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Fuzzy set theoretic approach of assigning weights to objectives in multicriteria decision making. (English) Zbl 0679.90079

Summary: A rational procedure is developed for ranking the multiobjectives of a vector maximum problem, thereby leading to proper assignment of weights to the objectives. To achieve this, we determine the range of each decision variable from the constraints set and transform them into the unit interval. After scaling the decision variables, we scale down the objectives also into the unit interval. Following R. Yager [Inf. Sci. 24, 143-161 (1981; Zbl 0459.04004)], a ordering function of the objectives is determined. This ordering function value is nothing but the strength of preference inherent in the objectives. Accepting the strength of preference, we obtain the weights for the respective objectives. A numerical example is given to illustrate the procedure.

MSC:

90C31 Sensitivity, stability, parametric optimization
03E72 Theory of fuzzy sets, etc.
90B50 Management decision making, including multiple objectives

Citations:

Zbl 0459.04004
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References:

[1] GOICOECHEA A., Multiobjective Decision Analysis with Engineering and Business Applications (1982) · Zbl 0584.90045
[2] DOI: 10.1016/0165-0114(81)90002-6 · Zbl 0465.90080
[3] HWANG C. L., Multiple Attribute Decision Making – Methods and Applications (1981)
[4] SAATY , T. L. , 1972 , Hierarchies properties and eigenvalues . Working paper , University of Pennsylvania , Philadelphia .
[5] DOI: 10.1016/0020-0255(81)90017-7 · Zbl 0459.04004
[6] DOI: 10.1016/0165-0114(78)90031-3 · Zbl 0364.90065
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