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A Framework for Triangular Fuzzy Random Multiple-Criteria Decision Making

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Abstract

Most real-world decisions practically occur in extremely complex environments characterized by both fuzziness and randomness. This phenomenon highlights the requirement for new evaluation methods in a fuzzy random environment and new ways to address fuzzy random multiple-criteria decision-making (MCDM) problems. This study reviews fuzzy random variable (FRV) to evaluate fuzzy random decision-making environment. Given the inaccuracy of certain precision formulas proposed in previous studies for the variance of a triangular FRV, this work presents the detailed process of calculating precision variance formulas and discusses several properties of the expectation and variance of triangular FRVs (TFRVs). The united variance of a TFRV vector is also proven to possess non-additive properties. Thus, an ordered weighted averaging (OWA) operator is extended to aggregate fuzzy random data by proposing a triangular fuzzy random OWA operator. Motivated by the idea of mean–variance analysis, an expectation-variance-based method is employed to rank TFRVs. Furthermore, a novel triangular fuzzy random MCDM method is developed, and certain numerical examples are provided to demonstrate the ability of TFRVs to comprehensively assess the performance of a specific alternative. This work also illustrates how the triangular fuzzy random MCDM framework can be extended to any fuzzy random decision-making process.

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Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (Project Nos. NSFC71371156 and NSFC70971017) and partially by the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No. CityU-112111).

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Authors and Affiliations

  1. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Zhen-Song Chen & Yan-Lai Li

  2. National United Engineering Laboratory of Integrated and Intelligent Transportation, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Zhen-Song Chen & Yan-Lai Li

  3. Department of System Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, People’s Republic of China

    Kwai-Sang Chin

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  1. Zhen-Song Chen
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Chen, ZS., Chin, KS. & Li, YL. A Framework for Triangular Fuzzy Random Multiple-Criteria Decision Making. Int. J. Fuzzy Syst. 18, 227–247 (2016). https://doi.org/10.1007/s40815-015-0109-1

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