期刊
FUZZY SETS AND SYSTEMS
卷 446, 期 -, 页码 193-221出版社
ELSEVIER
DOI: 10.1016/j.fss.2020.12.005
关键词
Semiring; Pseudo -integral; Choquet integral; Fuzzy integral; Generalized Choquet integral
资金
- National Natural Science Fund of China [11271062]
- Natural Science Fund of Jilin Province, PR China [20190201014JC, APVV-18-0052]
- GACR [18-06915S]
- project on Artificial Intelligence ATLAS by Science Fund of the Republic Serbia [6524105]
This paper generalizes the Choquet integral and obtains various types of nonadditive integrals. The paper also proves related theorems and inequalities.
Due to many applications, the Choquet integral as a powerful tool for modeling non-deterministic problems needs to be further extended. Therefore the paper is devoted to a generalization of the Choquet integral. As a basis, the pseudo-integral for bounded integrand is extended to the case for nonnegative integrands at first, and then the generalized Choquet integral is defined. As special cases, pseudo-Choquet Stieltjes integrals, pseudo-fuzzy Stieltjes integrals, g-Choquet integrals, pseudo-(N)fuzzy integrals and pseudo-(S)fuzzy integrals are obtained, and various kinds of properties and convergence theorems are shown, meanwhile Markov, Jensen, Minkowski and Holder inequalities are proved. In the end, the generalized discrete Choquet integral is discussed. The obtained results for the generalized Choquet integral cover some previous results on different types of nonadditive integrals.(c) 2020 Elsevier B.V. All rights reserved.
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