Why Lattice-Valued Fuzzy Values? A Mathematical Justification

Authors

Rujira Ouncharoen, Chiang Mai UniversityFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Hung T. Nguyen, New Mexico State University - Main CampusFollow

Publication Date

1-2015

Comments

Technical Report: UTEP-CS-14-57a

To appear in Journal of Intelligent and Fuzzy Systems

Abstract

To take into account that expert's degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0,1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice.