Linear Programming Problems with Generalized Fuzzy Sets

Abstract

In this thesis, the limitations and shortcomings of existing methods for solving linear programming problems with fuzzy sets are pointed out. To overcome the limitations and shortcomings of existing methods, some new ranking approaches are proposed for comparing generalized fuzzy sets and vague sets. On the basis of proposed ranking approaches, some new methods are proposed to nd the appropriate solution of such linear programming problems with generalized fuzzy sets and vague sets in which only the parameters cost (or pro t) are represented by fuzzy sets or vague sets. The chapter wise summary of the thesis is as follows: In Chapter 1, a brief review of the work done in the area of linear programming problems with fuzzy sets is presented. In Chapter 2, it is shown that the existing method for solving linear programming problems with fuzzy sets can be used only for solving such linear programming problems in which either the parameters are represented by normal fuzzy sets or generalized fuzzy sets having equal height. Although, the limitations of the existing method can be removed by replacing an appropriate ranking approach instead of already used existing ranking approach for comparing fuzzy sets but there are some shortcomings in all the existing ranking approaches so none of the existing ranking iii iv approach can be used to overcome the limitations of existing method. To overcome the limitations of existing method, a new ranking approach is proposed for comparing generalized trapezoidal fuzzy sets and on the basis of proposed ranking approach a new method is proposed for solving linear programming problems with generalized fuzzy sets. In Chapter 3, the limitations of some existing results for comparing generalized p-norm fuzzy sets are pointed out and with the help of the ranking approach, proposed in Chapter 2, some new results are proposed by modifying the existing results to overcome the limitations of existing results.