Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Patricia Melin, Tijuana Institute of TechnologyFollow
Oscar Castillo, Tijuana Institute of TechnologyFollow

Publication Date

6-1-2022

Comments

Technical Report: UTEP-CS-22-66

Abstract

It is known that to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately, it turned out that type-3 fuzzy sets are also useful in some applications. Because of this practical importance, it is necessary to design efficient algorithms for data processing under such type-3 (and higher order) fuzzy uncertainty. In this paper, we show how we can combine known efficient algorithms for processing type-1 and type-2 uncertainty to come up with a new algorithm for the type-3 case.