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.

To characterize the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. We consider two types of RUs: S-shaped, representing decision makers who are risk-seeking for relative losses, and non-S-shaped, representin...

In a rather general, essentially aggregation operator based discussion of the traditional fuzzy control strategies known as FATI and FITA strategies, a way to reduce these strategies to one another has been to define pairs of aggregation distributive aggregation operators. In this paper it is shown that for some often used special cases this reduction condition allows only the set theoretic uni...

In this paper, we firstly propose some generalized prioritized aggregation operators to aggregate the intuitionistic fuzzy values (IFVs), such as the generalized intuitionistic fuzzy prioritized weighted geometric (GIFPWG) operator and the generalized intuitionistic fuzzy prioritized weighted average (GIFPWA) operator. It is shown that some existing intuitionistic fuzzy aggregation operators ar...

Yager et al. first introduce compensatory operators. This paper further introduces a kind of weighted compensatory operators, and a kind of prioritised compensatory operators. The difference between these similar classes of operators are identified. In addition, the paper introduces the concepts of ordered weighted/prioritised compensatory aggregation. Keywords—Compensatory aggregation, weight,...

Aggregation operators transform a finite number of inputs, called arguments, into a single output. They are applied in many theoretical and practical domains and in particular aggregation operators play important role in different approaches to decision making, where values to be aggregated are typically preference or satisfaction degrees. Many operators of different type have been considered i...

This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the ...