Calculation method of nonmonotonic interval-valued and fuzzy-valued Choquet integrals

2010 ◽  
Author(s):  
Lingyu Huo ◽  
Bingwu Liu ◽  
Li Zhou ◽  
Jianzhang Wu
Keyword(s):  
Calculation Method ◽  
Choquet Integrals ◽  
Interval Valued

scholarly journals Choquet Integral of Fuzzy-Number-Valued Functions: The Differentiability of the Primitive with respect to Fuzzy Measures and Choquet Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zengtai Gong ◽  
Li Chen ◽  
Gang Duan
Keyword(s):  
Integral Equations ◽  
Real Line ◽  
Fuzzy Number ◽  
Laplace Transformation ◽  
Choquet Integral ◽  
Fuzzy Measures ◽  
Nonadditive Measure ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Interval Valued

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.

A Method for Multi-Attribute Group Decision Making Based on Generalized Interval-Valued Intuitionistic Fuzzy Choquet Integral Operators

2017 ◽  
Vol 25 (05) ◽  
pp. 821-849 ◽  
Author(s):  
Fanyong Meng ◽  
Chunqiao Tan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Choquet Integrals ◽  
The Given ◽  
Interval Valued

As an extension of the classical averaging operators, Choquet integral has been shown a powerful tool for decision theory. In this paper, a method based on the generalized interval-valued intuitionistic fuzzy Choquet integrals w.r.t. the generalized interaction indices is proposed for multiattribute group decision making problems, where the importance of the elements is considered, and their interactions are reflected. Based on the given operational laws on interval-valued intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy Choquet integrals with respect to the generalized Shapley and Banzhaf indices are defined. Moreover, some of their properties are studied, such as idempotency, boundary, comonotonic linearity and μ–linearity. Furthermore, a decision procedure based on the proposed operators is developed for solving multi-attribute group decision making under interval-valued intuitionistic fuzzy environment. Finally, a numerical example is provided to illustrate the developed procedure.

OWA Operators and Choquet Integrals in the Interval-Valued Setting

2016 ◽  
pp. 65-79
Author(s):  
H. Bustince ◽  
J. Fernandez ◽  
L. De Miguel ◽  
E. Barrenechea ◽  
M. Pagola ◽  
...  
Keyword(s):  
Owa Operators ◽  
Choquet Integrals ◽  
Interval Valued

A New Approach to Interval-Valued Choquet Integrals and the Problem of Ordering in Interval-Valued Fuzzy Set Applications

2013 ◽  
Vol 21 (6) ◽  
pp. 1150-1162 ◽  
Author(s):  
Humberto Bustince ◽  
Mikel Galar ◽  
Benjamin Bedregal ◽  
Anna Kolesarova ◽  
Radko Mesiar
Keyword(s):  
Fuzzy Set ◽  
New Approach ◽  
Choquet Integrals ◽  
Interval Valued
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