Min and Max Operators for Gradual Intervals

This paper presents a new and a more general formulation of the min and max operations for gradual intervals, initially proposed for the special case of triangular fuzzy intervals. Gradual intervals generalize the conventional interval representation by increasing its specificity, thereby making it...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2018-12, Vol.26 (6), p.3569-3578
Main Authors: Boukezzoula, Reda, Galichet, Sylvie, Foulloy, Laurent
Format: Article
Language:English
Subjects:
Cognition
Computer Science
Decision making
Engineering Sciences
Genetic expression
Gradual intervals
Indexes
Intervals
Mathematical model
Mathematics
Merging
midpoint–radius representation (MR)
min and max operators
Numerical Analysis
Representations
Uncertainty
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Summary:This paper presents a new and a more general formulation of the min and max operations for gradual intervals, initially proposed for the special case of triangular fuzzy intervals. Gradual intervals generalize the conventional interval representation by increasing its specificity, thereby making it possible to represent the imprecision and the uncertainty via the notion of gradualness. In this context, a new interpretation of fuzzy intervals through the notion of gradual intervals is developed. The originality of the proposed methodology lies in the extension of inter-interval relations to the gradual case according to midpoint-radius representation.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2018.2837651