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1. Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators

Creator:
Agahi, Hamzeh, Mesiar, Radko, and Ouyang, Yao
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Sugeno integral, fuzzy measure, comonotone functions, Chebyshev´s inequality, t-norm, t-conorm, and T-(S-)evaluators
Language:
English
Description:
In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function H and a scale transformation φ is given. Consequences for T-(S-)evaluators are established.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On ⋆-associated comonotone functions

Creator:
Hutník, Ondrej and Pócs, Jozef
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
comonotone functions, binary operation, ⋆-associatedness, and Sugeno integral
Language:
English
Description:
We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper \cite{BK}. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to +-associatedness of functions (as proved by Boczek and Kaluszka), but also to their ⋆-associatedness with ⋆ being an arbitrary strictly monotone and right-continuous binary operation. The second open problem deals with an existence of a pair of binary operations for which the generalized upper and lower Sugeno integrals coincide. Using a fairly elementary observation we show that there are many such operations, for instance binary operations generated by infima and suprema preserving functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. 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