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Novel Correlation and Entropy Measures of Hesitant Fuzzy Sets

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Hesitant Fuzzy Decision Making Methodologies and Applications

Part of the book series: Uncertainty and Operations Research ((UOR))

Abstract

Correlation is one of the most widely used indices in data analysis, pattern recognition, machine learning, decision making, etc. It measures how well two variables move together in a linear fashion.

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References

  • Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305–316

    Article  Google Scholar 

  • Bustince H, Burillo P, Soria F (2003) Automorphisms, negations and implication operators. Fuzzy Sets Syst 134:209–229

    Article  Google Scholar 

  • Bustince H, Pagola M, Mesiar R, Hullermeier E, Herrera F (2012) Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Trans Fuzzy Syst 20:405–415

    Article  Google Scholar 

  • Chaudhuri BB, Bhattacharya A (2001) On correlation between two fuzzy sets. Fuzzy Sets Syst 118:447–456

    Article  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their application to clustering analysis. Appl Math Model 37:2197–2211

    Article  Google Scholar 

  • Chiang DA, Lin NP (1999) Correlation of fuzzy sets. Fuzzy Sets Syst 102:221–226

    Article  Google Scholar 

  • De Luca A, Termini S (1972) A definition of a non probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20:301–312

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Friedman M, Last M, Makover Y, Kandel A (2007) Anomaly detection in web documents using crisp and fuzzy-based clustering methodology. Inf Sci 177:467–475

    Google Scholar 

  • Garmendia L, Yager RR, Trillas E, Salvador A (2003) On t-norms based measures of specificity. Fuzzy Sets Syst 133:237–248

    Article  Google Scholar 

  • Gerstenkorn T, Manko J (1991) Correlation of intuitionistic fuzzy sets. Fuzzy Sets Syst 44:39–43

    Article  Google Scholar 

  • Hong DH (2006) Fuzzy measures for a correlation coefficient of fuzzy numbers under T w (the weakest t-norm)-based fuzzy arithmetic operations. Inf Sci 176:150–160

    Article  Google Scholar 

  • Hong DH, Hwang SY (1995) Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets Syst 75:77–81

    Article  Google Scholar 

  • Hung WL (2001) Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. Int J Uncertainty Fuzziness Knowl Based Syst 9:509–516

    Article  Google Scholar 

  • Hung WL, Wu JW (2002) Correlation of intuitionistic fuzzy sets by centroid method. Inf Sci 144:219–225

    Article  Google Scholar 

  • Kaufmann A, Swanson D (1975) Introduction to the theory of fuzzy subsets: fundamental theoretical elements. Academic Press, New York

    Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ (2015) Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl-Based Syst 82:115–127

    Article  Google Scholar 

  • Liu ST, Gao C (2002) Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets Syst 128:267–275

    Article  Google Scholar 

  • Mitchell HB (2004) A correlation coefficient for intuitionistic fuzzy sets. Int J Intell Syst 19:483–490

    Article  Google Scholar 

  • Murithy CA, Pal SK, Dutta-Majumder D (1985) Correlation between two fuzzy membership functions. Fuzzy Sets Syst 17:23–38

    Article  Google Scholar 

  • Pal NR, Bustince H, Pagola M, Mukherjee UK, Goswami DP, Beliakov G (2013) Uncertainties with Atanassov’s intuitionistic fuzzy sets: Fuzziness and lack of knowledge. Inf Sci 228:61–74

    Article  Google Scholar 

  • Parkash O, Sharma P, Mahajan R (2008) New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Inf Sci 178:2389–2395

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2010) Correlation of intuitionistic fuzzy sets. In: Hüllermeier E, Kruse R, Hoffmann F. (eds), IPMU 2010, LNAI 6178, pp. 169–177

    Google Scholar 

  • Wei CP, Liang X, Zhang YZ (2012) A comparative analysis and improvement of entropy measures for intuitionistic fuzzy sets. J Syst Sci Math Sci 32:1437–1448

    Google Scholar 

  • Xu ZS (2006) On correlation measures of intuitionistic fuzzy sets. Lect Notes Comput Sci 4224:16–24

    Article  Google Scholar 

  • Xu ZS, Xia MM (2011a) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26:410–425

    Article  Google Scholar 

  • Xu ZS, Xia MM (2011b) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138

    Article  Google Scholar 

  • Xu ZS, Xia MM (2012) Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int J Intell Syst 27(9):799–822

    Article  Google Scholar 

  • Yager RR (1979) On the measure of fuzziness and negation part I: membership in the unit interval. Int J Gen Syst 5:221–229

    Article  Google Scholar 

  • Yager RR (1992) Default knowledge and measures of specificity. Inf Sci 61:1–44

    Article  Google Scholar 

  • Yager RR (1998) Measures of specificity. In: Computational intelligence: soft computing and fuzzy-neuro integration with applications. Springer, pp 94–113

    Google Scholar 

  • Yager RR (2008) Measures of specificity over continuous spaces under similarity relations. Fuzzy Sets Syst 159:2193–2210

    Article  Google Scholar 

  • Yu CH (1993) Correlation of fuzzy numbers. Fuzzy Sets Syst 55:303–307

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zhao N, Xu ZS, Liu FJ (2015) Uncertainty measures for hesitant fuzzy information. Int J Intell Syst 30(7):818–836

    Article  Google Scholar 

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Authors and Affiliations

  1. Business School, Sichuan University, 29 Wangjiang Road, Chengdu, Sichuan, China

    Huchang Liao & Zeshui Xu

Authors
  1. Huchang Liao
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  2. Zeshui Xu
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Correspondence to Huchang Liao .

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Liao, H., Xu, Z. (2017). Novel Correlation and Entropy Measures of Hesitant Fuzzy Sets. In: Hesitant Fuzzy Decision Making Methodologies and Applications . Uncertainty and Operations Research. Springer, Singapore. https://doi.org/10.1007/978-981-10-3265-3_2

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