Displaying similar documents to “QL-implications versus D-implications”

Basic Formal Properties of Triangular Norms and Conorms

Adam Grabowski (2017)

Formalized Mathematics

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In the article we present in the Mizar system [1], [8] the catalogue of triangular norms and conorms, used especially in the theory of fuzzy sets [13]. The name triangular emphasizes the fact that in the framework of probabilistic metric spaces they generalize triangle inequality [2]. After defining corresponding Mizar mode using four attributes, we introduced the following t-norms: minimum t-norm minnorm (Def. 6), product t-norm prodnorm (Def. 8), Łukasiewicz t-norm Lukasiewicz_norm...

Specifying t-norms based on the value of T (1/2, 1/2).

Marcin Detyniecki, Ronald R. Yager, Bernadette Bouchon-Meunier (2000)

Mathware and Soft Computing

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We study here the behavior of the t-norms at the point (1/2, 1/2). We indicate why this point can be considered as significant in the specification of t-norms. Then, we suggest that the image of this point can be used to classify the t-norms. We consider some usual examples. We also study the case of parameterized t-norms. Finally using the results of this study, we propose a uniform method of computing the parameters. This method allows not only having the same parameter-scale for all...

Characterizations of sub-semihypergroups by various triangular norms

B. Davvaz (2005)

Czechoslovak Mathematical Journal

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We investigate the structure and properties of T L -sub-semihypergroups, where T is an arbitrary triangular norm on a given complete lattice L . We study its structure under the direct product and with respect to the fundamental relation. In particular, we consider L = [ 0 , 1 ] and T = min , and investigate the connection between T L -sub-semihypergroups and the probability space.

On the generators of T-indistinguishability operator.

Joan Jacas (1988)

Stochastica

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The structure of the generators' set of a T-indistinguishability operator is analyzed. A suitable characterization of such generators is given. T-indistinguishability operators generated by a single fuzzy set, in the sense of the representation problem, are studied.

Preservation of properties of fuzzy relations during aggregation processes

Józef Drewniak, Urszula Dudziak (2007)

Kybernetika

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Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n -ary operations is considered. Namely, with the use of fuzzy relations R 1 , ... , R n and n -argument operation F on the interval [ 0 , 1 ] , a new fuzzy relation R F = F ( R 1 , ... , R n ) is created....

On MPT-implication functions for fuzzy logic.

Enric Trillas, Claudi Alsina, Ana Pradera (2004)

RACSAM

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This paper deals with numerical functions J : [0,1] x [0,1] → [0,1] able to functionally express operators →: [0,1] x [0,1] → [0,1] defined as (μ → σ)(x,y) = J(μ(x),σ(y)), and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms T and strong-negation functions N for which it is either T(a, J(a,b)) ≤ b (Modus Ponens) or T(N(b), J(a,b)) ≤ N(a) (Modus Tollens), or both, for all a,b in [0,1] and a given J. Functions J...