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

Jian‐Zhang Wu; Gleb Beliakov

doi:10.1002/int.22049

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

International Journal of Intelligent Systems ◽

10.1002/int.22049 ◽

2018 ◽

Vol 34 (2) ◽

pp. 247-270 ◽

Cited By ~ 17

Author(s):

Jian‐Zhang Wu ◽

Gleb Beliakov

Keyword(s):

Decision Criteria ◽

Interaction Index ◽

Fuzzy Measures

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

Advances in Fuzzy Systems ◽

10.1155/2021/2319004 ◽

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.

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Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding

Mathematics ◽

10.3390/math8020301 ◽

2020 ◽

Vol 8 (2) ◽

pp. 301

Author(s):

Li Huang ◽

Jian-Zhang Wu ◽

Rui-Jie Xi

Keyword(s):

Generation Process ◽

Random Generation ◽

Decision Criteria ◽

Interaction Index ◽

Decision Aiding ◽

Satisfactory Performance ◽

Complex Constraints ◽

Interaction Phenomenon

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.

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