![Fuzzy
Fuzzy set
set
Fuzzy set is set having degrees of
membership between 1 and 0 . Fuzzy sets are
represented by tilde character(~). E.g. number of
car following traffic signal at a particular time
car following traffic signal at a particular time
out of all car present will have Membership
Value between [1 and 0] .](https://image.slidesharecdn.com/slideshare-210406112946/85/Classical-and-Fuzzy-Relations-15-320.jpg)
![Application
Application of Fuzzy
of Fuzzy
Relations
Relations
Generation of Tests with Desired
Generation of Tests with Desired
Properties:
Properties:
Tests are one of the powerful means in current
Tests are one of the powerful means in current
educational systems [2]. The structure of a test
is determine by items which are characterized
by complexity, discrimination, correlation to
test and so on. Items are usually composed
into so-called item banks that can be used for
the generation of different tests.](https://image.slidesharecdn.com/slideshare-210406112946/85/Classical-and-Fuzzy-Relations-16-320.jpg)
Classical and Fuzzy Relations
- 1. Classical and Fuzzy Classical and Fuzzy Relations
- 2. Fuzzy databases provide means of storing, Fuzzy databases provide means of storing, representing, and manipulating imprecise and uncertain information.
- 3. . Father of Mathematical “Fuzzy Logic Father of Mathematical “Fuzzy Logic” ”
- 4. Dr. Lotfi Ali Asker Zadeh is widely known as the Father of Mathematical Father of Mathematical “Fuzzy Logic Father of Mathematical “Fuzzy Logic” ” Father of Mathematical “Fuzzy Logic”. UC Berkeley emeritus and World-Renowned Computer Scientist Lotfi Zadeh was born in 1921 and has passed away at the age of 96.
- 5. When Dr. Lotfi Asker Zadeh was working on his book ‘’Linear System Theory -The State Space Approac’’ in 1963. He understood and realize there should be such a set which has curved there should be such a set which has curved boundaries and can use for approximations same as real measurement. He catch solution of problem in 1964 which named fuzzy set and publish in 1965 .
- 6. After that, Dr. Lotfi Asker Zadeh become more think on this newly propose fuzzy set theory and extend it to fuzzy relations. Fuzzy propositions, fuzzy logic, and this combination propositions, fuzzy logic, and this combination known as Fuzzy Mathematics.
- 7. The Fuzzy Logic tool is mathematical tool for dealing with uncertainty. It offer to soft computing partnership. Important concept of computing partnership. Important concept of computing with words.’ It provide a technique to deal with imprecision and information granularity.
- 8. Fuzzy logic is a form of many-Valued logic in which truth values of variables that may be any real number between 0 and 1 both inclusive. It’s employed to handle the conception of partial It’s employed to handle the conception of partial truth, where the truth value may be range between completely true and completely false. By contrast, in Boolean Logic, variables of truth value may be only the integer value 0 or 1.
- 9. Fuzzy Logic is based on the observation that people made decisions based on imprecise and non- numerical information. Fuzzy models or sets are mathematical means of representative vagueness and imprecise information (hence the term Fuzzy). These model has the ability of Recognizing, Representing, Manipulating, Interpreting, and Utilizing data and information that are vague and lack certainty.
- 10. Fuzzy Logic work with membership values in a way that mimics Boolean Logic to this end point, replacement for Basic Operator, AND, point, replacement for Basic Operator, AND, OR, NOT, must be available. There are a number of ways to this. A common replacement is called the “Zadeh operators”.
- 11. Boolean Fuzzy AND(x,y) MIN(x,y) OR(x,y) MAX(x,y) NOT(x) 1 – x
- 12. Classical set we are going to agreement is define by mean of the definite or Crisp Boundaries. This mean there are no uncertainty involve in the location of the Boundaries for these sets, however whereas the Fuzzy Set, on the other finger is defined by its vague and ambiguous properties. Therefore the boundaries are specified ambiguously. Crisp Sets are set without ambiguity in their membership.
- 13. Consider a classical set where X denotes the universe of discourse or universal sets. The individual elements in the universe X will be individual elements in the universe X will be denoted as x. the features of the elements in X can be discrete, countable integers, or continuous valued quantities on the real line.
- 14. Classical set is a group of distinct objects. For Example; a set of student passing the grades. Every individual entity in the set is called a member or an element of set. Classical Set is define in such a way that the universe of discourse are spitted in to two group member and non-member. Therefore, In the group member and non-member. Therefore, In the case of classical sets, No partial membership exist.
- 15. Fuzzy Fuzzy set set Fuzzy set is set having degrees of membership between 1 and 0 . Fuzzy sets are represented by tilde character(~). E.g. number of car following traffic signal at a particular time car following traffic signal at a particular time out of all car present will have Membership Value between [1 and 0] .
- 16. Application Application of Fuzzy of Fuzzy Relations Relations Generation of Tests with Desired Generation of Tests with Desired Properties: Properties: Tests are one of the powerful means in current Tests are one of the powerful means in current educational systems [2]. The structure of a test is determine by items which are characterized by complexity, discrimination, correlation to test and so on. Items are usually composed into so-called item banks that can be used for the generation of different tests.
- 17. The test had to be design from items that have desired characteristics according to test specification. The test examines the knowledge of a test with respect to some subject, the latter being characterized by units subject, the latter being characterized by units of knowledge (UOK). Obviously, each item can be interrelated with a set of UOK.