Fuzzy compatibility relations and pseudo-monometrics: Some correspondences

Gupta, Megha and Jayaram, Balasubramaniam (2022) Fuzzy compatibility relations and pseudo-monometrics: Some correspondences. Fuzzy Sets and Systems. pp. 1-19. ISSN 0165-0114

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Abstract

De Baets and Mesiar in a seminal work showed that Fuzzy Compatibility Relations (FCR) - reflexive and symmetric fuzzy relations - that are also T-transitive w.r.t. an Archimedean t-norm are in a one-to-one correspondence with pseudo-metrics. However, FCRs that are not T-transitive have not merited as much scrutiny. Recently, ternary relations on a set known as betweenness relations and monometrics on the obtained betweenness set, or a B-set, have garnered a lot of attention, especially for their role in decision making and penalty based data aggregation. In this work we show that there is a one-to-one correspondence between FCRs and distance functions, not necessarily metrics, through these betweenness relations. Through interesting correspondences between FCRs and pseudo-monometrics on a given B-set, we also give some pointers to one of the major challenges in this field - that of obtaining pseudo-monometrics on a given B-set.

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IITH Creators:

IITH Creators	ORCiD
Jayaram, Balasubramaniam	http://orcid.org/0000-0001-7370-3821

Item Type:

Article

Additional Information:

The second author would like to acknowledge the support obtained from SERB under the project MTR/2020/000506 for the work contained in this submission.

Uncontrolled Keywords:

Betweenness relation; Fuzzy compatibility relations; Non-T-transitivity; Pseudo-monometric

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

. LibTrainee 2021

Date Deposited:

01 Sep 2022 10:06

Last Modified:

01 Sep 2022 10:06