An algorithm for computing the generalized interaction index for k-maxitive fuzzy measures

2020 ◽  
Vol 38 (4) ◽  
pp. 4127-4137
Author(s):  
Javier Murillo ◽  
Serge Guillaume ◽  
Tewfik Sari ◽  
Pilar Bulacio
Keyword(s):  
Interaction Index ◽  
Fuzzy Measures

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.

Fuzzy Measures and Choquet Integrals based on Fuzzy Covering Rough Sets

2021 ◽  
pp. 1-1
Author(s):  
Xiaohong Zhang ◽  
Jingqian Wang ◽  
Jianming Zhan ◽  
Jianhua Dai
Keyword(s):  
Rough Sets ◽  
Fuzzy Measures ◽  
Choquet Integrals

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 Intramax and other objective functions: The case of Slovenia

2016 ◽  
Vol 24 (2) ◽  
pp. 12-25 ◽  
Author(s):  
Samo Drobne ◽  
Mitja Lakner
Keyword(s):  
Objective Function ◽  
The Other ◽  
Objective Functions ◽  
Interaction Index ◽  
Functional Regions ◽  
Hierarchical Aggregation ◽  
Administrative Units

Abstract The use of different objective functions in hierarchical aggregation procedures is examined in this paper. Specifically, we analyse the use of the original Intramax objective function, the sum-of-flows objective function, the sum-of-proportions-to-intra-regional-flows objective function, Smart’s weighted interaction index, the first and second CURDS weighted interaction indices, and Tolbert and Killian’s interaction index. The results of the functional regionalisation have been evaluated by self-containment statistics, and they show that the use of the original Intramax procedure tends to delineate operationally the most persuasive and balanced regions that, regarding the intra-regional flows, homogeneously cover the analysed territory. The other objective functions give statistically better but operationally less suitable results. Functional regions modelled using the original Intramax procedure were compared to the regions at NUTS 2 and NUTS 3 levels, as well as to administrative units in Slovenia. We conclude that there are some promising directions for further research on functional regionalisation using hierarchical aggregation procedures.

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