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$p$ -symmetric bi-capacities

Pedro Miranda, Michel Grabisch (2004)

Kybernetika

Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order $3^{n}$ , instead of $2^{n}$ for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of $p$ -symmetric bi- capacities, in the same spirit as for $p$ -symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature,...

Pointwise measurability in nonstandard models.

Dieter Landers, Lothar Rogge (1990)

Mathematica Scandinavica

Possibilistic alternatives of elementary notions and relations of the theory of belief functions

Ivan Kramosil (2001)

Kybernetika

The elementary notions and relations of the so called Dempster–Shafer theory, introducing belief functions as the basic numerical characteristic of uncertainty, are modified to the case when probabilistic measures and basic probability assignments are substituted by possibilistic measures and basic possibilistic assignments. It is shown that there exists a high degree of formal similarity between the probabilistic and the possibilistic approaches including the role of the possibilistic Dempster...

Possibly there is no uniformly completely Ramsey null set of size $2^{ω}$

Andrzej Nowik (2002)

Colloquium Mathematicae

We show that under the axiom $C P A_{c u b e}$ there is no uniformly completely Ramsey null set of size $2^{ω}$ . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.

Probabilistic propositional calculus with doubled nonstandard semantics

Ivan Kramosil (1999)

Kybernetika

The classical propositional language is evaluated in such a way that truthvalues are subsets of the set of all positive integers. Such an evaluation is projected in two different ways into the unit interval of real numbers so that two real-valued evaluations are obtained. The set of tautologies is proved to be identical, in all the three cases, with the set of classical propositional tautologies, but the induced evaluations meet some natural properties of probability measures with respect to nonstandard...

Program for generating fuzzy logical operations and its use in mathematical proofs

Tomáš Bartušek, Mirko Navara (2002)

Kybernetika

Fuzzy logic is one of the tools for management of uncertainty; it works with more than two values, usually with a continuous scale, the real interval $[0, 1]$ . Implementation restrictions in applications force us to use in fact a finite scale (finite chain) of truth degrees. In this paper, we study logical operations on finite chains, in particular conjunctions. We describe a computer program generating all finitely-valued fuzzy conjunctions ( $t$ -norms). It allows also to select these $t$ -norms according to...

Pseudo-Delta Functions and Sequences in the Optimization Theory

Endre Pap, Nenad Teofanov (1998)

The Yugoslav Journal of Operations Research

Pushing down Loeb measures.

Hermann Render (1993)

Mathematica Scandinavica

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