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On a fuzzy set approach to solving multiple objective linear fractional programming problem. (English) Zbl 1026.90106
Summary: In 1984, Luhandjula used a linguistic variable approach in order to present a procedure for solving multiple objective linear fractional programming problem (MOLFPP). In 1992, D. Dutta, R. N. Tiwari and J. R. Rao [Fuzzy Sets Syst. 52, 39-45 (1992; Zbl 0786.90088)] modified the linguistic approach of Luhandjula such as to obtain efficient solution to problem MOLFPP. The aim of this paper is to point out certain shortcomings in the work of Dutta et al. and give the correct proof of theorem which validates the obtaining of the efficient solutions. We notice that the method presented there as a general one does only work efficiently if certain hypotheses (restrictive enough and hardly verified) are satisfied. The example considered by Dutta et al. is again used to illustrate the approach.
MSC:
90C70Fuzzy programming
90C27Combinatorial optimization