A Study of Fuzzy Approach for problem solving using Mixed Intuitionistic Ranking Approach

Enhancing Mathematical Programming with Fuzzy Approaches

Abstract

Mathematical programming is the use of mathematical models, such as optimising models, tohelp people make decisions. The term programming means making a plan for what you're going to do. Ifyou're working on a math problem, you're trying to find the best way to solve a problem. You have to keepcertain things in mind when you do this This is a type of decision-making problem called a mathematicalprogramming problem. In this type of problem, preferences between alternatives are described by anobjective function that is defined on the set of alternatives in a way that greater (or smaller) values of thisfunction correspond to more preferable alternatives. Values of the objective function show what happensif you choose one or another option over the other. In any case, the results of an analysis using a givenformulation of the mathematical programming problem depend a lot on how well it is written. Some ofthe things that make up real systems or a process are shown in the description of the objective functionand the constraints. In an intermediate and flexible way, experts' understanding of the nature of theparameters could be represented in the model as a fuzzy set of their possible values. This way, themodel could be more flexible. New types of mathematical programming problems are created when fuzzyparameters are used. To solve these new types of problems, fuzzy set theory tools must be used in aconsistent way when they are used. This is how we get a new type of mathematical programmingproblem with fuzzy parameters. Control theory and management sciences, mathematical modelling,operation research, and many industrial applications have used fuzzy set theory to make things easier tounderstand.