Study of Optimality for Multi objective Programming Problems Under Fuzzy Environment

Abstract

newlineAbstract newlineMulti-objective Optimization (MOO) emerges as a powerful framework to address newlinecomplexities, providing a systematic approach to finding optimal solutions newlinein the presence of competing objectives. The decision-maker may be faced with newlineambiguity while deciding how to meet optimality due to the competing nature newlineof objective functions. This inspires us to pursue optimality research in a fuzzy newlineenvironment with pertinent applications. This study looks into multi-objective newlineoptimization in a fuzzy environment and how it applies to supply chain and newlineinventory management. Additionally, the thesis s work on fractional programming newlineproblems under novel settings allows for the achievement of appropriate newlineresults when compared to the researcher s previous findings. This thesis deals newlinewith multi-objective optimization problems and different methods which are applicable newlinein solving those kind of problems. newlineA brief outline of our contribution in this thesis as follows: newlineIn second chapter, we have shown how to solve intuitionistic fuzzy multi-objective newlinelinear fractional programming problems (IFMOLFPP) involving pentagonal fuzzy newlinenumbers. And it is also describe how the IFMOLPP is converted into CMOLPP newlineunder well-defined accuracy function. Finally a numerical example is stated to newlineillustrate the present procedure. In third chapter, we have described how a new newlinelinear ranking function is used to defuzzify the pentagonal intuitionistic fuzzy newlinenumbers. Also we present how the Zimmerman s technique is used under suitable newlinenonlinear membership function, CMONLPP is reduced to a standard NLPP newlinewhich can be easily solved by any NLPP algorithm or software. In fourth chapter, newlinewe have presented some methods for converting MOLFPP to MOLPP following newlinedifferent linearisation process. A comparative study is presented to layout the newlinedifference between proposed method and the existing one. In fifth chapter, we newlinehave shown how a multi-objective optimization problem is used in inventory newlinemodel to minimizing the average cost. In sixth chapter, we have described how newlinevi newlinewe select the level of supplier by using the concept of binary coded genetic algorithm newlinewith the help of tournament selection process. In seventh chapter we have newlinedescribed conclusion and future work. newlineKeywords: Pentagonal intuitionistic fuzzy number, Nonlinear membership function, newlineAccuracy function, Green production, Carbon emission, Binary coded genetic newlinealgorithm, Supplier selection, Intuitionistic fuzzy number, Supply chain newlinemanagement, Tournament selection. newlinevii