From MCDA to Fuzzy MCDA: violation of basic axiom and how to fix it

Abstract

The use of fuzzy numbers (FNs) for managing uncertainty in multi-criteria decision analysis (MCDA) demands a thorough exploring multi-criteria decision problem under fuzzy environment. Fuzzy MCDA (FMCDA) model implies comparison, choice or ranking alternatives based on assessing corresponding functions with subsequent ranking of FNs. Despite the wide use of FMCDA in recent decades, the effect of the violation of axioms for fuzzy ranking methods on FMCDA models has not been explored yet. This paper aims at demonstrating the violation of the basic MCDA axiom, associated with ranking of dominating and dominated in Pareto alternatives, by fuzzy TOPSIS and fuzzy MAVT models as an example. The suggestion to implement FMCDA models in applications without violation of the basic axiom is elicited based on the use of distinguishable fuzzy numbers.

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Acknowledgements

This work is supported by the Russian National research project RFBR-19-07-01039 and the Spanish National research project PGC2018-099402-B-I00 and ERDF.

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Correspondence to Luis Martínez.

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Yatsalo, B., Korobov, A. & Martínez, L. From MCDA to Fuzzy MCDA: violation of basic axiom and how to fix it. Neural Comput & Applic (2020). https://doi.org/10.1007/s00521-020-05053-9

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Keywords

  • Fuzzy multi-criteria decision analysis
  • Ranking of fuzzy numbers
  • Overestimation
  • Transformation methods
  • Fuzzy TOPSIS
  • Fuzzy MAVT
  • Distinguishable fuzzy numbers