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Approximations of lattice-valued possibilistic measures

Ivan Kramosil (2005)

Kybernetika

Lattice-valued possibilistic measures, conceived and developed in more detail by G. De Cooman in 1997 [2], enabled to apply the main ideas on which the real-valued possibilistic measures are founded also to the situations often occurring in the real world around, when the degrees of possibility, ascribed to various events charged by uncertainty, are comparable only quantitatively by the relations like “greater than” or “not smaller than”, including the particular cases when such degrees are not...

Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. Doré, A. Martin, I. Abi-Zeid, A.-L. Jousselme, P. Maupin (2010)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. Doré, A. Martin, I. Abi-Zeid, A.-L. Jousselme, P. Maupin (2011)

RAIRO - Operations Research

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

Borel extensions of Baire measures in ZFC

Menachem Kojman, Henryk Michalewski (2011)

Fundamenta Mathematicae

We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.

Can we assign the Borel hulls in a monotone way?

Márton Elekes, András Máthé (2009)

Fundamenta Mathematicae

A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ G δ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone G δ hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....

Choquet-like integrals with respect to level-dependent capacities and ϕ -ordinal sums of aggregation function

Radko Mesiar, Peter Smrek (2015)

Kybernetika

In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a ϕ -ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.

Classes of fuzzy measures and distortion

Ľubica Valášková, Peter Struk (2005)

Kybernetika

Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.

Conditional states and joint distributions on MV-algebras

Martin Kalina, Oľga Nánásiová (2006)

Kybernetika

In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.

Construction of aggregation operators: new composition method

Tomasa Calvo, Andrea Mesiarová, Ľubica Valášková (2003)

Kybernetika

A new construction method for aggregation operators based on a composition of aggregation operators is proposed. Several general properties of this construction method are recalled. Further, several special cases are discussed. It is also shown, that this construction generalizes a recently introduced twofold integral, which is exactly a composition of the Choquet and Sugeno integral by means of a min operator.

Covering locally compact groups by less than 2 ω many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if C E K is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of C E K . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...

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