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. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm.

[1]  Abraham Charnes,et al.  Programming with linear fractional functionals , 1962 .

[2]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[3]  I. M. Stancu-Minasian,et al.  A sixth bibliography of fractional programming , 2006 .

[4]  D. Dubois,et al.  FUZZY NUMBERS: AN OVERVIEW , 1993 .

[5]  T. Bogdanik [Use of fuzzy set theory in diagnostics]. , 1995, Polskie Archiwum Medycyny Wewnetrznej.

[6]  Goran Ćirović,et al.  Production planning in mines using fuzzy linear programming , 1996 .

[7]  Boriana L. Milenova,et al.  Fuzzy and neural approaches in engineering , 1997 .

[8]  C Tofallis,et al.  Fractional Programming: Theory, Methods and Applications , 1997, J. Oper. Res. Soc..

[9]  James J. Buckley,et al.  Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming , 2000, Fuzzy Sets Syst..

[10]  Jian-Bo Yang,et al.  On the centroids of fuzzy numbers , 2006, Fuzzy Sets Syst..

[11]  Dinesh K. Sharma,et al.  Fuzzy goal programming for agricultural land allocation problems , 2007 .

[12]  I. M. Stancu-Minasian,et al.  A method of solving fully fuzzified linear fractional programming problems , 2008 .

[13]  Iuliu Maniu,et al.  On Solving Fully Fuzzified Linear Fractional Programs , 2009 .

[14]  Milanka Gardasevic-Filipovic,et al.  MULTICRITERIA OPTIMIZATION IN A FUZZY ENVIRONMENT: THE FUZZY ANALYTIC HIERARCHY PROCESS , 2010 .

[15]  Mashaallah Mashinchi,et al.  Ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number , 2011, Comput. Math. Appl..

[16]  Abdollah Hadi-Vencheh,et al.  A new fuzzy MCDM approach based on centroid of fuzzy numbers , 2011, Expert Syst. Appl..