Ranking Approach to Solve Linear Programming Problems with Fuzzy Sets

Linear programming is one of the most frequently applied operations research techniques. The classical tool for solving the linear programming problem in practice is the class of simplex algorithm which was proposed and developed by Dantzig. A lot of real world decision problems are described by linear programming models and sometimes it is necessary to formulate them with elements of imprecision or uncertainty. This imprecise nature has long been studied with the help of the probability theory. However, the probability theory might not provide the correct interpretation to solve some practical decision making problems. In these cases, the fuzzy set theory might be more helpful. In this book, the limitations and shortcomings of existing methods for solving linear programming problems with fuzzy sets are pointed out. Some new ranking approaches for the ordering of fuzzy sets and vague sets are developed and also new methods to find the unique optimal solutions of linear programming problems under fuzzy environment and vague environment are presented.