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Ranking Alternatives by Pairwise Comparisons Matrix with Fuzzy Elements on Alo-Group

  • Jaroslav Ramík
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 57)

Abstract

The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the decision maker in the form of an n by n pairwise comparisons matrix. Here, we deal with a pairwise comparisons matrix with fuzzy elements (PCF matrix). Fuzzy elements of the pairwise comparisons matrix are applied whenever the decision maker is not sure about the value of his/her evaluation, or, the elements of the PCF matrix are aggregated crisp evaluations in a group decision making problem. We investigate pairwise comparisons matrices with elements from an abelian linearly ordered group (alo-group) over a real interval. We propose a method starting from construction of fuzzy elements of a reciprocal PCF matrix, calculating its consistency and resulting into computation of the priority vector associated to the ranking of the alternatives. Illustrating examples are presented and discussed.

Keywords

Ranking alternatives Pairwise comparisons matrix Reciprocity Consistency Fuzzy elements 

Notes

Acknowledgments

This research has been supported by GACR project No. 14-02424S.

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© Springer International Publishing Switzerland 2016

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Authors and Affiliations

  1. 1.Faculty of Business Administration in KarvináSilesian University in OpavaKarvináCzech Republic

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