A \(T\)-sum bound of LR-fuzzy numbers. (English) Zbl 0920.04010

Hong, Dug Hun; Hwang, Changha

Fuzzy Sets Syst. 91, No. 2, 239-252 (1997).

Summary: We provide an upper bound and a lower bound of the \(T\)-sum of LR-fuzzy numbers with different spreads, where \(T\) is an Archimedean \(t\)-norm, and show in three examples how close they are to actual membership functions. Furthermore, we study when the membership function of a \(T\)-sum achieves the upper bound.

MSC:

03E72

Theory of fuzzy sets, etc.

Keywords:

fuzzy arithmetic; \(t\)-norm based addition; \(T\)-sum of LR-fuzzy numbers; membership function of a \(T\)-sum; upper bound; lower bound

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