Search

Start Over Subject Sugeno integral

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