tailieunhanh - Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. | Yugoslav Journal of Operations Research 22 (2012), Number 1, 41-50 DOI: EVALUATING FUZZY INEQUALITIES AND SOLVING FULLY FUZZIFIED LINEAR FRACTIONAL PROGRAMS1 B. STANOJEVIĆ Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia . STANCU-MINASIAN The Romanian Academy, Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania Received: May 2011 / Accepted: January 2012 Abstract: In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm. Keywords: Fuzzy programming, triangular fuzzy number, fractional programming, centroid of triangle. MSC: 90C32, 90C70. 1 This research was partially supported by the Ministry of Science and Technological Development, Republic of Serbia, Project number TR36006. 42 B. Stanojević, . Minasian-Stancu / Evaluating Fuzzy Inequalities 1. INTRODUCTION There have been significant developments in the theory and applications of fractional programming in the last decades. For more information about fractional programming problems, the reader may consult the bibliography with 491 entries presented in Stancu-Minasian [11], covering mainly the years from 1997 to 2005, which gives a clear idea of the amount of work invested in this field. Fractional programming is important to our daily life, because various optimization problems from engineering, social life, and economy consider .