The Relationship between Interval, Fuzzy and Possibilistic Optimization

Authors:
Weldon A. Lodwick
Affiliations:
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, U.S.A. 80217-3364
Venue:
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Year:
2009

Citing 3
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Abstract

The relationship between fuzzy set theory (in particular fuzzy arithmetic) and interval analysis is well-know. This study explores the interconnections between interval analysis, fuzzy interval analysis, and interval and fuzzy/possibilistic optimization. Two key ideas are considered herein: (1) constraint set computation and (2) the clear distinctions and relationships between interval, fuzzy, and possibilistic entities as they are used in optimization within an historical and taxonomic context. Constraint fuzzy interval arithmetic is used to compute constraint sets.