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1. Choquet-like integrals with respect to level-dependent capacities and φ-ordinal sums ofaggregarion function

Creator:
Mesiar, Radko and Smrek, Peter
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Choquet integral, Choquet-like integral, level-dependent capacity, and φ-ordinal sum of aggregation functions
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Fuzzification of Choquet integral and its application in multiple criteria decision making

Creator:
bebčáková , Iveta, Talšová , Jana, and Pavlačka, Ondřej
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Aggregation oparetors, Choquet integral, and fuzzification
Language:
English
Description:
A common approach in the multiple criteria decision making is to obtain the overall evaluation by aggregating the partial evaluations. For this, a member of a large family of aggregation operators is used. Many of these operators commonly employed in decision making (weighted average, ordered weighted average, minimum, maximum, ...) can be used only when criteria are independent. On the other hand, the Choquet integral, a generalization of the aforementioned operators, can be used even when some interactions between criteria occur. We present a fuzzified Choquet integral capable of dealing not only with fuzzy partial evaluations (first level fuzzification), but also with fuzzy weights (second level fuzzification). We also provide an effective way to evaluate the fully fuzzified integral, which allows its straightforward application to decision making problems with inherent uncertainty.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On application of choquet integral in possibilistic information theory

Creator:
Kroupa, Tomáš
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
possibility theory, information theory, and Choquet integral
Language:
English
Description:
The aim of this paper is to introduce the Choquet integral representation of some information quantities in the possibility theory. A possibilistic T-independence concept is further analyzed with respect to its information-theoretic properties. The main result is then the introduction of a so called general ineasure of T-dependence. It is further proven that the general measure of T-dependence exhibits significant properties froin an information-theoretic point of view and can be conceived as an apt analogy of the well-known probabilistic inutual information.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. The Choquet integral as Lebesgue integral and related inequalities

Creator:
Mesiar, Radko, Li, Jun, and Pap, Endre
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Choquet integral, comonotone functions, integral inequalities, monotone measure, and modularity
Language:
English
Description:
The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered functions is shown to be a sufficient constraint ensuring the validity of all discussed inequalities for the Choquet integral, independently of the underlying monotone measure.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public