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Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems

Author

Listed:
  • Dheeraj Kumar Joshi

    (Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand 263145, India)

  • Ismat Beg

    (Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan)

  • Sanjay Kumar

    (Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand 263145, India)

Abstract

Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element (HFLE) and define hesitant probabilistic fuzzy linguistic set (HPFLS) for ill structured and complex decision making problem. HPFLS provides a single framework where both stochastic and non-stochastic uncertainties can be efficiently handled along with hesitation. We have also proposed expected mean, variance, score and accuracy function and basic operations for HPFLS. Weighted and ordered weighted aggregation operators for HPFLS are also defined in the present study for its applications in multi-criteria group decision making (MCGDM) problems. We propose a MCGDM method with HPFL information which is illustrated by an example. A real case study is also taken in the present study to rank State Bank of India, InfoTech Enterprises, I.T.C., H.D.F.C. Bank, Tata Steel, Tata Motors and Bajaj Finance using real data. Proposed HPFLS-based MCGDM method is also compared with two HFL-based decision making methods.

Suggested Citation

  • Dheeraj Kumar Joshi & Ismat Beg & Sanjay Kumar, 2018. "Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems," Mathematics, MDPI, vol. 6(4), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:47-:d:138156
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    References listed on IDEAS

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    1. Bin Zhu & Zeshui Xu & Meimei Xia, 2012. "Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, May.
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    5. Zhiming Zhang, 2013. "Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-33, August.
    6. Merigó, José M. & Palacios-Marqués, Daniel & Zeng, Shouzhen, 2016. "Subjective and objective information in linguistic multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(2), pages 522-531.
    7. Zhou, Wei & Xu, Zeshui, 2016. "Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites," European Journal of Operational Research, Elsevier, vol. 254(2), pages 610-621.
    8. Zeshui Xu & Wei Zhou, 2017. "Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 481-503, December.
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    Cited by:

    1. M. G. Brikaa & Zhoushun Zheng & El-Saeed Ammar, 2020. "Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals," Mathematics, MDPI, vol. 8(3), pages 1-30, February.
    2. Armita Khorsandi & Bing-Yuan Cao & Hadi Nasseri, 2019. "A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    3. Sarka Hoskova-Mayerova & Madeline Al Tahan & Bijan Davvaz, 2020. "Fuzzy Multi-Hypergroups," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    4. Hüseyin Akay & Müsteyde Baduna Koçyiğit, 2021. "An Approach for Determination of the Drainage Network Effect on GIUH Using Hesitant Probabilistic Fuzzy Linguistic Sets," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(11), pages 3873-3902, September.
    5. Huiping Chen & Guiqiong Xu & Pingle Yang, 2019. "Multi-Attribute Decision-Making Approach Based on Dual Hesitant Fuzzy Information Measures and Their Applications," Mathematics, MDPI, vol. 7(9), pages 1-18, August.
    6. Huijuan Wang & Xin Wang & Lidong Wang, 2019. "Multicriteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms," Complexity, Hindawi, vol. 2019, pages 1-19, December.
    7. Harish Garg & Gagandeep Kaur, 2018. "Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators with New Distance Measures," Mathematics, MDPI, vol. 6(12), pages 1-30, November.

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    More about this item

    Keywords

    hesitant fuzzy set; hesitant probabilistic fuzzy linguistic set; score and accuracy function; multi-criteria group decision making; aggregation operator;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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