Learning Choquet-Integral-Based Metrics for Semisupervised Clustering

2011 ◽  
Vol 19 (3) ◽  
pp. 562-574 ◽  
Author(s):  
Gleb Beliakov ◽  
Simon James ◽  
Gang Li
Keyword(s):  
Choquet Integral ◽  
Semisupervised Clustering

On a Choquet-Stieltjes type integral on intervals

2019 ◽  
Vol 69 (4) ◽  
pp. 801-814 ◽  
Author(s):  
Sorin G. Gal
Keyword(s):  
Lebesgue Measure ◽  
Choquet Integral ◽  
Stieltjes Integral ◽  
Line Integral ◽  
Type Integral ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Stieltjes Type

Abstract In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ. For g(t) = t, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtained.

Regional integrated energy system schemes selection based on risk expectation and Mahalanobis-Taguchi system

2021 ◽  
pp. 1-18
Author(s):  
Jiahang Yuan ◽  
Yun Li ◽  
Xinggang Luo ◽  
Lingfei Li ◽  
Zhongliang Zhang ◽  
...  
Keyword(s):  
Energy Demand ◽  
Choquet Integral ◽  
Subjective Evaluation ◽  
Risk Attitude ◽  
Energy System ◽  
Energy Utilization ◽  
Utilization Efficiency ◽  
Energy Structure ◽  
Fuzzy Measures ◽  
Integrated Energy System

Regional integrated energy system (RIES) provides a platform for coupling utilization of multi-energy and makes various energy demand from client possible. The suitable RIES composition scheme will upgrade energy structure and improve integrated energy utilization efficiency. Based on a RIES construction project in Jiangsu province, this paper proposes a new multi criteria decision-making (MCDM) method for the selection of RIES schemes. Because that subjective evaluation on RIES schemes benefit under criteria has uncertainty and hesitancy, intuitionistic trapezoidal fuzzy number (ITFN) which has the better capability to model ill-known quantities is presented. In consideration of risk attitude and interdependency of criteria, a new decision model with risk coefficients, Mahalanobis-Taguchi system and Choquet integral is proposed. Firstly, the decision matrices given by experts are normalized, and then are transformed to minimum expectation matrices according to different risk coefficients. Secondly, the weights of criteria from different experts are calculated by Mahalanobis-Taguchi system. Mobius transformation coefficients based on interaction degree are to calculate 2-order additive fuzzy measures, and then the comprehensive weights of criteria are obtained by fuzzy measures and Choquet integral. Thirdly, based on group decision consensus requirement, the weights of experts are obtained by the maximum entropy and grey correlation. Fourthly, the minimum expectation matrices are aggregated by the intuitionistic trapezoidal fuzzy Bonferroni mean operator. Thus, the ranking result according to the comparison rules using the minimum expectation and the maximum expectation is obtained. Finally, an illustrative example is taken in the present study to make the proposed method comprehensible.

scholarly journals A characterization of the 2-additive Choquet integral through cardinal information

2011 ◽  
Vol 184 (1) ◽  
pp. 84-105 ◽  
Author(s):  
Brice Mayag ◽  
Michel Grabisch ◽  
Christophe Labreuche
Keyword(s):  
Choquet Integral
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