Maximum and Minimum of Triangular Fuzzy Numbers and Their Graphs: The Computational Methods of Maximum and Minimum of Fuzzy Numbers

Over the Years Fuzzy Set Theory has been playing an important role to deal with the problems having uncertainty, vagueness, doubtful data and so on, which cannot be solved with the help of available classical methods. In1965, L. A. Zadeh introduced the concept of fuzzy set theory to deal all those problems in a precise manner. This book attempts to provide the notion of computing the maximum and the minimum of triangular fuzzy numbers. Here we have developed an algorithm to compute the maximum and the minimum of any two triangular fuzzy numbers, so that one can visualize their analytic expressions and the corresponding graphical representations. It also provides some different methods for computation of membership functions of the maximum and minimum of more than two triangular fuzzy numbers or upper semi-continuous fuzzy numbers. The methods are also applicable for piece-wise continuous fuzzy numbers or the fuzzy numbers which are only continuous from right or only continuous from left.

Shapla Shirin is an Associate Professor, Department of Mathematics, University of Dhaka, Bangladesh. She obtained B. Sc. (Hons.) and M. Sc. (Pure Math.) degree from same university. She also received M. S. degree from the Department of Computer Science and Computer Engineering, La Trobe University, Australia. She loves to work in Fuzzy Set Theory.