Dominance in the family of Sugeno-Weber t-norms. (English) Zbl 1250.03115
Dominance relation is an important tool in the class of aggregation functions to ensure preservation of some properties, such as the transitivity of aggregated fuzzy equivalence relations or fuzzy orders. Dominance in several parametric families of triangular norms was studied in the framework of functional inequalities since the eighties; see, e.g., [H. Sherwood, Aequationes Math. 27, 255–273 (1984; Zbl 0598.26032)]. The present paper focuses on the study of the dominance relation in the family of Sugeno-Weber triangular norms. In the central Theorem 2, the authors completely describe all couples of Sugeno-Weber t-norms linked by the dominance relation, which is shown to be transitive in these cases, and hence an equivalence relation over the family studied.
Reviewer: Radko Mesiar (Bratislava)
MSC:
| 03E72 | Theory of fuzzy sets, etc. |
| 03B52 | Fuzzy logic; logic of vagueness |
| 03C10 | Quantifier elimination, model completeness, and related topics |
Citations:
Zbl 0598.26032Software:
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