Anna Gołecka , Tomasz Małolepszy , Janusz Matkowski
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引用次数: 0
Abstract
The means and t-norms are considered. A weak associativity property of the weighted quasi-arithmetic means, connecting these two families of functions, is introduced. It is observed that the symmetry of every t-norm follows from a modified system of the remaining axioms. The conditions under which a rational function is a bivariate homogeneous mean in are given. The invariance of means and functions with respect to the mean-type mappings and t-(norm,conorm)-type mappings is considered with some applications.
期刊介绍：
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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