QA267 : Efficient solutions of fuzzy multiple objective linear fractional programming problem
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2015
Authors:
Somayeh Bagheri [Author], Mehrdad Ghaznavi[Supervisor], Maryam Ghorani[Advisor]
Abstarct: In this thesis, we first explain weak efficiency and efficiency concepts for multi objective linear fractional programming problems and a linear programming approach to test efficiency is proposed. Then, we focus on multi objective linear fractional programming problems with fuzzy parameters and baxsed on the concepts of possibility and necessity for fuzzy numbers extended the ordinary pareto optimality concept. We using four indices for ranking two fuzzy numbers, four types of efficient solutions are defined and relationships among them are examined. Then, we use of Taylor series method for solving fuzzy multi objective linear fractional programming problems. In the proposed approach, for each objective of the fuzzy multi objective linear fractional programming problem a membership function is assosiated, and using Taylor series the membership functions are converted to linear form. The problem is reduced to a single objective. The practical applications and numerical examples are used in order to show the efficiency of the proposed approach. By applying a geometrical interpretation, a linear programming approach is achieved to test weak efficiency. Also, in order to test efficiency of a given feasible solution, a linear programming approach is proposed. finally, a fuzzy set approach to solve a multiple objective linear fractional programming problem is explained. In this method, a multi objective linear fuzzy fractional problem equivalent to the non fuzzy multi objective problem is obtained and the equivalent single objective programming problem is solved. This approach is shown the relation between multi objective linear fractional programming problems and fuzzy multi objective linear fractional programming problems.
Keywords:
#Fuzzy multi objective linear fractional programming problem #Membership function #Taylor series approach #Efficient solution Link
Keeping place: Central Library of Shahrood University
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