A novel fuzzy methodology applied for ranking trapezoidal fuzzy numbers and new properties

ABSTRACT

Ranking fuzzy numbers is a key tool in decision making and other fuzzy analysis. Several strategies have been proposed for this task. However, none of them is universally accepted because counter-intuitive examples appear in all cases. Very recently, a novel methodology for ordering fuzzy numbers that satisfy several human-according properties has been introduced. This procedure overcomes some drawbacks of previous techniques and it is not based on a ranking index. In this paper, due to its feasible application in computation, we show how the novel fuzzy ranking can be particularly applied to trapezoidal (and triangular) fuzzy numbers by analysing all possible cases. Hence, new properties appear. Finally, a comparison (with other existing methods) study is carried out to show the reasonability of the obtained orderings and to illustrate the advantages of the proposed methodology.

KEYWORDS:

• Fuzzy number
• ranking
• fuzzy ranking
• decision making
• fuzzy set

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 46T99
• 47H10
• 47H09
• 54H25

Acknowledgments

We thank the anonymous reviewers for their careful reading of this manuscript and their many insightful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Antonio Francisco Roldán López de Hierro  http://orcid.org/0000-0002-6956-4328

Concepción Roldán  http://orcid.org/0000-0001-7732-3041

Additional information

Funding

This manuscript has been partially supported by Junta de Andalucía by Projects FQM-268 and FQM-235 of the Andalusian CICYE, and also by Project TIN2017-89517-P of Ministerio de Economía, Industria y Competitividad.