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Goal programming approach to derive intuitionistic multiplicative weights based on intuitionistic multiplicative preference relations

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Abstract

The intuitionistic multiplicative preference relation (IMPR) was introduced by Xia et al. [25] to deal with situations in which the decision makers (DMs) exhibit the characteristics of affirmation, negation and hesitation for the preference degrees over paired comparisons of alternatives. The IMPR can reflect the preference information of the DMs over alternatives more comprehensively than the multiplicative preference relation (MPR). In this paper, a new method for decision making is proposed to derive normalized intuitionistic multiplicative weights on the basis of the order consistent IMPR and the consistent IMPR. We first define the concepts of order consistent IMPR, consistent IMPR and normalized intuitionistic multiplicative weights, and then discuss some properties of the consistent IMPR. After that, we investigate a transformation formula to convert the normalized intuitionistic multiplicative priority weights into a consistent IMPR. An optimization model is constructed to generate the normalized intuitionistic multiplicative weights of IMPR, and the optimal deviation values obtained from the model enable us to improve the consistency of the given IMPR, such that the repaired IMPR is consistent. In the end, a numerical example is provided, and comparative analysis with Xu’s approach [26] is performed to demonstrate the validity and applicability of the proposed method.

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Acknowledgments

The work was supported by National Natural Science Foundation of China (Nos. 71371011, 71490725, 91546108). The authors are thankful to the anonymous reviewers and the editor for their valuable comments and constructive suggestions that have led to an improved version of this paper.

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Authors and Affiliations

  1. School of Management, Hefei University of Technology, Hefei, Anhui, 230009, China

    Feifei Jin, Zhiwei Ni & Yaping Li

  2. Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei, Anhui, 230009, China

    Feifei Jin, Zhiwei Ni & Yaping Li

  3. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China

    Lidan Pei & Huayou Chen

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  1. Feifei Jin
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  2. Zhiwei Ni
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  3. Lidan Pei
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  4. Huayou Chen
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  5. Yaping Li
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Correspondence to Feifei Jin.

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Jin, F., Ni, Z., Pei, L. et al. Goal programming approach to derive intuitionistic multiplicative weights based on intuitionistic multiplicative preference relations. Int. J. Mach. Learn. & Cyber. 9, 641–650 (2018). https://doi.org/10.1007/s13042-016-0590-3

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  • DOI: https://doi.org/10.1007/s13042-016-0590-3

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