A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type 2'
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The document presents a method for solving a type-2 intuitionistic fuzzy transportation problem using triangular intuitionistic fuzzy numbers, aiming to address uncertainties in real-life decisions. The proposed method allows for obtaining optimal solutions without needing existing techniques like the intuitionistic fuzzy modified distribution or zero point methods. Through illustrative numerical examples, the document highlights the method's advantages and discusses the limitations of previous approaches.
A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type 2'
- 2. 102 Int. J. Logistics Systems and Management, Vol. 29, No. 1, 2018 Copyright © 2018 Inderscience Enterprises Ltd. A note on ‘a new approach for solving intuitionistic fuzzy transportation problem of type-2’ P. Senthil Kumar PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamilnadu, India Email: senthilsoft_5760@yahoo.com Email: senthilsoft1985@gmail.com Abstract: In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which costs are triangular intuitionistic fuzzy numbers, supplies and demands are crisp numbers. In this paper, a simple method for solving type-2 intuitionistic fuzzy transportation problem (type-2 IFTP) is proposed and optimal solution is obtained without using intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of three real life numerical examples. Defect of existing results proposed by Singh and Yadav (2016a) is discussed. Validity of Pandian’s (2014) method is reviewed. Finally, the comparative study, results and discussion are given. Keywords: intuitionistic fuzzy set; type-2 intuitionistic fuzzy transportation problem; triangular intuitionistic fuzzy number; optimal solution. Reference to this paper should be made as follows: Kumar, P.S. (2018) ‘A note on ‘a new approach for solving intuitionistic fuzzy transportation problem of type-2’’, Int. J. Logistics Systems and Management, Vol. 29, No. 1, pp.102–129. Biographical notes: P. Senthil Kumar is an Assistant Professor in PG and Research Department of Mathematics at Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu, India. He has six years of teaching experience. He received his BSc, MSc and MPhil from Jamal Mohamed College, Tiruchirappalli in 2006, 2008, 2010, respectively. He completed his BEd in Jamal Mohamed College of Teacher Education in 2009. He completed PGDCA in 2011 in the Bharathidasan University and PGDAOR in 2012 in Annamalai University, Tamil Nadu, India. He has submitted his PhD thesis in the area of intuitionistic fuzzy optimisation technique to the Bharathidasan University in 2015. He has published many research papers in referred national and international journals like Springer, IGI Global, etc. He also presented his research in Elsevier Conference Proceedings (ICMS-2014), MMASC-2012, etc. His areas of interest include operations research, fuzzy optimisation, intuitionistic fuzzy optimisation, numerical analysis and graph theory, etc.
- 3. Reference to this paper should be made as follows: Kumar, P.S. (2018) ‘A note on ‘a new approach for solving intuitionistic fuzzy transportation problem of type-2’’, Int. J. Logistics Systems and Management, Vol. 29, No. 1, pp.102–129. DOI: 10.1504/IJLSM.2018.10009204 MLA Kumar, P. Senthil. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'." International Journal of Logistics Systems and Management 29.1 (2018): 102-129. DOI: 10.1504/IJLSM.2018.10009204 APA Kumar, P. S. (2018). 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.2018.10009204 Chicago Kumar, P. Senthil. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'." International Journal of Logistics Systems and Management 29, no. 1 (2018): 102-129. DOI: 10.1504/IJLSM.2018.10009204 Harvard Kumar, P.S., 2018. A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'. International Journal of Logistics Systems and Management, 29(1), pp.102-129. DOI: 10.1504/IJLSM.2018.10009204 Vancouver Kumar PS. A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'. International Journal of Logistics Systems and Management. 2018;29(1):102-29. DOI: 10.1504/IJLSM.2018.10009204
- 4. 124 P.S. Kumar 0, for 202, 202 , for 202 588, 386 ( ) 1, for 588, 1256 , for 588 c 1256, 668 0, for 1256, IZ c c c μ c c c c <⎧ ⎪ −⎪ ≤ ≤ ⎪ ⎪ = =⎨ ⎪ − ⎪ ≤ ≤ ⎪ ⎪ >⎩ (3) and 1, for 74, 588 , for 74 588, 514 ( ) 0, for 588, 588 , for 588 1384, 796 1, for 1384. IZ c c c c c c c c <⎧ ⎪ −⎪ ≤ ≤ ⎪ ⎪ = =⎨ ⎪ − ⎪ ≤ ≤ ⎪ ⎪ >⎩ ϑ (4) 7 Conclusions The type-2 IFTPs are solved by the proposed method which differs from the existing methods namely, intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. The main advantage of this method is that the obtained solution is always optimal. To apply this method, there is no necessity to have (m + n–1) number of non-negative allotted entries (i.e., basic feasible solution). Also, we need not test the optimality condition. It is applicable to type-1, type-2, type-3 and type-4 IFTPs. The proposed method can help decision-makers in the logistics related issues of real-life problems by aiding them in the decision-making process and providing an optimal solution in a simple and effective manner. Further, it can be served as an important tool for a decision-maker when he/she handles various types of logistic problems having different types of parameters. References Aggarwal, S. and Gupta, C. (2014) Algorithm for Solving Intuitionistic Fuzzy Transportation Problem with Generalized Trapezoidal Intuitionistic Fuzzy Number via New Ranking Method, Cornell University, Ithaca, USA, arXiv preprint arXiv:1401.3353. Angelov, P.P. (1997) ‘Optimization in an intuitionistic fuzzy environment’, Fuzzy Sets and Systems, Vol. 86, No. 3, pp.299–306. Antony, R.J.P., Savarimuthu, S.J. and Pathinathan, T. (2014) ‘Method for solving the transportation problem using triangular intuitionistic fuzzy number’, International Journal of Computing Algorithm, Integrated Intelligent Research (IIR), Chennai, Tamilnadu, India, Vol. 3, pp.590–605. Atanassov, K.T. (1983) Intuitionistic Fuzzy Sets, VII ITKR’s Session, Sofia, June, Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84, in Bulg.
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