A Possibilistic Approach for Multiobjective Programming Problems. Efficiency of Solutions

Fuzzy Sets and Possibility Theory have been extensively used in designing a wide class of resolution methods for Multicriteria Decision Problems and more particularly in Multiobjective Programming. Such methods appear without common relation as each of them arises from a particular and suitable set of hypotheses about factors such that the framework of the problem, its nature, decision-maker’s behavior, etc. In this paper we present a general formulation for using possibility theory, or fuzzy sets, to solve multiobjective problems, which contains all of aforementioned methods as particular cases because all of them may be obtained from a common auxiliary problem. First we analyze how this auxiliary problem is constructed, its main properties as well as different solution methods. After that, the efficiency of the corresponding solutions is dealt with. The paper finishes with some remarks and examples.

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