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Differential inequality conditions for dominance between continuous Archimedean t-norms [PDF]
Mathematical Inequalities & Applications, 2009 Dominance between triangular norms (t-norms) is a versatile relationship. For continuous Archimedean t-norms, dominance can be verified by checking one of many sufficient conditions derived from a generalization of the Mulholland inequality. These conditions pertain to various convexity properties of compositions of additive generators and their ...
Susanne Saminger‐Platz +2 more
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A generalization of the Mulholland inequality for continuous Archimedean t-norms
Journal of Mathematical Analysis and Applications, 2008 Motivated by the study of the dominance relation between Archimedean \(t\)-norms the authors make an interesting contribution generalizing Mulholland inequality. More precisely, the following result is proved: Theorem. Consider a function \(h:[0, \infty ] \to [0 , \infty]\) and some fixed value \(t \in ]0, \infty[\) such that (h1) \(h\) is continuous ...
Susanne Saminger‐Platz +2 more
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International Journal of Approximate Reasoning, 2012 In this short article we present corrections of some results presented in Baczynski (2010) [6] and Qin and Yang (2010) [13] which are connected with the distributive equation I(x,T"1(y,z))=T"2(I(x,y),I(x,z)) and the contrapositive symmetry I(x,y)=I(N(y),N(x)) when T"1, T"2 are continuous t-norms, N is a strong negation and I an unknown binary function,
Michał Baczyński, Feng Qin
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Some New Structures in Neutrosophic Metric Spaces [PDF]
Neutrosophic Sets and Systems, 2021 Neutrosophic sets deals with inconsistent, indeterminate and imprecise datas. The concept of Neutrosophic Metric Space (NMS) uses the idea of continuous t- norm and continuous t - conorm in intuitionistic fuzzy metric spaces.
M. Jeyaraman +3 more
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Formal balls of Q-categories [PDF]
Categories and General Algebraic Structures with Applications, 2023 The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to Q-categories by Kostanek and Waszkiewicz, where Q is a commutative and unital quantale.
Xianbo Yang, Dexue Zhang
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Archimedean-Compensatory Fuzzy Logic Systems [PDF]
International Journal of Computational Intelligence Systems, 2015 The paper aims to define a new kind of logic, referred to as Archimedean-Compensatory Logic, which is constructed from the unification of two different fuzzy logic systems, namely a continuous Archimedean fuzzy logic and a compensatory fuzzy logic.
Rafael A. Espin-Andrade +3 more
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Aggregation of Indistinguishability Fuzzy Relations Revisited
Mathematics, 2021 Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in ...
Juan-De-Dios González-Hedström +2 more
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Relaxed Indistinguishability Relations and Relaxed Metrics: The Aggregation Problem
Axioms, 2022 The main purpose of this paper is to study the relationship between those functions that aggregate relaxed indistinguishability fuzzy relations with respect to a collection of t-norms and those functions that merge relaxed pseudo-metrics, extending the ...
Juan-De-Dios González-Hedström +2 more
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T-Equivalences: The Metric Behavior Revisited
Mathematics, 2020 Since the notion of T-equivalence, where T is a t-norm, was introduced as a fuzzy generalization of the notion of crisp equivalence relation, many researchers have worked in the study of the metric behavior of such fuzzy relations.
Pilar Fuster-Parra +3 more
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A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics
Mathematics, 2020 In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X.
Valentín Gregori +2 more
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