Compensatory operators in fuzzy linear programming with multiple objectives

Authors:
M. K. Luhandjula
Affiliations:
-
Venue:
Fuzzy Sets and Systems
Year:
1982

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Abstract

Previously, H.J. Zimmermann [11] presented a fuzzy approach to solve the linear vectormaximum problem. In the mentioned approach, the author uses the minimum or the product operators to translate the semantic meaning of the 'and'. The aim of this paper is to reconsider this approach by using operators which allow some degree of compensation between aggregated membership functions. Firstly the @c-operator already defined in [12] is used to combine our fuzzy objectives. It is shown that solutions obtained by this way are always efficient. Unfortunately, the substitute problem is not generally computationally feasible. We suggest then the min-bounded sum operator which is a compensatory one, has some desired properties and is supported by empirical arguments. It allows a considerable decrease of the computational burden in the substitute problem and leads to a solution which is attractive from the stand-point of efficiency.