Some functional equations in the space of uniform distribution functions.
A synthesis of multidimensional judgements consistent with linear transformations.
A characterization of convolution and related operations.
On convex triangle functions.
On a method of Pi-Calleja for describing additive generators of associative functions.
On the stability of a functional equation related to associativity
Triangle functions and composition of probability distribution functions.
The equations of left and right distributivity of composition of distribution functions over triangle functions are solved in a restricted domain.
Producto, convexificación y completación de espacios métricos generalizados y probabilísticos.
En 1967 E. Trillas introdujo la noción de espacio métrico generalizado, al considerar métricas abstractas valoradas en semigrupos ordenados, unificando con este punto de vista algebraico-reticular las estructuras métricas reales de M. Fréchet ([5]) y los espacios métricos probabilísticos de K. Menger ([6]) (así como los espacios Booleanos de Blumenthal ([4]) y las métricas naturales definidas en grupos ordenados). En el presente artículo se abordan los problemas de la topología del orden, del producto,...
On associative developable surfaces
Proportion functions in three dimensions.
Sur les mesures du degré de flou.
On caractérise toutes les entropies-floues qui sont des valuations des treillis P(X) des parties floues d'un ensemble fini X, on presente la construction de certaines entropies floues et on analyse leur caractère de valuation de treillis aiguisés Sh(g), g belonging to P(X).
On sums of dependent uniformly distributed random variables.
We study and solve several functional equations which yield necessary and sufficient conditions for the sum of two uniformly distributed random variables to be uniformly distributed.
Sobre L-órdenes entre t-normas estrictas.
Several order relations in the set of strict t-norms are investigated.
On natural metrics.
In the present note we study the effective construction of a natural generalized metric structure (on a set), obtaining as particular case the result of Menger. In the case of groups, we analyze its topology and its structure of natural proximity space (in the sense of Efremovic).
A reflection on what is a membership function.
This paper is just a first approach to the idea that the membership function μ of a fuzzy set labelled P is, basically, a measure on the set of linguistic expressions x is P for each x in the corresponding universe of discourse X. Estimating that the meaning of P (relatively to X) is nothing else than the use of P on X, these measures seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the predicate...
Didactical note: probabilistic conditionality in a Boolean algebra.
This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will...
Combining degrees of impairment: the case of the index of Balthazard.
Using techniques for modeling indices by means of functional equations and resources from fuzzy set theory, the classical Balthazard index used in order to combine several degrees of impairment is characterized in two natural ways and its use is criticized. In addition some hints are given on how to study better solutions than Balthazard's one for the problem of combining impairment degrees.
Gaudí, geométricamente.
On MPT-implication functions for fuzzy logic.
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 are taken among...
A short note on lattices allowing disjunctive reasoning.
This short note shows that the scheme of disjunctive reasoning, , not , does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality , forces the structure to be a boolean algebra.
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