Fuzzy implications: alpha migrativity and generalised laws of importation

In this work, we discuss the law of α-migrativity as applied to fuzzy implication functions in a meaningful way. A generalisation of this law leads us to Pexider-type functional equations connected with the law of importation, viz., the generalised law of importation I(C(x,α),y)=I(x,J(α,y)) (GLI) and the generalised cross-law of importation I(C(x,α),y)=J(x,I(α,y)) (CLI), where C is a generalised conjunction. In this article we investigate only (GLI). We begin by showing that the satisfaction of law of importation by the pairs (C, I) and/or (C, J) does not necessarily lead to the satisfaction of (GLI). Hence, we study the conditions under which these three laws are related

Migrativity properties of 2-uninorms over semi-t-operators

summary:In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$

Funciones t-migrativas t-overlap: una generalización de migratividad en funciones t-overlap

Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real alfa; en este trabajo se trabaja este número alfa con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funciones.This paper introduces a generalization of migrative functions by extending the conditions of the product operation applied in the variables. We operate a number with the variables according to a t-norm instead of multiplying the variable x by this number. Such generalization, whenever it occurs, is called a t-migrative function with respect to such t-norm. Furthermore, we analyse the main properties of t-migrative and t-overlap functions. We introduce some interesting methods of construction of such functions

Consensus image method for unknown noise removal

Noise removal has been, and it is nowadays, an important task in computer vision. Usually, it is a previous task preceding other tasks, as segmentation or reconstruction. However, for most existing denoising algorithms the noise model has to be known in advance. In this paper, we introduce a new approach based on consensus to deal with unknown noise models. To do this, different filtered images are obtained, then combined using multifuzzy sets and averaging aggregation functions. The final decision is made by using a penalty function to deliver the compromised image. Results show that this approach is consistent and provides a good compromise between filters.This work is supported by the European Commission under Contract No. 238819 (MIBISOC Marie Curie ITN). H. Bustince was supported by Project TIN 2010-15055 of the Spanish Ministry of Science

Distributivity of ordinal sum implications over overlap and grouping functions

summary:In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given

Funciones t-migrativas t-overlap: una generalización de migrtividad en funciones t-overlap

Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real α, en este trabajo se trabaja este número α con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funcionesThis paper introduces a generalization of migrative functions by extending the conditions of the product operation applied in the variables. More specifically, instead of requiring to multiply the variable x by a real number α, in this work we operate this α number with the variables according to a t-norm. We call such generalization as a t-migrative function with respect to such t-norm. Then we analyze the main properties of t-migrative t-overlap functions and introduce some construction method

On Some Functional Equations Related to Alpha Migrative t-conorms

In this contribution, we analyse in details the recently introduced definition of migrative tconorms [see Fuzzy implications: alpha migrativity and generalised laws of importation, M. Baczy´nski, B. Jayaram, R. Mesiar, 2020]. We also focus on some general functional equations, which might be obtained from such a notion. We concentrate on some particular well-known families of fuzzy implications and show solutions of those equations among this kind of fuzzy implication functions