Fully Fuzzy Multi-Choice Multi-Objective Linear Programming Solution via Deviation Degree

The purpose of this paper is to study fully fuzzy multi-choice multi- objective linear programming problem (FFMMOLPP), in which, right hand side of each constraint has two choices. With the help of ranking function, deviation distance and deviation degree between two fuzzy numbers are defined. A new method is proposed to find the  - fuzzy pareto optimal solution of FFMMOLPP which is defuzzified by using deviation degree and ranking function. Furthermore, a comparative study of the existing methods in the literature and proposed method is conducted for the particular case of FFMMOLPP. Hereafter, a real world problem is presented to illustrate the efficiency of proposed method.

[1]  T. Allahviranloo,et al.  Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution , 2009 .

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

[3]  H. Zimmermann Fuzzy programming and linear programming with several objective functions , 1978 .

[4]  Jolly Puri,et al.  Fuzzy Linear Programming and its Applications , 2009 .

[5]  Jagdeep Kaur,et al.  Mehar’s method for solving fully fuzzy linear programming problems with L-R fuzzy parameters , 2013 .

[6]  J. Buckley Possibilistic linear programming with triangular fuzzy numbers , 1988 .

[7]  由希 辻 Representation , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[8]  Tong Shaocheng,et al.  Interval number and fuzzy number linear programmings , 1994 .

[9]  Chin-Nung Liao,et al.  Formulating the multi-segment goal programming , 2009, Comput. Ind. Eng..

[10]  Kamran Shahanaghi,et al.  Fuzzy multi-choice goal programming , 2012 .

[11]  Srikumar Acharya,et al.  Transformation of a multi-choice linear programming problem , 2009, Appl. Math. Comput..

[12]  Debashis Dutta,et al.  MULTI-CHOICE GOAL PROGRAMMING APPROACH FOR A FUZZY TRANSPORTATION PROBLEM , 2010 .

[13]  Esmaile Khorram,et al.  A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem , 2015 .

[14]  Stanislaw Heilpern,et al.  Representation and application of fuzzy numbers , 1997, Fuzzy Sets Syst..

[15]  T. Allahviranloo,et al.  SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEM BY THE RANKING FUNCTION , 2008 .

[16]  Srikumar Acharya,et al.  Solving multi-choice linear programming problems by interpolating polynomials , 2011, Math. Comput. Model..

[17]  Amit Kumar,et al.  A new method for solving fully fuzzy linear programming problems , 2011 .

[18]  Jagdeep Kaur,et al.  A New Method for Solving Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers , 2011 .

[19]  J. Buckley Solving possibilistic linear programming , 1989 .

[20]  Piero P. Bonissone,et al.  A Linguistic Approach to Decisionmaking with Fuzzy Sets , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  B. Julien An extension to possibilistic linear programming , 1994 .

[22]  Amit Kumar,et al.  APPLICATION OF LINEAR PROGRAMMING FOR SOLVING FUZZY TRANSPORTATION PROBLEMS , 2011 .

[23]  Ching-Ter Chang,et al.  Multi-choice goal programming , 2007 .

[24]  Haifang Cheng,et al.  Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method , 2013 .

[25]  Hsuan-Shih Lee,et al.  Optimal consensus of fuzzy opinions under group decision making environment , 2002, Fuzzy Sets Syst..

[26]  S H Chen,et al.  REPRESENTATION, RANKING AND DISTANCE OF FUZZY NUMBER WITH EXPONENTIAL MEMBERSHIP FUNCTION USING GRADED MEAN INTEGRATION METHOD , 2000 .