Choquet integral of fuzzy-number-valued functions: the differentiability of the primitive with respect to fuzzy measures and Choquet integral equations
type: Item
instance of: scholarly article
title: Choquet integral of fuzzy-number-valued functions: the differentiability of the primitive with respect to fuzzy measures and Choquet integral equations
zbMATH Open document ID: 1474.28029
DOI: 10.1155/2014/953893
author: Li Chen
author: Gang Duan
author: Zengtai Gong
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper deals with the Choquet integral of fuzzy-number-valued functions based on the nonnegative real line. We firstly give the definitions and the characterizations of the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on the nonadditive measure. Furthermore, the operational schemes of above several classes of integrals on a discrete set are investigated which enable us to calculate Choquet integrals in some applications. Secondly, we give a representation of the Choquet integral of a nonnegative, continuous, and increasing fuzzy-number-valued function with respect to a fuzzy measure. In addition, in order to solve Choquet integral equations of fuzzy-number-valued functions, a concept of the Laplace transformation for the fuzzy-number-valued functions in the sense of Choquet integral is introduced. For distorted Lebesgue measures, it is shown that Choquet integral equations of fuzzy-number-valued functions can be solved by the Laplace transformation. Finally, an example is given to illustrate the main results at the end of the paper.
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 45N05
zbMATH DE Number: 7023390
Wikidata QID: Q59043087
describes a project that uses: kappalab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/953893
OpenAlex ID: W2141682149
cites work: Theory of capacities
cites work: Non-additive measure and integral
cites work: Non-monotonic fuzzy measures and the Choquet integral
cites work: A new type of nonlinear and the computational algorithm
cites work: Subjective Probability and Expected Utility without Additivity
cites work: \(k\)-order additive discrete fuzzy measures and their representation
cites work: A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: applications of the Kappalab R package
cites work: Convergence properties of the monotone expectation and its application to the extension of fuzzy measures
cites work: A theory of fuzzy measures: Representations, the Choquet integral, and null sets
cites work: CONVERGENCE THEOREMS FOR SEQUENCES OF CHOQUET INTEGRALS
cites work: On the space of measurable functions and its topology determined by the Choquet integral
cites work: The Choquet integral representability of comonotonically additive functionals in locally compact spaces
cites work: Numerical method for solving linear Fredholm fuzzy integral equations of the second kind
cites work: Fuzzy differential equations
cites work: Fuzzy integral equations
cites work: A note on derivatives of functions with respect to fuzzy measures
cites work: An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
cites work: Q4859898
cites work: Fuzzy number fuzzy measures and fuzzy integrals. I: Fuzzy integrals of functions with respect to fuzzy number fuzzy measures
cites work: Fuzzy numbers and fuzzification of the Choquet integral
cites work: On the fuzzy initial value problem
Recommended article: ON CHOQUET INTEGRALS OF MEASURABLE FUZZY NUMBER-VALUED FUNCTIONS
Recommended article: Q3052209
Recommended article: Fuzzy-valued Choquet integrals. II: The Choquet integral of functions with respect to fuzzy-valued fuzzy measures
Recommended article: Q4640887
Recommended article: Q5472752
Recommended article: Q3406255
Recommended article: Fuzzy numbers and fuzzification of the Choquet integral
Recommended article: An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure
Recommended article: Q4456649
Recommended article: On integrals of \(n\)-dimensional fuzzy-number-valued functions
description: scientific article; zbMATH DE number 7023390