S- and R-implications from uninorms continuous in \(]0,1[^2\) and their distributivity over uninorms
type: Item
instance of: scholarly article
title: S- and R-implications from uninorms continuous in \(]0,1[^2\) and their distributivity over uninorms
zbMATH Open document ID: 1184.03014
published in: Fuzzy Sets and Systems
publication date: 2009-11-17T00:00:00Z
review text: In the classical logic based on the Boolean truth-values scale, residual implication (R-implication for short) and S-implication (derived from the disjunction and the negation) coincide. This is no longer true in the case of fuzzy logics based on the \([0,1]\) truth-degrees scale. Uninorms, as binary operations on \([0,1]\), can be split into two disjoint classes -- conjunctive and disjunctive uninorms. Thus, based on uninorms, both R- and S-implications can be considered. In this paper, uninorms continuous on \(]0,1[^2\) are considered. General expressions for both kinds of implications in special cases are found. Moreover, several properties of such implications are studied. Special attention is paid to the distributivity of R- and S-implications over conjunctive and disjunctive uninorms.
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 5634412
zbMATH Keywords: uninorm
zbMATH Keywords: S-implication
zbMATH Keywords: R-implication
zbMATH Keywords: contrapositive symmetry
zbMATH Keywords: exchange principle
zbMATH Keywords: distributivity
author: D. Ruiz-Aguilera
author: Joan Torrens
reviewed by: Radko Mesiar
MaRDI profile type: Publication
full work available at URL: j.fss.2008.05.015
OpenAlex ID: W2066782180
cites work: Idempotent uninorms
cites work: Basic concepts for a theory of evaluation: The aggregative operator
cites work: Q5389813
cites work: Q3440327
cites work: Q4315286
cites work: Structure of Uninorms
cites work: The structure of continuous uni-norms
cites work: Triangular norms
cites work: On locally internal monotonic operations
cites work: The distributivity condition for uninorms and t-operators
cites work: DISTRIBUTIVE IDEMPOTENT UNINORMS
cites work: Q5389740
cites work: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm
cites work: Q5389878
cites work: Distributivity of residual implications over conjunctive and disjunctive uninorms
DOI: 10.1016/J.FSS.2008.05.015
description: scientific article; zbMATH DE number 5634412