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Generalized hesitant fuzzy knowledge measure with its application to multi-criteria decision-making

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Abstract

Hesitant fuzzy (HF) entropy and HF-knowledge measures are two dual concepts that have similar practical applications despite different mathematical structures. In some real-life scenarios, one particular entropy/knowledge measure may not be reasonable due to some undesirable and counter-intuitive situations. In this paper, we introduce a one-parametric generalized knowledge measure in the HF-setting. Such a generalization provides a class of HF-knowledge measures and hence the flexibility in the practical problems. We show the advantages of the generalized measure over the existing HF-entropy/knowledge measures in view of weight computation in the decision-making problems and ambiguity computation of two different hesitant fuzzy elements. At last, we apply the proposed generalized knowledge measure of HFSs in multi-criteria decision-making (MCDM) using the bidirectional projection method in the hesitant fuzzy environment.

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References

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  Google Scholar 

  • Bhandari D, Pal NR (1993) Some new information measures for fuzzy sets. Inf Sci 67:209–228

    Article  MathSciNet  Google Scholar 

  • Chen SM (1996) A fuzzy reasoning approach for rule-based systems based on fuzzy logics. IEEE Trans Syst Man Cybernet Part B (Cybernetics) 26(5):769–778

    Article  Google Scholar 

  • Chen SM, Huang CM (2003) Generating weighted fuzzy rules from relational database systems for estimating null values using genetic algorithms. IEEE Trans Fuzzy Syst 11(4):495–506

    Article  Google Scholar 

  • Chen SM, Jong WT (1997) Fuzzy query translation for relational database systems. IEEE Trans Syst Man Cybernet Part B (Cybernetics) 27(4):714–721

    Article  Google Scholar 

  • Faizi S, Rashid T, Salabun W, Zafar S, Watrobski J (2018) Decision making with uncertainty using hesitant fuzzy sets. Int J Fuzzy Syst 20:93–103

    Article  MathSciNet  Google Scholar 

  • Fan JL, Ma YL (2002) Some new fuzzy entropy formulas. Fuzzy Sets Syst 128:277–284

    Article  MathSciNet  Google Scholar 

  • Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129–144

    Article  MathSciNet  Google Scholar 

  • Garg H (2018) Pythagorean fuzzy sets and their aggregation operators in multiple-attribute decision making. Int J Uncertain Quamtific 8:267–289

    Article  MathSciNet  Google Scholar 

  • Garg H (2019) Hesitant Pythagorean fuzzy Maclaurim symmetric mean operators and its applications to multi attribute decision-making process. Int J Intell Syst 34:601–626

    Article  Google Scholar 

  • Hooda DS, Bajaj RK (2010) Useful measures of fuzzy information, total ambiguity and fuzzy directed divergence. Int J Gen Syst 39:647–658

    Article  MathSciNet  Google Scholar 

  • Hu J, Yang Y, Zhang X, Chen X (2018) Similarity and entropy measures for hesitant fuzzy sets. Int T Oper Res 25:857–886

    Article  MathSciNet  Google Scholar 

  • Lalotra S, Singh S (2018) On a knowledge measure and an unorthodox accuracy measure of an intuitionistic fuzzy set(s) with their applications. Int J Comput Intell Syst 11:1338–1356

    Article  Google Scholar 

  • Lalotra S, Singh S (2020) Knowledge measure of hesitant fuzzy set and its application in multi-attribute decision-making. Comput Appl Math 39(2):1–31

    Article  MathSciNet  Google Scholar 

  • Li D, Zeng W, Li J (2018) New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision-making. Int J Fuzzy Syst 20:2111–2121

    Article  Google Scholar 

  • Liao H, Xu Z (2013) A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Ma 12:373–392

    Article  MathSciNet  Google Scholar 

  • Liao H, Xu Z (2014) Subtraction and division operations over hesitant fuzzy sets. J Intell Fuzzy Syst 27:65–72

    Article  MathSciNet  Google Scholar 

  • Liu XC (1992) Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst 52:305–318

    Article  MathSciNet  Google Scholar 

  • Liu X, Zhu J, Liu S (2014) Bidirectional projection method with hesitant fuzzy information. Syst Eng-Theory Pract 34:2637–2644

