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Gradual Numbers and their Application to Fuzzy Interval Analysis
, 2008
"... We introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual num ..."
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Cited by 15 (4 self)
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We introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual numbers basically have the same algebraic properties as real numbers, but they are functions. A fuzzy interval is then viewed as a pair of fuzzy thresholds, which are monotonic gradual real numbers. This view enable interval analysis to be directly extended to fuzzy intervals, without resorting tocuts, in agreement with Zadeh’s extension principle. Several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds. Our approach is illustrated on two known problems: computing fuzzy weighted averages, and determining fuzzy floats and latest starting times in activity network scheduling.
FUZZY ELEMENTS IN A FUZZY SET
"... ABSTRACT: This paper introduces a new concept in fuzzy set theory, that of a fuzzy element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and ideas of imprecision. A fuzzy element is to a fuzzy set what an element is to a set. A fuzzy element is as pr ..."
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Cited by 8 (3 self)
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ABSTRACT: This paper introduces a new concept in fuzzy set theory, that of a fuzzy element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and ideas of imprecision. A fuzzy element is to a fuzzy set what an element is to a set. A fuzzy element is as precise as an element, just more gradual that the latter. Applications of this notion to fuzzy cardinality, fuzzy interval analysis and defuzzification principles are outlined.
BottomUp Extraction and TrustBased Refinement of Ontology Metadata
"... Abstract—We present a way of building ontologies that proceeds in a bottomup fashion, defining concepts as clusters of concrete XML objects. Our rough bottomup ontologies are based on simple relations like association and inheritance, as well as on value restrictions, and can be used to enrich and ..."
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Cited by 7 (4 self)
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Abstract—We present a way of building ontologies that proceeds in a bottomup fashion, defining concepts as clusters of concrete XML objects. Our rough bottomup ontologies are based on simple relations like association and inheritance, as well as on value restrictions, and can be used to enrich and update existing upper ontologies. Then, we show how automatically generated assertions based on our bottomup ontologies can be associated with a flexible degree of trust by nonintrusively collecting user feedback in the form of implicit and explicit votes. Dynamic trustbased views on assertions automatically filter out imprecisions and substantially improve metadata quality in the long run. Index Terms—Semantic Web, bottomup ontology, ad hoc conceptualization, metadata extraction and maintenance, fuzzy clustering techniques, trusted assertions. 1
A Novel Histogram Definition for Fuzzy Color Spaces
"... Abstract — In this paper we introduce fuzzy naturalsbased histograms on fuzzy color spaces. In our approach, histograms are fuzzy probability distributions on a fuzzy color space, where the fuzzy probability is calculated as the quotient between a fuzzy natural number and the number of pixels in th ..."
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Abstract — In this paper we introduce fuzzy naturalsbased histograms on fuzzy color spaces. In our approach, histograms are fuzzy probability distributions on a fuzzy color space, where the fuzzy probability is calculated as the quotient between a fuzzy natural number and the number of pixels in the image, the former being a fuzzy (nonscalar) cardinality of a fuzzy set. This approach to histograms avoids the wellknown disadvantages of the ordinary sigmacount as an estimation of the probability. We illustrate the potential application of the proposal by applying it to the problem of dominant color selection. I.
A generalization of the OWA operator to evaluate non monotonic quantifiers”, in : Joint Conference of the European Society for Fuzzy Logic and Techniques and Rencontres Francophones sur la Logique Floue et ses Applications (EUSFLATLFA’05), p. 183– 188
, 2005
"... This paper is devoted to the evaluation of quantified statements in flexible querying of relational databases. