For general type-2 fuzzy sets, the defuzzification process is very complex, and the exhaustive direct method of implementing type-reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type-2 fuzzy inferencing systems in real world applications. The present situation will not be expected to change, unless an efficient and fast met...

In this paper we propose a generalization of Atanassov’s operators and we prove that these generalized operators and OWA operators of dimension 2 provide the same numerical results. We apply Atanassov’s operators to image compression and use different families of OWA operators in order to calculate the coefficient α of the Atanassov’s operator. Keywords— Image compressing, OWA operators, Atanas...

In reply to Péter Majlender, the connection between the (maximum spread) equidifferent OWA operator weights and the analytical method for the minimum variance OWA operator problem [R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems 136 (2003) 203–215] is pointed out and the differences between them are clarified. 2006 Elsevier Inc. All rights ...

Environmental indices (EI) are common communication tool used to describe the overall status of environmental systems (e.g. air, water, soil). Development of EI entails the use of mathematical operators to aggregate various non-commensurate input parameters in a logical manner. Ordered weighted averaging (OWA) operator is a general mean type operator that provides flexibility in the aggregation...

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...

The Multicriteria Decision Analysis (MCDA) and Geographical Information Systems (GIS) are used to provide more accurate decisions to the decision makers in order to evaluate the effective factors in the natural science. One of the popular algorithm of multicriteria analysis is Ordered Weighted Averaging (OWA). The OWA procedure depends on some parameters, which can be 15 specified by means of f...

In this paper we introduce a class of linear orders for discrete gradual real numbers. Based on the linear orders we propose an OWA operator on the set of discrete gradual numbers and discuss some its properties. This is a first step of our intentions to introduce a class of linear orders, and consequently also OWA operator, for the set of discrete gradual intervals. Because the set of all fuzz...

Yager @IEEE Trans Syst Man Cybern B 2004;34:1952–1963# introduced a continuous interval argument OWA ~C-OWA! operator, which extends the ordered weighted averaging ~OWA! operator, introduced by Yager @IEEE Trans Syst Man Cybern B 1988;18:183–190#, to the case in which the given argument is a continuous valued interval rather than a finite set of values. In this article, we utilize the C-OWA ope...

Chiclana, Herrera and Herrera-Viedma studied conditions under which the reciprocity property is maintained in the aggregation of reciprocal fuzzy preference relations using the OWA operator guided by a relative linguistic quantifier. In this note, we focus on the reciprocity in the aggregation of fuzzy preference relations (that is, the additive reciprocity is not assumed) using the OWA operato...

The hybrid averaging (HA) is an aggregation operator that uses the weighted average (WA) and the ordered weighted averaging (OWA) operator in the same formulation. In this paper, we introduce several generalizations of the HA operator by using generalized and quasi-arithmetic means, fuzzy numbers and order inducing variables in the reordering step of the aggregation process. We present the fuzz...