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Group decision making based on the relationships between the information measures for additive and multiplicative linguistic term sets

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Abstract

This paper investigates the systematic transformation of the information measures including the distance, similarity and entropy measures of linguistic term sets (LTSs) into each other. Firstly, we present the bilateral transforming approach of the distance measure into the similarity measure for both additive LTSs (ALTSs) and multiplicative LTSs. Then, the transformation of the distance measure into the entropy measure for ALTSs is investigated. This cycle of transformation is completed by investigating the transformation of the similarity measure into the entropy measure for ALTSs, and vice versa. In the sequel, in analogous to the results of linguistic arguments, the results of linguistic preference relations are achieved. Further, a rational approach is proposed to evaluate the relative weights of decision makers in the form of linguistic preference information.

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References

  • Bordogna G, Passi G (1993) A fuzzy linguistic approach generalizing boolean information retrieval: a model and its evaluation. J Am Soc Inf Sci 44:70–82

    Article  Google Scholar 

  • Chang P, Chen Y (1994) A fuzzy multicriteria decision making method for technology transfer strategy selection in biotechnology. Fuzzy Sets Syst 63:131–139

    Article  Google Scholar 

  • Degani R, Bortolan G (1988) The problem of linguistic approximation in clinical decision making. Int J Approx Reason 2:143–162

    Article  Google Scholar 

  • Delgado M, Verdegay JL, Vila MA (1993) Linguistic decision making models. Int J Intell Syst 7:479–492

    Article  MATH  Google Scholar 

  • Dong YC, Xu YF, Yu S (2009) Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Trans Fuzzy Syst 17:1366–1378

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Farhadinia B (2013b) A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure. J Knowl Based Syst 39:79–84

    Article  Google Scholar 

  • Farhadinia B (2014a) Distance and similarity measures for higher order hesitant fuzzy sets. Knowl-Based Syst 55:43–48

    Article  MATH  Google Scholar 

  • Farhadinia B (2014b) An efficient similarity measure for intuitionistic fuzzy sets. J Soft Comput 18:85–94

    Article  MATH  Google Scholar 

  • Farhadinia B (2014c) Fuzzy multicriteria decision-making method based on a family of novel measured functions under vague environment. J Intell Fuzzy Syst 27:2797–2808

    MathSciNet  MATH  Google Scholar 

  • Farhadinia B (2014d) An efficient similarity measure for intuitionistic fuzzy sets. Soft Comput 18:85–94

    Article  MATH  Google Scholar 

  • Farhadinia B, Ban AI (2013) Developing new similarity measures of generalized intuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers from similarity measures of generalized fuzzy numbers. J Math Comput Model 57:812–825

    Article  MathSciNet  MATH  Google Scholar 

  • Herrera F, Herrera-Viedma E, Martinez L (2008) A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 16:354–370

    Article  Google Scholar 

  • Herrera F, Martinez L (2001) A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision making. IEEE Trans Syst Man Cybern B 31:227–234

    Article  Google Scholar 

  • Law CK (1996) Using fuzzy numbers in educational grading system. Fuzzy Sets Syst 83:311–323

    Article  Google Scholar 

  • Lee H (1996) Group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in software development. Fuzzy Sets Syst 80:261–271

    Article  Google Scholar 

  • Liao HC, Wu XL, Liang XD, Yang JB, Xu DL, Herrera F (2018) A continuous interval-valued linguistic ORESTE method for multi-criteria group decision making. Knowl-Based Syst 153:65–77

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ, Merig JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76:127–138

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142

    Article  MathSciNet  MATH  Google Scholar 

  • Liao HC, Xu ZS, Herrera-Viedma E, Herrera F (2018) Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the art survey. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-017-0432-9

  • Malczewski J (2006) Ordered weighted averaging with fuzzy quantifiers: GIS-based multicriteria evaluation for land-use suitability analysis. Int J Appl Earth Obs Geoinf 8:270–277

    Article  Google Scholar 

  • Pedrycz W, Ekel P, Parreiras R (2010) Fuzzy multicriteria decision making: models methods and applications. Wiley, Chichester, UK

    Book  MATH  Google Scholar 

  • Turksen IB (2007) Meta-linguistic axioms as a foundation for computing with words. Inf Sci 177:332–359

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JH, Hao JY (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14:435–445

    Article  Google Scholar 

  • Wang JH, Hao JY (2007) An approach to computing with words based on canonical characteristic values of linguistic labels. IEEE Trans Fuzzy Syst 15:593–604

    Article  Google Scholar 

  • Wu XL, Liao HC (2018) An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making. Inf Fus 43:13–26

    Article  Google Scholar 

  • Xu ZS (2004) EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int J Uncertain Fuzziness Knowl Based Syst 12:791–810

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS (2006) Induced uncertain linguistic OWA operators applied to group decision making. Inf Fusion 7:231–8

    Article  Google Scholar 

  • Xu ZS (2005) Deviation measures of linguistic preference relations in group decision making. Omega 33:249–54

    Article  Google Scholar 

  • Xu ZS (2012) Linguistic decision making: theory and methods. Science Press, Beijing

    Book  MATH  Google Scholar 

  • Xu ZS (2004) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166:19–30

    Article  MathSciNet  MATH  Google Scholar 

  • Yager RR, Goldstein LS, Mendels E (1994) FUZMAR: an approach to aggregating market research data based on fuzzy reasoning. Fuzzy Sets Syst 68:1–11

    Article  Google Scholar 

  • Zhang H, Zhang W, Mei C (2009) Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl-Based Syst 22:449–454

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Quchan University of Technology, Quchan, Iran

    Bahram Farhadinia

  2. Business School, Sichuan University, Chengdu, 610064, China

    Huchang Liao

Authors
  1. Bahram Farhadinia
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  2. Huchang Liao
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Correspondence to Bahram Farhadinia.

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Communicated by V. Loia.

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Farhadinia, B., Liao, H. Group decision making based on the relationships between the information measures for additive and multiplicative linguistic term sets. Soft Comput 23, 7901–7911 (2019). https://doi.org/10.1007/s00500-018-3420-6

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