Overlap and grouping functions are special kinds of non-necessarily associative aggregation operators recently proposed for applications in classification problems involving the overlap problem ...and/or when the associativity property is not strongly required, as in image processing and decision making based on fuzzy preference relations, respectively. The concepts of indifference and incomparability defined in terms of overlap and grouping functions may allow their application in several different contexts. This paper introduces the concept of (G,N)-implication, for a grouping function G and a fuzzy negation N. (G,N)-implications are weaker then (S,N)-implications for positive and continuous t-conorms S, in the sense that (G,N)-implications do not necessarily satisfy certain properties, as the exchange and the left neutrality principles, which are not demanded for applications in decision making based on fuzzy preference relations. We analyze several related important properties, providing a characterization of (G,N)-implications.
The Smets–Magrez axiomatic is usually used to define the class of fuzzy continuous implications which are both S and R-implications (Łukasiewicz implications). Another approach is the construction of ...such class starting from a basic implication and applying automorphisms. Literature has shown that there is a harmony between those approaches, however in this paper we show that the extension of the Łukasiewicz implication defined on 0,1 for interval values cannot be applied in a direct way.
We show that the harmony between the Smets–Magrez axiomatic approach and the one that comes from the generation by automorphisms is not preserved when such extension is done. One of the main consequences lies on the fact that the automorphism approach induces the loss of R-implications from the resulting class of implicators. More precisely, we show that the interval version of such approaches produce two disjunct classes of implicators, meaning that, unlike the usual case, the choice of the respective approach is an important step.
•Present three dynamic ensemble selection (DES) methods.•Evaluate the impact of proximity measures in DES methods.•Perform an empirical analysis with one-step and two-step DES methods.•Obtain the ...best results of the empirical analysis with two-step DES methods.•Obtain similar results of the empirical analysis with the use of proximity measures.
Ensemble of Classifiers are composed of parallel-organized components (individual classifiers) whose outputs are combined using a combination method that provides the final output for an ensemble. In this context, Dynamic Ensemble Systems (DES) is an ensemble-based system that, for each test pattern, a different ensemble structure is defined, in which a subset of classifiers is selected from an initial pool of classifiers. During the selection process of a DES, any criterion can be used, being the most important ones accuracy and distance. Distance measures are used to assess the distance of the classifier outputs within a validation set and the main examples of this measure are diversity and similarity. In this paper, we investigate the impact of selection criteria in DES methods. More specifically, we focus on the use of different distance measures (diversity and similarity) as selection criteria. In other to do this, an empirical analysis has been conducted using six different DES methods (three of them are existing methods and the remaining three are proposed in this paper) and with 20 different classification datasets. Our findings indicated that a distance measure improves the overall performance of the state-of-the-art ensemble generation methods.
The aim of this paper is to introduce the concepts of interval additive generators of interval t-norms and interval t-conorms, as interval representations of additive generators of t-norms and ...t-conorms, respectively, considering both the correctness and the optimality criteria. The formalization of interval fuzzy connectives in terms of their interval additive generators provides a more systematic methodology for the selection of interval t-norms and interval t-conorms in the various applications of fuzzy systems. We also prove that interval additive generators satisfy the main properties of additive generators discussed in the literature.
In this paper we extend the notion of interval representation for interval-valued Atanassov’s intuitionistic representations, in short Lx-representations, and use this notion to obtain the best ...possible one, of the Weighted Average (WA) and Ordered Weighted Average (OWA) operators. A main characteristic of this extension is that when applied to diagonal elements, i.e. fuzzy degrees, they provide the same results as the WA and OWA operators, respectively. Moreover, they preserve the main algebraic properties of the WA and OWA operators. A new total order for interval-valued Atanassov’s intuitionistic fuzzy degrees is also introduced in this paper which is used jointly with the best Lx-representation of the WA and OWA, in a method for multi-attribute group decision making where the assesses of the experts, in order to take in consideration uncertainty and hesitation, are interval-valued Atanassov’s intuitionistic fuzzy degrees. A characteristic of this method is that it works with interval-valued Atanassov’s intuitionistic fuzzy values in every moments, and therefore considers the uncertainty on the membership and non-membership in all steps of the decision making. We apply this method in two illustrative examples and compare our result with other methods.
On Generalized Mixture Functions Antonio Diego Silva Farias; Valdigleis da Silva Costa; Luiz Ranyer A. Lopes ...
Transactions on fuzzy sets and systems,
11/2022, Volume:
1, Issue:
2
Journal Article
Peer reviewed
Open access
In the literature it is very common to see problems in which it is necessary to aggregate a set of data into a single one. An important tool able to deal with these issues is the aggregation ...functions, which we can highlight as the OWA functions. However, there are other functions that are also capable of performing these tasks, such as the preaggregation function and mixture functions. In this paper we investigate two special types of functions, the Generalized Mixture functions and Bounded Generalized Mixture functions, which generalize both OWA and Mixture functions. We also prove some properties, constructions and examples of these functions. Both the Generalized and Bounded Generalized Mixture functions are developed in such a way that the weight vectors are variables that depend on the input vector, which generalizes the aggregation functions: Minimum, Maximum, Arithmetic Mean and Median, and are extensively used in image processing. Finally, we propose a Generalized Mixture function, denoted by $\mathbf{H}$, and we show that $\mathbf{H}$ satisfies a series of properties in order to apply this function in an illustrative example of application: The image reduction process.
The fuzzy mathematical morphology extends the binary morphological operators to gray-scale and coloured images using concepts of fuzzy logic. To define the morphological operators of fuzzy erosion ...and dilatation it is used the implications and conjunctions respectively. This work presents an analysis of some R-implications to verify if the pairs of implications and T-norms (conjunctions) were adjunctions. It was used a fuzzy application developed in the Matlab for implementation and tests with the respectively results.
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