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Fuzzy-TISM: A Fuzzy Extension of TISM for Group Decision Making

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Abstract

This paper proposes Fuzzy-TISM, approach for group decision making process. The proposed approach is a fuzzy extension of TISM, which is a multi-criteria decision making technique. TISM is an effective technique and is applied widely to identify relationships among different criteria by creating a comprehensive systematic model of directly and indirectly related criteria. The proposed Fuzzy-TISM approach consolidates the process of group preference aggregation in the fuzzy environment, which can be easily applied to any real world group decision making problem. The proposed approach is a novel attempt to integrate TISM approach with the fuzzy sets. The integration of TISM with fuzzy sets provides flexibility to decision makers to further understand the level of influences of one criteria over another, which was earlier present only in the form of binary (0,1) numbers. 0 represents no influence and 1 represents influence. Due to this, the decision maker is left with only the option of saying 0 or 1 irrespective of the level of influence whether it is low, high, or very high. The proposed Fuzzy-TISM approach take care of this issue and gives a wider flexibility to express the level of influence using fuzzy numbers. The working methodology of proposed Fuzzy-TISM is demonstrated through an illustrative example based on vendor selection.

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Acknowledgments

The communicating author expresses his sincere thanks to Prof. Sushil, Department of Management Studies, IIT Delhi and anonymous referees for their constructive suggestions, which has led to significant improvement in the quality of this manuscript.

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Authors and Affiliations

  1. Indian Institute of Management Rohtak, Rohtak, India

    Gaurav Khatwani, Ashish Trivedi & Ankur Chauhan

  2. Indian Institute of Technology Delhi, Delhi, India

    Surya Prakash Singh

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  1. Gaurav Khatwani
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  3. Ashish Trivedi
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Correspondence to Surya Prakash Singh.

Appendix

Appendix

See Appendix Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Table 3 SSIM matrix of expert # 1
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Table 4 SSIM matrix of expert # 2
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Table 5 SSIM matrix of expert # 3
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Table 6 SSIM matrix of expert # 4
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Table 7 SSIM matrix of expert # 5
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Table 8 Fuzzy reachability matrix based on Aggregated fuzzy SSIM matrix
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Table 9 Final fuzzy reachability matrix \( \tilde{Z} \) of 5 experts with fuzzy and crisp values of driving power and dependence of criteria
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Table 10 Driving power and Dependence Matrix (MICMAC) based on fuzzy reachability matrix of Table 9
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Table 11 Defuzzified reachability matrix with fuzzy linguistic terms Very High Influence (VH) and High Influence (H) as 1 and rest as 0. Shaded region indicates transitive links
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Table 12 Driving power- Dependence Matrix (MICMAC) based on defuzzified reachability matrix based on Table 11
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Table 13 First Iteration of final fuzzy reachability matrix partition
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Table 14 Second Iteration of final fuzzy reachability matrix partition
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Table 15 Third Iteration of final fuzzy reachability matrix partition
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Table 16 Fourth Iteration of final fuzzy reachability matrix partition
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Khatwani, G., Singh, S.P., Trivedi, A. et al. Fuzzy-TISM: A Fuzzy Extension of TISM for Group Decision Making. Glob J Flex Syst Manag 16, 97–112 (2015). https://doi.org/10.1007/s40171-014-0087-4

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