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Parameterized utility functions on interval-valued intuitionistic fuzzy numbers with two kinds of entropy and their application in multi-criteria decision making

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Abstract

In this study, the entropy of interval-valued intuitionistic fuzzy numbers (IVIFNs) is analyzed, and two kinds of entropy factors are proposed. By using the normalized score function, normalized Type-1 entropy factor, and normalized Type-2 entropy factor, a series of utility functions on IVIFNs are proposed. In particular, one of the proposed utility functions is structured based on integral. By using the proposed utility functions, IVIFNs can be compared and ranked. The characteristic of these proposed utility functions is that they are objective on comparing IVIFNs from the point of probability. Thereafter, two kinds of fuzzy multi-criteria decision-making methods in interval-valued intuitionistic fuzzy setting are introduced by using the proposed entropy functions. Finally, an example is given to demonstrate the effectiveness of the proposed utility functions and the fuzzy multi-criteria decision-making methods.

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Acknowledgements

The authors are thankful to the editor Dr. Endre Pap, and the anonymous reviewers for their constructive comments in improving this paper.

Funding

The work was supported in part by the project of National Natural Science Fund of China (No. 51508319), the research program of “the National Special Authorized Social Science Fund of China (No. 07@ZH005), the key project of National Natural Science Fund of China (No. 51338003), the Nature and Science Fund from Zhejiang Province Ministry of Education (No. Y201327642)”.

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Authors and Affiliations

  1. College of Transport and Communications, Shanghai Maritime University, Shanghai, 201306, China

    Fangwei Zhang & Guoqiang Tan

  2. School of Education, Zhaoqing University, Zhaoqing, 526061, Guangdong, China

    Weiwei Huang

  3. Faculty of Public Security, Shanghai Police College, Shanghai, 200137, China

    Qiang Li

  4. School of Computing, National University of Singapore, Singapore, 118411, Singapore

    Shuhong Wang

Authors
  1. Fangwei Zhang
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  2. Weiwei Huang
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  3. Qiang Li
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  4. Shuhong Wang
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  5. Guoqiang Tan
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Correspondence to Weiwei Huang.

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The authors declare that they have no conflict of interest.

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This study does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by V. Loia.

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Zhang, F., Huang, W., Li, Q. et al. Parameterized utility functions on interval-valued intuitionistic fuzzy numbers with two kinds of entropy and their application in multi-criteria decision making. Soft Comput 24, 4667–4674 (2020). https://doi.org/10.1007/s00500-019-04227-5

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