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

Vladik Kreinovich, Olga Kosheleva, Patricia Melin and Oscar Castillo
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Vladik Kreinovich: Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
Olga Kosheleva: Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USA
Patricia Melin: Division of Graduate Studies and Research, Tijuana Institute of Technology, Tomas Aquino, Tijuana 22685, Baja California, Mexico
Oscar Castillo: Division of Graduate Studies and Research, Tijuana Institute of Technology, Tomas Aquino, Tijuana 22685, Baja California, Mexico

Mathematics, 2022, vol. 10, issue 13, 1-15

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.

Keywords: fuzzy techniques; type-2 fuzzy sets; type-3 fuzzy sets; data processing; Zadeh’s extension principle; efficient algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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