Methods for Solving Fully Fuzzy Linear Programming Problem

Abstract

Linear programming problem is one of the important branch of Mathematical programming problems. Applications of LP exist in almost all the areas like military, industry, agriculture, transportation, economics, health systems and even behavioural and social sciences. But in real world all situations may not be deterministic. There may exist different kinds of uncertainties in social, industrial and economic systems, such as events may occur randomly, unavailability of system data and due to the error in measurements, etc. For dealing with such vagueness and ambiguities fuzzy decision-making methods are used and in this decision-making process, either coefficients or variables in the objective function or constraints or both are taken as fuzzy in nature. In this thesis, fully fuzzy linear programming problems is discussed in which all the parameters of LPP are fuzzy in nature. In first chapter of the dissertation, fully fuzzy linear programming problem is introduced. The brief description of basic concepts, definitions, arithmetic operations that are used throughout work and detailed literature survey of fully fuzzy linear programming problem and summary of the thesis has also been discussed in this chapter. In Chapter 2, an algorithm for ordering the generalized and normal trapezoidal fuzzy numbers on the basis of their rank, mode, divergence, and spread are discussed. Numerical examples are also discussed which elaborate the concept of ordering of fuzzy numbers. Further, in Chapter 3 a method is presented for solving the fully fuzzy linear problem with equality constraints using the concept of ranking function in which all the parameters are triangular fuzzy numbers and the numerical examples are shown. In the last chapter, another method known as Mehar's method with Yager's ranking approach have been discussed for solving fully fuzzy linear programming problem, where all the parameters are unrestricted L-R fuzzy numbers or L-R at fuzzy numbers, numerical examples are discussed to elaborate the algorithm.