Choquet integral optimisation with constraints and the buoyancy property for fuzzy measures

2021 ◽  
Author(s):  
Gleb Beliakov ◽  
Simon James
Keyword(s):  
Choquet Integral ◽  
Fuzzy Measures

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 Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lazim Abdullah ◽  
Noor Azzah Awang ◽  
Mahmod Othman
Keyword(s):  
Shapley Value ◽  
Choquet Integral ◽  
Evaluation Process ◽  
Aggregation Operator ◽  
Interaction Index ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
New Development ◽  
The Future

Choquet integral is a type of aggregation operator that is commonly used to aggregate the interrelated information. Nowadays, this operator has been successfully embedded with fuzzy measures in solving various evaluation problems. Inspired from this new development, this paper aims to introduce a combined Choquet integral-fuzzy measures (CI-FM) operator that uses the Shapley value standard and interaction index to deal with the interactions between elements of information. The proposed operator takes into account not only the importance of elements or their ordered positions but also the interaction among criteria during the evaluation process. A case of customers’ satisfaction over two fast restaurants in Malaysia is presented to illustrate the application of the proposed aggregation operator. Based on three customers’ satisfaction criteria, restaurant 1 and restaurant 2 received CI-FM scores of 0.711011 and 0.704945, respectively. Interestingly, the criterion “services” constantly received the highest rating across both restaurants. In addition, the proposed aggregation operator successfully identified which restaurant is superior in the eyes of customers. Finally, this study offers some research ideas for the future.

scholarly journals The Choquet integral with respect to fuzzy measures and applications

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Anna Rita Sambucini
Keyword(s):  
Choquet Integral ◽  
Fuzzy Measures

AbstractFuzzy measures and Choquet asymmetric integral are considered here. As an application to economics some Core-Walras results are given.

Towards a New Multicriteria Decision Support Method Using Fuzzy Measures and the Choquet Integral

2016 ◽  
Vol 5 (1) ◽  
pp. 57-86 ◽  
Author(s):  
Emdjed Alnafie ◽  
Djamila Hamdadou ◽  
Karim Bouamrane
Keyword(s):  
Sensitivity Analysis ◽  
Decision Support ◽  
Input Data ◽  
Choquet Integral ◽  
Multicriteria Analysis ◽  
Analysis Method ◽  
Fuzzy Measures ◽  
Local Aggregation ◽  
Decision Support Method ◽  
Multicriteria Decision Support

In literature, there is a large panoply of multicriteria analysis methods (MCAM), each one is characterized by the nature of its input data, the way to edit its outputs and the operations used to perform calculations especially the performances aggregation. Aggregation is the operation consisting in grouping several quantities in a unique value in order to facilitate the manipulation and the interpretation of the original values. MCAM are classified according to the type of aggregation that they perform, so we can distinguish total, partial and local aggregation. Each MCAM has advantages and suffers from some limits. In this paper, the authors proposed a new multicriteria analysis method (AMFI) dedicated to solve ranking decision support problems. AMFI is based on the use of fuzzy measures and Choquet integral to represent interactions between criteria and improve the coherence of the results. The authors proceeded to a series of experimentations allowing highlighting theoretical elements of the proposed method and they performed sensitivity analysis to test its robustness.

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