    Google Scholar 

  • Luca DA, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy theory. Inf Contr 20:301–312

    Article  Google Scholar 

  • Lv J, Guo S, Guo F (2019) Study on hesitant fuzzy information measures and their clustering application. Comput Intell Neurosci. https://doi.org/10.1155/2019/5370763

    Article  Google Scholar 

  • Manoj TV, Leena J, Soney RB (1998) Knowledge representation using fuzzy Petri nets-revisited. IEEE Trans Knowl Data Eng 10(4):666–667

    Article  Google Scholar 

  • Meng F, Chen W, Chen X, Zhang Q (2016) Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on Shapley function. Int J Intell Syst 31:17–43

    Article  Google Scholar 

  • Mishra AR, Rani P, Pardasani KR (2019) Multiple-criteria decision-making for service quality selection based on Shapley COPRAS method under hesitant fuzzy sets. Granul Comp 4(3):435–449

    Article  Google Scholar 

  • Rani P, Jain D, Hooda DS (2019) Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision-making method based on shapely weighted divergence measure. Granul Comp 4:407–420

    Article  Google Scholar 

  • Shang XG, Jiang WS (1997) A note on fuzzy information measures. Pattern Recogn Lett 18:425–432

    Article  Google Scholar 

  • Singh S, Lalotra S, Sharma S (2019) Dual concepts in fuzzy theory: entropy and knowledge measure. Int J Intell Syst 34:1034–1059

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118:467–477

    Article  MathSciNet  Google Scholar 

  • Szmidt E, Kacprzyk J, Bujnowski P (2014) How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Inf Sci 257:276–285

    Article  MathSciNet  Google Scholar 

  • Tang J, Chen SM, Meng F (2019) Group decision making with multiplicative interval linguistic hesitant fuzzy preference relations. Inform Sci 495:215–233

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  • Wei C, Yan F, Rodrıguez RM (2016) Entropy measures for hesitant fuzzy sets and their application in multi-criteria decision-making. J Intell Fuzzy Syst 31(1):673–685

    Article  Google Scholar 

  • Xu Z, Xia M (2012) Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int J Intell Syst 27:799–822

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets Inf Contr 8:338–353

    Article  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199–249

    Article  MathSciNet  Google Scholar 

  • Zeng W, Li D, Yin Q (2016) Distance and similarity measures between hesitant fuzzy sets and their applications in pattern recognition. Pattern Recogn Lett 84:267–271

    Article  Google Scholar 

  • Zhang Z, Chen SM (2019) A consistency and consensus-based method for group decision making with hesitant fuzzy linguistic preference relations. Inform Sci 501:317–336

    Article  MathSciNet  Google Scholar 

  • Zhang Z, Chen SM (2020) Group decision making with hesitant fuzzy linguistic preference relations. Inform Sci 514:354–368

    Article  MathSciNet  Google Scholar 

  • Zhang X, Xu Z (2015) Novel distance and similarity measures on hesitant fuzzy sets with application on cluster analysis. J Intell Fuzzy Syst 28:2279–2296

    Google Scholar 

  • Zhao H, Xu Z, Liu FJ (2015) Uncertainty measures for hesitant fuzzy information. Int J Intell Syst 30:818–836

    Article  Google Scholar 

  • Zhao H, Xu Z, Cui F (2016) Generalized hesitant fuzzy harmonic mean operators and their applications in group decision making. Int J Fuzzy Syst 18:685–696

    Article  MathSciNet  Google Scholar 

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Acknowledgements

Authors are highly thankful to the anonymous reviewers and the Editor for their constructive suggestions and for bringing the paper in the present form.

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Authors and Affiliations

  1. School of Mathematics, Faculty of Sciences, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, 182320, India

    Surender Singh & Abdul Haseeb Ganie

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  1. Surender Singh
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  2. Abdul Haseeb Ganie
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Correspondence to Surender Singh.

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Singh, S., Ganie, A.H. Generalized hesitant fuzzy knowledge measure with its application to multi-criteria decision-making. Granul. Comput. 7, 239–252 (2022). https://doi.org/10.1007/s41066-021-00263-5

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  • DOI: https://doi.org/10.1007/s41066-021-00263-5

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