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Preference Matrices with Fuzzy Elements in Decision Making

In: Decision Making and Optimization

Author

Listed:
  • Martin Gavalec

    (University of Hradec Kralove)

  • Jaroslav Ramík

    (Silesian University in Opava)

  • Karel Zimmermann

    (Charles University in Prague)

Abstract

This chapter is aimed on pairwise comparison matrices with fuzzy elements. Fuzzy elements of the pairwise comparison matrix are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We particularly deal with pairwise comparison matrices with fuzzy number elements and investigate some properties of such matrices. In comparison with pairwise comparison matrices with crisp elements investigated in the previous chapter, here we investigate pairwise comparison matrices with elements from alo-group over a real interval. In some sense, this chapter is a continuation of the second part of the previous chapter. Such an approach allows for a generalization dealing with additive, multiplicative and fuzzy pairwise comparison matrices with fuzzy elements. Moreover, we deal with the problem of measuring the inconsistency of fuzzy pairwise comparison matrices by defining corresponding inconsistency indexes. Numerical examples are presented to illustrate the concepts and derived properties.

Suggested Citation

  • Martin Gavalec & Jaroslav Ramík & Karel Zimmermann, 2015. "Preference Matrices with Fuzzy Elements in Decision Making," Lecture Notes in Economics and Mathematical Systems, in: Decision Making and Optimization, edition 127, chapter 0, pages 91-115, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-08323-0_3
    DOI: 10.1007/978-3-319-08323-0_3
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