In axiomatic way, in fuzzy setting, we introduce the measure of crispness and the measure of conditional clearness. For these measures we propose a functional form. Then, for the last measure, we give some aggregation operators. Keywords— Aggregation operators, functional equations, fuzzy sets, measures of fuzziness, crispness measures, conditional crispness.

We analyze different types of aggregation operators. We focus on the generalized OWA (GOWA) operator and the Quasi-OWA operator which generalize a wide range of aggregation operators. We also analyze a recent approach that unifies the weighted average and the OWA operator in the same formulation called ordered weighted averaging – weighted averaging (OWAWA) operator. We introduce the fuzzy gene...

Methods for aggregating intuitionistic trapezoidal fuzzy information are investigated. Some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy ordered weighted averaging (ITFOWA) operator and intuitionistic trapezoidal fuzzy hybrid aggregation (ITFHA) operator, are p...

The aggregation of preference relations in group decision-making (GDM) problems can be carried out based on either the reliability of the preference values to be aggregated, as is the case with ordered weighted averaging operators, or on the reliability of the source of information that provided the preferences, as is the case with weighted mean operators. In this paper, we address the problem ...

We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using modified transfer and smoothing operators. The estimat...

This paper summarizes some results of the authors’ research that have been carried out in recent years on generalization of conventional aggregation operators. Aggregation of information represented by membership functions is a central matter in intelligent systems where fuzzy rule base and reasoning mechanism are applied. Typical examples of such systems consist of, but not limited to, fuzzy c...

SUOWA operators are a new family of aggregation functions that simultaneously generalize weighted means and OWA operators. Semi-uninorms, which are an extension of uninorms by dispensing with the symmetry and associativity properties, play a fundamental role in their definition. In this paper we show several procedures to construct semi-uninorms. The first one allows us to obtain continuous sem...

We consider the aggregation operators which are ⊕-additive for commonotone functions. The main result is that any operator is expressed by a kind of general fuzzy integral which uses a family of fuzzy measures connected by a ⊕-additive Cauchy’s equations. In particular, the family of fuzzy measures can be obtained by a ⊕-fitting pseudomultiplication. In this case, the aggregation operator is ex...

Fuzzy Description Logics (Fuzzy DLs) are logics that allow to deal with structured knowledge affected by fuzziness. Fuzzy DLs are at the heart of Fuzzy OWL 2, a fuzzy version of the standard ontology language OWL 2. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In particu...

A class of extended aggregation operators, called impact functions, is proposed and their basic properties are examined. Some important classes of functions like generalized ordered weighted averaging (OWA) and ordered weighted maximum (OWMax) operators are considered. The general idea is illustrated by the Producer Assessment Problem which includes the scientometric problem of rating scientist...