Graphical representations of membership functions of maximum and minimum of two fuzzy numbers using computer program

Abstract

The set of real numbers R is linearly ordered, but in the fuzzy set theory, this relation is true only for some set of fuzzy numbers where the sets of fuzzy numbers are expressed as the linguistic variables. Different types of Fuzzy machines based on fuzzy logic have been invented where fuzzy logics are described by fuzzy numbers and the fuzzy numbers are needed to compare. Besides these, many techniques are available to assist decision-makers to compare different fuzzy numbers. For these reasons, it is necessary to compute the maximum and the minimum of fuzzy numbers. Till now many researchers introduced different methods for computation, which are done by hand calculation, but these are very disgusting and time consuming to us. In this paper, we presents an algorithm to compute the maximum and the minimum of any two triangular fuzzy numbers, so that one can compare two fuzzy numbers easily in a short time and visualize the analytic expressions and the graphical representations of the maximum and the minimum of any two triangular fuzzy numbers. By using CAS (MATHEMATICA 7.0), the algorithm is implemented in a computer program in order to do these. This algorithm can easily be extended to apply for any type of fuzzy numbers which are comparable. Even it is able to compare more than two fuzzy numbers by comparing the maximum fuzzy number or minimum fuzzy number with another new fuzzy number.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10313GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 105-115