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An Interval Type-2 Fuzzy Likelihood-Based MABAC Approach and Its Application in Selecting Hotels on a Tourism Website

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Abstract

As an extension of type-1 fuzzy sets (T1FSs), interval type-2 fuzzy sets (IT2FSs) can be used to model both extrinsic and intrinsic uncertainties. Based on the likelihood of interval type-2 fuzzy numbers (IT2FNs), this paper proposes a new multi-attributive border approximation area comparison (MABAC) approach to solve multi-criteria decision-making (MCDM) problems. First, an algorithm to decompose IT2FNs into the embedded type-1 fuzzy numbers (T1FNs) is proposed. Second, based on the closeness degree of T1FNs, the likelihood of IT2FNs is defined using the decomposition algorithm, and related properties are discussed. Third, the total ranking of alternatives is obtained using the MABAC approach based on the likelihood of IT2FNs. Finally, a practical example of selecting hotels from a tourism website is presented to verify the validity and feasibility of the proposed approach. A comparative analysis with existing methods is also described.

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Acknowledgments

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 71271218, 71571193, and 71431006).

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  1. School of Business, Central South University, Changsha, 410083, People’s Republic of China

    Su-min Yu, Jing Wang & Jian-qiang Wang

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  1. Su-min Yu
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  2. Jing Wang
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Correspondence to Jian-qiang Wang.

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Appendix

Appendix

\(\tilde{A} = \left[ {\left( {0.6,0.7,0.7,0.8;0.9} \right),\left( {0.5,0.7,0.7,0.9;1} \right)} \right]\), let n = 100; then the embedded T1TrFNs can be identified as shown in Table 7.

Table 7 Embedded T1FNs of \(\tilde{A} = \left[ {\left( {0.6,0.7,0.7,0.8;0.9} \right),\left( {0.5,0.7,0.7,0.9;1} \right)} \right]\) for n = 100
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Yu, Sm., Wang, J. & Wang, Jq. An Interval Type-2 Fuzzy Likelihood-Based MABAC Approach and Its Application in Selecting Hotels on a Tourism Website. Int. J. Fuzzy Syst. 19, 47–61 (2017). https://doi.org/10.1007/s40815-016-0217-6

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