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A new approach for ranking of \(L\)-\(R\) type generalized fuzzy numbers. (English) Zbl 1276.03042

Summary: Ranking of fuzzy numbers plays an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. C.-H. Cheng [Fuzzy Sets Syst. 95, No. 3, 307–317 (1998; Zbl 0929.91009)] pointed out that the proof of the statement “Ranking of generalized fuzzy numbers does not depend upon the height of fuzzy numbers”, stated by T.-S. Liou and M. J. J. Wang [Fuzzy Sets Syst. 50, No. 3, 247–255 (1992; Zbl 1229.03043)], is not true. In this paper, by giving an alternative proof it is proved that the above statement is correct. Also, with the help of several counterexamples it is proved that the results proposed by S. M. Chen and J. H. Chen [“Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads”, Expert Syst. Appl. 36, 6833–6842 (2009)] are not accurate. The main aim of this paper is to modify the Liou and Wang approach for the ranking of \(L\)-\(R\)-type generalized fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities.

MSC:

03E72 Theory of fuzzy sets, etc.
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
91B06 Decision theory
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