Automorphisms, negations and implication operators

DOI10.1016/S0165-0114(02)00214-2zbMath1010.03017OpenAlexW1986391289MaRDI QIDQ1867699

Publication date: 2 April 2003

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0165-0114(02)00214-2

zbMATH Keywords

automorphism t-norm t-conorm strong negation fuzzy negation implication operations

Mathematics Subject Classification ID

Fuzzy logic; logic of vagueness (03B52)

Related Items

Fuzzy rough set models over two universes using textures ⋮ A Survey of the Distributivity of Implications over Continuous T-norms and the Simultaneous Satisfaction of the Contrapositive Symmetry ⋮ (S,N)-Implications on Bounded Lattices ⋮ Xor-Implications and E-Implications: Classes of Fuzzy Implications Based on Fuzzy Xor ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ About the Use of Admissible Order for Defining Implication Operators ⋮ The Notion of Pre-aggregation Function ⋮ Constructing conjunctive left (right) semi-uninorms and implications satisfying the neutrality principle ⋮ MEASURING INCLUSION, SIMILARITY AND COMPATIBILITY BETWEEN ATANASSOV'S INTUITIONISTIC FUZZY SETS ⋮ Constructing implications and coimplications on a complete lattice ⋮ On distributivity equations of implications and contrapositive symmetry equations of implications ⋮ On a New Class of Implications in Fuzzy Logic ⋮ Atanassov’s Intuitionistic Contractive Fuzzy Negations ⋮ \((S,N)\)- and \(R\)-implications: A state-of-the-art survey ⋮ On the first place antitonicity in QL-implications ⋮ On the characterizations of fuzzy implications satisfying \(I(x,y)=I(x,I(x,y))\) ⋮ On the characterizations of \((S,N)\)-implications ⋮ The law of importation for discrete implications ⋮ Rule reduction for efficient inferencing in similarity based reasoning ⋮ A characterization of residual implications derived from left-continuous uninorms ⋮ Contrapositive symmetrisation of fuzzy implications -- revisited ⋮ Restricted equivalence functions ⋮ On the \(T_L\)-transitivity of fuzzy similarity measures ⋮ Three constructive methods for the definition of interval-valued fuzzy equivalencies ⋮ Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images ⋮ The best interval representations of t-norms and automorphisms ⋮ Multidimensional fuzzy implications ⋮ Canonical representation of the Yager's classes of fuzzy implications ⋮ The \(\circledast\)-composition of fuzzy implications: closures with respect to properties, powers and families ⋮ Interval-valued implications and interval-valued strong equality index with admissible orders ⋮ Properties of Raha's similarity-based approximate reasoning method ⋮ Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures ⋮ Distributivity between semi-uninorms and semi-t-operators ⋮ Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions ⋮ REVISITING Xor-IMPLICATIONS: CLASSES OF FUZZY (CO)IMPLICATIONS BASED ON f-Xor (f-XNor) CONNECTIVES ⋮ Pseudo-uninorms and Atanassov’s intuitionistic pseudo-uninorms ⋮ New measures of homogeneity for image processing: an application to fingerprint segmentation ⋮ Distributive equations of implications based on nilpotent triangular norms ⋮ Fuzzy XNOR connectives in fuzzy logic ⋮ Representation of fuzzy subsets by Galois connections ⋮ Solutions to the functional equation \(I(x, y) = I(x, I(x, y))\) for three types of fuzzy implications derived from uninorms ⋮ About the Use of Admissible Order for Defining Implication Operators ⋮ Some Results on Extension of Lattice-Valued XOR, XOR-Implications and E-Implications ⋮ Left and right distributivity between semi-uninorms and semi-\(S\)-uninorms ⋮ Algebraic structures of interval-valued fuzzy \((S,\mathcal N)\)-implications ⋮ Comment on: ``Image thresholding using type II fuzzy sets. Importance of this method ⋮ Robustness of fuzzy connectives and fuzzy reasoning ⋮ How to modify a fuzzy implication function to satisfy a desired property ⋮ The law of \(O\)-conditionality for fuzzy implications constructed from overlap and grouping functions ⋮ On the characterizations of fuzzy implications satisfying \(I(x,I(y,z))=I(I(x,y),I(x,z))\) ⋮ Moderate deviation and restricted equivalence functions for measuring similarity between data ⋮ New trends on the permutability equation ⋮ GENERALIZED ATANASSOV'S