We will investigate so-called commuting operators and their relationship to bisymmetry and domination. In the case of bisymmetric aggregation operators we will show a sufficient condition ensuring that two operators commute, while for bisymmetric aggregation operators with neutral element we will even give a full characterization of commuting n-ary operators by means of unary commuting operators.

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.

We present different constructions for non-prioritized belief revision, that is, belief changes in which the input sentences are not always accepted. First, we present the concept of explanation in a deductive way. Second, we define multiple revision operators with respect to sets of sentences (representing explanations), giving representation theorems. Finally, we relate the formulated operato...

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...

We introduce a general framework for reasoning with prioritized data by aggregation of distance functions, study some basic properties of the entailment relations that are obtained, and relate them to other approaches for maintaining uncertain information.

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...

In this article we explore multiple change operators, that is, operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, in which both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of p...

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...