Admissible orders on fuzzy numbers

Abstract

From the more than two hundred partial orders for fuzzy numbers proposes in the literature, only a few are totals. In this paper, we introduce the notion of admissible orders for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, is given special attention when thr partial order is the proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a strictly increasing upper dense sequence, proving that this order is admissible for a given partial order.

A New Total Order for Triangular Fuzzy Numbers with an Application

“…There are several proposal for orders on fuzzy numbers in general [Buckley 2005, Wang and Wang 2014, Zumelzu et al 2020] and for TFN in particular (see for example [Akyar et al 2012, Asmus.T.C. et al 2017, Nasseri and Behmanesh 2013) and here we propose a new total order for TFNs which be compatible, in some sense, with the addition and subtraction.…”