Journal ArticleDOI
Fuzzy real numbers as Dedekind cuts with respect to a multiple-valued logic
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TLDR
The Dedekind-MacNeille completion of a partially ordered L-valued set is established, and specializing this situation to the set of all crisp rational numbers the authors obtain in a unique way the fuzzy Dedeksind real numbers.About:
This article is published in Fuzzy Sets and Systems.The article was published on 1987-12-01. It has received 52 citations till now. The article focuses on the topics: Fuzzy number & Dedekind cut.read more
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Book ChapterDOI
Fuzzy Interval Analysis
TL;DR: This chapter is an overview of past and present works dealing with fuzzy intervals and their operations, and contains a reasoned survey of methods for comparing and ranking fuzzy intervals.
Journal ArticleDOI
Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets
Didier Dubois,Henri Prade +1 more
TL;DR: This paper discusses basic notions underlying fuzzy sets, especially gradualness, uncertainty, vagueness and bipolarity, in order to clarify the significance of using fuzzy sets in practice.
Journal ArticleDOI
Gradual Numbers and Their Application to Fuzzy Interval Analysis
TL;DR: A new way of looking at fuzzy intervals is introduced, which enables interval analysis to be directly extended to fuzzy intervals, without resorting to alpha-cuts, in agreement with Zadeh's extension principle.
Journal ArticleDOI
Gradual elements in a fuzzy set
Didier Dubois,Henri Prade +1 more
TL;DR: A new concept in fuzzy set theory is introduced, that of a gradual element, that embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and imprecision.
Journal ArticleDOI
An enriched category approach to many valued topology
TL;DR: A basic question in fuzzy set theory: what is a many valued topology on a set X?
References
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Book
Topoi: The Categorial Analysis of Logic
TL;DR: In this article, the authors introduce the concept of topoi, a topos structure for algebra of subobjects, and introduce a set theory of set concepts and its logic, namely, set concepts, set theory, set notions, and set concepts.
Journal ArticleDOI
Fuzzy real algebra: Some results
Didier Dubois,Henri Prade +1 more
TL;DR: A three parameters representation for fuzzy numbers is shown to be very convenient to perform usual operations for normalized convex fuzzy subsets of the real line, i.e. fuzzy numbers.
Journal ArticleDOI