Abstract
For the same of two fuzzy sets with different supports, this study investigates the entropy relationship between both of them. For the fuzzy numbers with triangular membership function, the entropy change between the resultant fuzzy numbers through some arithmetic operations and the original fuzzy numbers is studied. Since, the entropy can be used as a crisp approximation of a fuzzy number, therefore the resultant value is used to rank the fuzzy numbers. The main advantage of the proposed approach is that the proposed ranking method provides the correct ordering of fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems.
Highlights
Fuzzy set theory is a powerful tool to deal with real life situations
Real numbers can be linearly ordered by ≥ or ≤, this type of inequality does not exist in fuzzy numbers
An efficient approach for ordering the fuzzy numbers is by the use of a ranking function ܴ ∶ ܴ → )ܴ(ܨ, where )ܴ(ܨis a set of fuzzy numbers defined on real line, which maps each fuzzy number into the real line, where a natural order exists
Summary
Fuzzy set theory is a powerful tool to deal with real life situations. Real numbers can be linearly ordered by ≥ or ≤, this type of inequality does not exist in fuzzy numbers. Chen (1985) considered the overall possibility distributions of fuzzy numbers in their evaluations and proposed a ranking method. Cheng (1998) proposed a ranking method based on preference function which measures the fuzzy numbers point by point and at each point the most preferred number is identified. Chen (1985) presented a method for ranking generalized trapezoidal fuzzy numbers.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
