In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of L-fuzzy settheoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furth...

In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.

In this work, we first make a survey of the existing main aggregation operators and then propose some new aggregation operators such as the induced ordered weighted geometric averaging (IOWGA) operator, generalized induced ordered weighted averaging (GIOWA) operator, hybrid weighted averaging (HWA) operator, etc., and study their desirable properties. Finally, we briefly classify all of these a...

This paper investigates the satisfaction of the Non-Contradiction Law (NC) within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC with respect to (w.r.t.) some given strong negation, as well as for those satisfying the law w.r.t. any strong negation. The results obtained are applied to some of the most important known class...

The aim of this paper is to present the first considerations and examples of interval– valued aggregation operators, which allow to extend the usual concept of aggregation operator. We will define this new kind of operators and present its basic properties, as well as the main requirements needed to maintain the properties of standard aggregation operators. Finally, we present a characterizatio...

Several new results in the field of aggre-gation operators are recalled. Most of them were or will be presented at 24 th Finally, a personal vision of the future development of the theory of aggregation operators is given.

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...