Displaying similar documents to “Considering uncertainty and dependence in Boolean, quantum and fuzzy logics”

Sum of observables in fuzzy quantum spaces

Anatolij Dvurečenskij, Anna Tirpáková (1992)

Applications of Mathematics

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We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.

A new approach to representation of observables on fuzzy quantum posets

Le Ba Long (1992)

Applications of Mathematics

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We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general.

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...