remote Healthcare 348, 353, 372
GFN 133, 139, 152, 322, 324, 327, 334, 336-337, 339
Ghost Rule 177, 191-192, 194
H
Hands-free control 1-2, 5, 25-26
High Order 298
Hippocampus 79, 86, 90-91
Human-Machine Interface 30
Hybrid PSO-GA 175, 178, 187, 190-192, 194
I
Interfaces 2-3, 34, 36, 80, 84, 89, 155, 267, 355
Internet of Things (IoT) 42, 47
Interval 35, 44, 56, 113, 176, 180, 221, 298, 300-302,
304, 311, 317, 319-320, 322, 324, 328-329, 335
K
Kuhn 286, 289-290
L
Lakatos 289-291
Landmark 58, 61-63
Linear Order 49, 55-57, 59, 63
Living Lab 43, 47
Lost Rule 177, 187
M
Medical Assessment 48
Membership 15, 17, 159, 178, 180-182, 187, 191,
220-222, 224, 297, 299-302, 304, 306, 319-320,
326, 328, 340
MH 124-127, 132-134, 138, 140, 152
MOPOSO-CD 152
Movement Trajectory 42, 48
N
Navigation 3, 49-51, 54, 63-64, 86, 91
O
Ontology 55, 82, 267, 289-290, 397, 399-401, 403,
405, 407-408, 414-415, 419-420, 424-428, 430-
432, 434
Ontology Learning 397, 399-401, 403, 414, 419-420
Optimal Solution 126-127, 130, 167, 177, 219-223,
229, 231, 233-236, 238, 242, 244, 246, 249
Orientation3,36-39,49-51,55-59,61-63,284,287,289
P
paradigm 261, 284-286, 288-291, 293-294, 349, 352,
380, 398
Particle swarm optimization 126-127, 130-131, 143,
152-153, 156, 158, 166, 177-179, 184, 194, 298
Position 2, 5-6, 24, 33, 130, 158, 184-185, 187, 203,
222, 285, 297, 305
Pressure Sensor 4, 48
Proximity Sensing 33, 48
PSK Method 219, 222-224, 231-233, 235-236, 244,
248-249
PSO 123, 126-128, 130, 132-133, 138, 140-141, 143-
144, 146, 152, 158, 167, 175, 177-179, 184-185,
187, 191-192, 194, 298-299
R
Redundancy 34, 48, 355
research programme 285, 288-294
Riskassessment316-320,327,332,335-336,338,340
Route 17, 19, 22, 49-51, 53, 55-63
RSM 125-126, 152
Rule Hiding 179, 189
S
Scalability 81, 155, 348, 350, 353
Semantic 83, 284, 397-400, 403, 407, 410-413, 417-
420, 425-429, 431-432, 434
Sensitive Rules 175, 177-179, 185, 187, 189, 191-192
Service Recommendation 397, 399, 409-410
Service Selection 411, 417
500

Index
Services 36, 47, 79-84, 87, 89-91, 200, 220, 258-259,
263-265, 268-270, 272, 280, 287, 355-356, 360,
397-403, 407-420
Simulation82-83,125,200-201,203,206,210,212,318
Sketch Maps 49-55, 57-64
Social Structures 280
Software Product Lines 380-381, 383
Spatial Relations 49-52, 55, 62
Sustainability 199-203, 212
System Dynamics 199-203, 212
System Dynamics Model 199, 201-203
T
Textile Underlay 33-34, 48
TFN 317
Topology 49-50, 55-56, 59, 62-63
TrFN 223-226, 238, 242-244, 249
Type-1 FTP 228, 237-238
Type-2 FTP 228, 244-247, 249
Type-3 FTP 228, 239-240
Type-4 FTP 223, 228, 240, 243, 248-249
U
Uncertainty Handling 318
Uni-Modal 1, 5, 8, 17, 24-25, 30
UTS 152
V
Verbal Descriptions 49-53, 57-64
W
Web Service Clustering 418, 420
Wireless Transmission 34, 48
Y
Yi 128, 152, 425
YS 152
501

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