‎On Generalized Mixture Functions

Subject Areas : Transactions on Fuzzy Sets and Systems

Antonio Diego Silva Farias ¹ , Valdigleis da Silva Costa ² , Luiz Ranyer A. Lopes ³ , Regivan Hugo Nunes Santiago ⁴ , Benjamin Bedregal ⁵

1 - Department of Exact and Natural Sciences, Federal Rural University of Semi-Arid–UFERSA, Pau dos Ferros-RN, Brazil.
2 - Collegiate of Computer Science, Federal University of Vale do S˜ao Francisco–UNIVASF, Salgueiro-PE, Brazil.
3 - Federal Institute of Rio Grande Norte–IFRN, Natal-RN, Brazil.
4 - Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte–UFRN, Natal-RN, Brazil.
5 - Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte–UFRN, Natal-RN, Brazil.

Received: 2022-07-08 Accepted : 2022-07-22 Published : 2022-11-07

Keywords: Aggregation functions‎, ‎Preaggregation functions‎, ‎OWA functions‎, ‎Generalized Mixture functions‎, ‎Image reduction‎,

Abstract :

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 H, and we show that H satisfies a series of properties in order to apply this function in an illustrative example of application: The image reduction process.

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