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Preliminaries

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Pairwise Comparisons Method

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 690))

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Abstract

This chapter presents basic preliminary concepts and results that will be used in the following chapters: fuzzy sets, fuzzy relations, fuzzy numbers, triangular fuzzy numbers, fuzzy matrices, abelian linearly ordered groups and others.

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References

  1. Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):141–164

    Article  Google Scholar 

  2. Bourbaki N (1990) Algebra II. Springer, Berlin

    Google Scholar 

  3. Cavallo B, DApuzzo L (2009) A general unified framework for pairwise comparison matrices in multicriteria methods. Int J Intell Syst 24(4):377–398

    Article  Google Scholar 

  4. Cavallo B, DApuzzo L, Squillante M (2012) About a consistency index for pairwise comparison matrices over a divisible Alo-Group. Int J Intell Syst 27:153–175

    Article  Google Scholar 

  5. Cavallo B, DApuzzo L (2012) Deriving weights from a pairwise comparison matrix over an alo-group. Soft Comput 16:353–366

    Article  Google Scholar 

  6. Dubois D et al (2000) Fuzzy interval analysis. In: Fundamentals of fuzzy sets, series on fuzzy sets, vol 1. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  7. Ralescu D (1979) A survey of the representation of fuzzy concepts and its applications. In: Gupta MM, Regade RK, Yager R (eds) Advances in fuzzy sets theory and applications. North Holland, Amsterdam, pp 77–91

    Google Scholar 

  8. Ramík J, Římánek J (1985) Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets Syst 16:123–138

    Article  Google Scholar 

  9. Ramík J, Vlach M (2001) Generalized concavity in optimization and decision making. Kluwer Publishers Company, Dordrecht

    Google Scholar 

  10. Ramík J (1986) Extension principle in fuzzy optimization. Fuzzy Sets Syst 19:29–37

    Article  Google Scholar 

  11. Yager RR (1980) On a general class of fuzzy connectives. Fuzzy Sets Syst 4:235–242

    Article  Google Scholar 

  12. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Article  Google Scholar 

  13. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci Part I 8:199–249; Part II 8:301–357; Part III 9:43–80

    Article  Google Scholar 

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Authors and Affiliations

  1. School Business Administration, Silesian University in Opava, Karvina, Czech Republic

    Jaroslav Ramík

Authors
  1. Jaroslav Ramík
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Correspondence to Jaroslav Ramík .

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Ramík, J. (2020). Preliminaries. In: Pairwise Comparisons Method. Lecture Notes in Economics and Mathematical Systems, vol 690. Springer, Cham. https://doi.org/10.1007/978-3-030-39891-0_1

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