INTUITIONISTIC FUZZY INDEX: CONSTRUCTION OF ATANASSOV'S FUZZY ENTROPY FROM FUZZY IMPLICATION OPERATORS ⋮ Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms ⋮ Aggregating fuzzy implications ⋮ \(K\)-operators: an approach to the generation of interval-valued fuzzy implications from fuzzy implications and vice versa ⋮ Distributivity of \(N\)-ordinal sum fuzzy implications over \(t\)-norms and \(t\)-conorms ⋮ Distance measures on intuitionistic hesitant fuzzy set and its application in decision-making ⋮ Sufficient and necessary conditions for Boolean fuzzy systems as universal approximators ⋮ On \((G, N)\)-implications derived from grouping functions ⋮ A framework for edge detection based on relief functions ⋮ Implications in bounded systems ⋮ Dissimilarity functions and divergence measures between fuzzy sets ⋮ \(QL\)-operations and \(QL\)-implication functions constructed from tuples \((O,G,N)\) and the generation of fuzzy subsethood and entropy measures ⋮ On residual implications derived from overlap functions ⋮ A review of the relationships between implication, negation and aggregation functions from the point of view of material implication ⋮ Homomorphisms on the monoid of fuzzy implications and the iterative functional equation \(I(x, I(x, y)) = I(x, y)\) ⋮ Characterizations of residual coimplications of pseudo-uninorms on a complete lattice ⋮ Convex combinations of fuzzy logical operations ⋮ Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions ⋮ Intersections between some families of \((\mathrm U, \mathrm N)\)- and \(\mathrm{RU}\)-implications ⋮ A characterization of (U,N), RU, QL and D-implications derived from uninorms satisfying the law of importation ⋮ On dependencies and independencies of fuzzy implication axioms ⋮ On the distributivity of fuzzy implications over continuous and Archimedean triangular conorms ⋮ Relating De Morgan triples with Atanassov's intuitionistic De Morgan triples via automorphisms ⋮ QL-implications: some properties and intersections ⋮ Contrast of a fuzzy relation ⋮ On interval fuzzy S-implications ⋮ On fuzzy implications determined by aggregation operators ⋮ Solutions to the functional equation \(I(x,y)=I(x,I(x,y))\) for a continuous D-operation ⋮ Construction of interval-valued fuzzy entropy invariant by translations and scalings ⋮ On the distributivity of fuzzy implications over representable uninorms ⋮ Continuous R-implications generated from representable aggregation functions ⋮ On interval fuzzy negations ⋮ SISO fuzzy relational inference systems based on fuzzy implications are universal approximators ⋮ Composition of interval-valued fuzzy relations using aggregation functions ⋮ Optimal solution of multi-objective linear programming with \(\inf\)-\(\to\) fuzzy relation equations constraint ⋮ Definition and construction of fuzzy DI-subsethood measures ⋮ Fuzzy implications in lattice effect algebras ⋮ Natural negation of interval-valued \(t\)-(co) norms and implications ⋮ Characterizations of \((U^2,N)\)-implications generated by 2-uninorms and fuzzy negations from the point of view of material implication ⋮ On some classes of directionally monotone functions ⋮ Inflationary BL-algebras obtained from 2-dimensional general overlap functions ⋮ Ordinal sums of the main classes of fuzzy negations and the natural negations of t-norms, t-conorms and fuzzy implications ⋮ New measures for comparing matrices and their application to image processing ⋮ Distributivity Equations Between Semi-t-operators Over Semi-uninorms ⋮ Migrativity of aggregation functions ⋮ Distance measures on intuitionistic fuzzy sets based on intuitionistic fuzzy dissimilarity functions ⋮ The role a fuzzy implication plays in a multi-criteria decision algorithm ⋮ Interval-valued fuzzy strong S-subsethood measures, interval-entropy and P-interval-entropy ⋮ Formulas for generators of R-implications ⋮ WEAK FUZZY S-SUBSETHOOD MEASURES: OVERLAP INDEX ⋮ On two types of discrete implications ⋮ Fuzzy Implication Classes Satisfying a Boolean-Like Law ⋮ Implications Generated by Triples of Monotone Functions ⋮ Some new approaches to constructing similarity measures ⋮ On the extension of lattice-valued implications via retractions ⋮ From semantic games to provability: the case of Gödel logic

Cites Work