We introduce a new way of constructing aggregation operators based on the metaphor of a balance. This method is enough general to include operators of the most common aggregation families and their specific comportments. So we obtain a general framework, that allows us to compare the different existing operators and to create new ones. The use of a metaphor provides an intuitive representation ...

In the paper the equation of the form A+B = P , w h e r e A and B are binary aggregation operators, is investigated. A necessary and suu-cient condition for binary aggregation operators to be solutions of this equation, is proved. Already known solutions in some special classes of aggrega-tion operators, e.g., in the class of triangular norms and conorms, in the class of quasi{arithmetic means ...

In face recognition, one of the most important problems to tackle is a large amount of data and the redundancy of information contained in facial images. There are numerous approaches attempting to reduce this redundancy. One of them is information aggregation based on the results of classifiers built on selected facial areas being the most salient regions from the point of view of classificati...

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negati...

Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of P...

This paper establishes tight upper and lower bounds on Lipschitz aggregation operators considering their diagonal, opposite diagonal and marginal sections. Also we provide explicit formulae to determine the bounds. These are useful for construction of these type of aggregation operators, especially using interpolation schemata.

The current paper provides a dialectical interpretation of the argumentation-based judgment aggregation operators of Caminada and Pigozzi. In particular, we define discussion-based proof procedures for the foundational concepts of down-admissible and up-complete. We then show how these proof procedures can be used as the basis of dialectical proof procedures for the sceptical, credulous and sup...

A summary on the symbolic basic arithmetic operators and aggregation operators of linguistic information developed by the authors is presented. In particular, label addition, label diierence, product of a label by a positive real number, and convex combination of labels are shown as the symbolic basic arithmetic operators, and two aggregation operators of linguistic information built using thos...

The Decision Support System (DSS) contains more than one antecedent and the degrees of strength of the antecedents need to be combined to determine the overall strength of the rule consequent. The membership values of the linguistic variables in Fuzzy have to be combined using an aggregation operator. But it is not feasible to predefine the form of aggregation operators in decision-making. Inst...

A crucial issue related to the Atanassov’s intuitionistic fuzzy operators is how to determine their weights. Various weighted methods have been proposed last decades, but it seems that there is no investigation on the monotonous and proportioninvariant properties, which is decisive for aggregation and comparison of Atanassov’s intuitionistic fuzzy values in group decision making. In this paper,...