QA507 : On Solving Fuzzy Multiobjective Linear Optimization Problems By Bipolar Approach
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2018
Authors:
Afsane Delkhah [Author], Mehrdad Ghaznavi[Supervisor], Maryam Ghorani[Supervisor]
Abstarct: The traditional frxameworks for fuzzy linear optimization problems that are inspired by the max–min model proposed by Zimmermann, use the Bellman–Zadeh extension principle to aggregate all the fuzzy sets representing flexible (fuzzy) constraints and objective functions together. In this thesis, we attempt to view fuzzy multi-objective linear programming problems (FMOLPPs) from a perspective of preference modeling. The multiobjective flexible linear programming (MOFLP) problems (or fuzzy multiobjective linear programming problems) are studied in the heterogeneous bipolar frxamework. Bipolarity allows us to distinguish between the negative and the positive preferences. Negative preferences denote what is unacceptable while positive preferences are less restrictive and express what is desirable. The fuzzy constraints are viewed as (representing) negative preferences, while the objective functions are viewed as positive preferences. The approach of bipolarity enables us to handle fuzzy sets representing constraints and objective functions separately and combine them in distinct ways. In this paper, an approach is proposed to single out such a solution of Pareto-optimality for MOFLP with highest possible degree of feasibility. The optimal solution of FMOLPP maximizes the disjunctive combination of the weighted positive preferences provided it satisfy the negative preferences combined in conjunctive way.
Keywords:
#Fuzzy mathematical programming #Fuzzy multi-objective linear programming #Bipolarity #Coherence condition #Aggregation operator #OWA operator #flexible linear programming #fuzzy sets #feasibility degree #Pareto-optimal solution #bipolarity Link
Keeping place: Central Library of Shahrood University
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