Lipschitzian aggregation operators with respect to the natural T indistinguishability operator ET and their powers, and with respect to the residuation → T with respect to a t-norm T and its powers are studied. A t-norm T is proved to be ET -Lipschitzian and → T -Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t, t...

Negotiations are common in engineering design, especially on large projects, and are typically conducted informally. Often, negotiation is used to handle the imprecision or uncertainty that is inherent in the design process. Performance targets, initially specified as hard numerical constraints, are adjusted throughout the design process in negotiations between engineers and managers. Crucial u...

Aggregation of fuzzy relations on alternatives with the help of aggregation operators is considered in two cases: – the weighted coefficients of the criteria are not present in the mathematical formula of the aggregation operators; – a fuzzy preference relation between the criteria importance is given. The main result consists in proving the properties of the aggregated relation in dependence w...

Ž . In this article we compare two contrasting methods, active set method ASM and genetic algorithms, for learning the weights in aggregation operators, such as weighted mean Ž . Ž . WM , ordered weighted average OWA , and weighted ordered weighted average Ž . WOWA . We give the formal definitions for each of the aggregation operators, explain the two learning methods, give results of processin...

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.