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This paper deals with OWA (ordered weighted average) operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. A qualitative orness measure for any OWA operator is suggested, based on its proximity to the OR operator that yields the maximum of the given data. In the particular case of a finite distributive lattice, considering the t-norm given by the meet and the t-conorm given by the join, this qualitative measure agrees with the value that some discrete Sugeno integral takes on the vector consisting of all the members of the lattice. Some applications of the qualitative orness of OWA operators to decision-making problems are shown. In addition, OWA operators defined on a finite product lattice are also applied in image processing. We analyze the effect of several OWA operators with respect to their orness. [ABSTRACT FROM AUTHOR]

A large number of methods in the edge detection literature are only prepared to deal with monochannel images, which represent the value at each pixel by means of scalar values. This fact hinders their applicability to many fields in which multichannel are common, including remote sensing or medical imagery. Very often, multichannel images have to be turned into grayscale images on which edge detection can be performed, but this is coupled to a loss of information that can be unbearable in certain scenarios. In this work we propose a technique for multichannel edge feature fusion technique that can be combined with any edge detection method using scalar edge features. In this way, we can extend edge detection methods by considering an initial phase of monochannel feature extraction followed by a subsequent phase of multichannel feature fusion. For the information fusion we make use of Ordered Weighted Averaging (OWA) operators, which are able to vary the relevance of each of the features to be aggregated depending upon their value. As an example, our proposal is tested with the Upper-Lower Edge Detector, despite it can be further combined with a wide range of edge detectors. [ABSTRACT FROM AUTHOR]

Abstract: We present the concept of strong equality index, basing ourselves on the definition of strong inclusion given by Dubois and Prade in 1980. We develop different construction methods using implication operators that satisfy two additional properties. We make an exhaustive study of these two properties. We also show another two construction theorems for strong equality indexes, one of them making use of order automorphisms and the other using the parametric families of t-norms, t-conorms and strong negations of Hamacher. We finish with an analysis of different relationships between fuzzy entropies and strong equality indexes. [Copyright &y& Elsevier]

Abstract: In this paper we consider aggregation operators satisfying non-decreasingness and some specific boundary conditions. We then analyze some properties of such a family of aggregation operators, introducing the semiautoduality condition, which is weaker than the standard autoduality condition (i.e., the standard self De Morgan identity). Particular families of aggregation operators will appear depending on the context. [Copyright &y& Elsevier]

Abstract: In this paper we present the concept of a restricted equivalence function. This concept arises on the one hand, from the definition of equivalence given by J. Fodor and M. Roubens, and on the other, from the properties usually demanded from the measures used for comparing images. We also study different methods for the construction of restricted equivalence functions from automorphisms and implication operators. Finally we analyze the manner of generating similarity measures of X. Liu and of J. Fan et al. from our restricted equivalence functions. [Copyright &y& Elsevier]

In this paper we present the definition and properties of intuitionistic fuzzy implication operators. We study the expression obtained from said operators when fuzzy implication and coimplication operators are applied to different aggregations of degrees of truth and non-truth of the propositions. [ABSTRACT FROM AUTHOR]

In this work we present an image reduction algorithm based on averaging aggregation functions. We axiomatically define the concepts of image reduction operator and local reduction operator. We study the construction of the latter by means of averaging functions and we propose an image reduction algorithm (image reduction operator). We analyze the properties of several averaging functions and their effect on the image reduction algorithm. Finally, we present experimental results where we apply our algorithm in two different applications, analyzing the best operators for each concrete application. [ABSTRACT FROM AUTHOR]

Abstract Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggregating functions, which obviously give different results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are defined on m -dimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator. [ABSTRACT FROM AUTHOR]

In this paper we propose an algorithm to solve group decision making problems using n -dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an increasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n -dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these conditions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples. [ABSTRACT FROM AUTHOR]