Generation of linear orders for intervals by means of aggregation functions

By Humberto Bustince, Javier Fernández, Anna Kazimírová Kolesárová, Radko Mesiar. Fuzzy Sets Syst., 2013

327 citations recorded by the source corpus.

The problem of choosing an appropriate total order is crucial for many applications that make use of extensions of fuzzy sets. In this work we introduce the concept of an admissible order as a total order that extends the usual partial order between intervals. We propose a method to build these admissible orders in terms of two aggregation functions and we prove that some of the most used examples of total orders that appear in the literature are specific cases of our construction.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7c6009651fdcfda4f24cdc351ed5b6b40e14a33b

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Citations in the corpus

A Historical Account of Types of Fuzzy Sets and Their Relationships (2016, methodology): “fore, it is necessary to study the conditions that determine the choice of one order or another [33].”
Hesitant Fuzzy Sets: State of the Art and Future Directions (2014, methodology): “…function through the use of a fuzzy set over the unit interval to model it, (iii) interval-valued fuzzy sets (IVFS), 8,9 in which the membership degree of an element is given by a closed subinterval of the unit interval in such a way that the length of that interval may be understood as a…”