5 research outputs found
Migrativity properties of 2-uninorms over semi-t-operators
summary:In this paper, we analyze and characterize all solutions about -migrativity properties of the five subclasses of 2-uninorms, i. e. , , , , , over semi-t-operators. We give the sufficient and necessary conditions that make these -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for , the -migrativity of over a semi-t-operator is closely related to the -section of or the ordinal sum representation of t-norm and t-conorm corresponding to . But for the other four categories, the -migrativity over a semi-t-operator is fully determined by the -section of
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
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
Invariability, orbits and fuzzy attractors
In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality