Probabilistic bipartition interaction index of multiple decision criteria associated with the nonadditivity of fuzzy measures

2018 ◽  
Vol 34 (2) ◽  
pp. 247-270 ◽  
Author(s):  
Jian‐Zhang Wu ◽  
Gleb Beliakov
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lazim Abdullah ◽  
Noor Azzah Awang ◽  
Mahmod Othman

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.


Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 301
Author(s):  
Li Huang ◽  
Jian-Zhang Wu ◽  
Rui-Jie Xi

The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. In this paper, we adopt a kind of explicit interaction index, the nonadditivity index, to construct two types of quasi-random generation methods of capacity under a given decision interaction preference. Compared to the existing random generation algorithms, the methods have relatively satisfactory performance on the statistics characteristic of generated capacities but need rather less calculation effort on the generation process. We also show the effectiveness of proposed quasi-random generation methods by an illustrative decision example.


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

2003 ◽  
Author(s):  
Erica Dawson ◽  
Thomas Gilovich ◽  
Dennis Regan
Keyword(s):  

Author(s):  
Xiaohong Zhang ◽  
Jingqian Wang ◽  
Jianming Zhan ◽  
Jianhua Dai

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