Methods for Solving Linear Fractional Programming Problems Under Fuzzy Environment

Abstract

The main and only one purpose of this thesis is to build and solve mathematical models for linear fractional programming (LFP) problems under uncertainty newlineenvironment, such as a fuzzy or neutrosophic environment. The entire work was newlinecompleted at the National Institute of Technology Jamshedpur in Jamshedpur. newlineThe thesis starts with an introductory chapter i.e. Chapter 1, then moves on to newlinefour key chapters i.e. Chapter 2-5, and finally concluding remarks is discussed in newlinelast chapter i.e. chapter 6. Each chapter opens with an introduction part that newlineincludes a literature review and discussion of the work s application. Following newlinethat, the mathematical formulation and method of solution are described. Finally, newlineconclusions are offered together with the results and discussion. newlineChapter 1 presents a brief discussion on the preliminary concepts of LFP newlineProblem in an uncertain environment. It also covers some fundamental concepts newlinelike fuzzy sets and neutrosophic sets. In addition, the chapter highlights the newlineoverview of the work reported in later chapters and gives a brief literature scan newlinelinked to the research work conducted in this thesis. newlineChapter 2 This chapter studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes a unique newlineapproach to solve it. The parameters are considered as a triangular neutrosophic newlinenumbers. The problem is turned into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and newlinea ranking function. After that, FGP is used to solve the MOLPP. For MOLPP, newlinewe looked at three FGP models and the optimum model for a problem can be newlineidentified using the Euclidean distance function. Finally, the usefulness of the newlineproposed technique is established using two mathematical models along with one newlinereal life problem (Transportation Problem). newlineChapter 3 In this chapter we developed a modified ranking function that newlinegenerated crisp linear programming (CLP) problems. A fully fuzzy linear programmin (FFLP