based on Detyniecki's doctoral thesis [15]: "Mathematical aggregation operators and their application to video querying", directed by B. Bouchon-Meunier and R. Yager. The complete document is available as a LIP6 research report: 2001-002. Ask for a printed version of the thesis or download it from http://www.lip6.fr/reports/index-eng.html. I also would like to thank Radko Mesiar for all the com...

The paper deals with an extension of aggregation operators from the set of real numbers (or interval [0, 1]) to the set of fuzzy truth values (fuzzy sets in [0, 1]). We define so-called type-2 aggregation operator and show that an extension of ordinary aggregation operator by convolution is a type-2 aggregation operator. Finally we show that ordinary aggregation operator, as well as aggregation...

Stability of aggregation operators is characterized and discussed. 1-stability turns to coincide with 1-Lipschitz p r o p erty. Several examples and basic results are given.

An aggregation operator [1, 5, 7, 8, 9, 12] is usually defined as a real function An such that, from n data items x1, . . . ,xn in [0,1], produces an aggregated value An(x1, . . . ,xn) in [0,1] [4]. This definition can be extended to consider the whole family of operators for any n instead of a single operator for an specific n. This has led to the current standard definition [4, 15] of a famil...

This paper give some motivations for introducing copulas and presents some recent results on them. There is presented an application of copulas in the theory of aggregation operators. Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. There is presented a result on an approximation of associative copulas by strict and nilpo...

The neutrosophic set (NS) can be better to express the incomplete, indeterminate and inconsistent information, and Hamacher aggregation operators extended the Algebraic and Einstein aggregation operators and the generalized aggregation operators can generalize the arithmetic, geometric, and quadratic aggregation operators. In this paper, we combined Hamacher operations and generalized aggregati...

Two basic aggregation methods of reals are idempotent ones (min, max, arithmetic mean) and Archimedean ones (sum, bounded sum). Under some additional requirements, these methods can be shown to be the only possible up to isomorphic transformation and composition of operators (e. g. ordinal sum), see for example Isemigroups of Mostert and Shields [15], compare also [9], or quasi-arithmetic means...

In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed.