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Axioms 2017, 6(4), 29; doi:10.3390/axioms6040029

Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness

1
Dipartimento di Ingegneria e Architettura, Università di Trieste, 34127 Trieste, Italy
2
Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche "Bruno de Finetti", Università di Trieste, 34127 Trieste, Italy
3
Dipartimento di Economia e Management, Università di Brescia, 25122 Brescia, Italy
Current address: via Università 1, 34123 Trieste, Italy.
*
Author to whom correspondence should be addressed.
Received: 6 October 2017 / Revised: 23 October 2017 / Accepted: 26 October 2017 / Published: 28 October 2017
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
View Full-Text   |   Download PDF [262 KB, uploaded 28 October 2017]

Abstract

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space. View Full-Text
Keywords: fuzzy binary relation; fuzzy Suzumura consistency; order-preserving function; maximal element fuzzy binary relation; fuzzy Suzumura consistency; order-preserving function; maximal element
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bevilacqua, P.; Bosi, G.; Zuanon, M. Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness. Axioms 2017, 6, 29.

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