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Several Generalized Interval-Valued 2-Tuple Linguistic Weighted Distance Measures and their Application

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Abstract

With respect to interval-valued 2-tuple linguistic variables, this paper first defines a generalized distance measure. Then, several generalized interval-valued 2-tuple linguistic weighted distance measures are presented. To consider the interactions between elements in a set, three correlative weighted distance measures named the generalized interval-valued 2-tuple linguistic Shapley weighted distance measure, the generalized interval-valued 2-tuple linguistic ordered Shapley weighted distance measure, and the generalized interval-valued 2-tuple linguistic hybrid Shapley weighted distance measure are provided. Meanwhile, several special cases and desirable properties are considered. To obtain the weight vectors, models based on the Euclidean distance measure are constructed. Subsequently, an approach to pattern recognition and to multi-attribute decision making with interval linguistic preference information is developed, and the associated examples are offered to show their concrete application.

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Acknowledgments

This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the National Natural Science Foundation of China (Nos. 71571192, 71501189, 71201089, 71271217, and 51204100), the Postdoctoral Science Special Foundation of China (2015T80901), and the Mobile E-business Collaborative Innovation Center 2011 of Hunan Province in China.

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Authors and Affiliations

  1. School of Management, Qingdao Technological University, Qingdao, 266520, China

    Hao Cheng

  2. School of International Audit, Nanjing Audit University, Nanjing, 211815, China

    Fanyong Meng

  3. Business School, Central South University, Changsha, 410083, China

    Fanyong Meng & Ke Chen

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  1. Hao Cheng
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  2. Fanyong Meng
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  3. Ke Chen
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Correspondence to Fanyong Meng.

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Cheng, H., Meng, F. & Chen, K. Several Generalized Interval-Valued 2-Tuple Linguistic Weighted Distance Measures and their Application. Int. J. Fuzzy Syst. 19, 967–981 (2017). https://doi.org/10.1007/s40815-016-0218-5

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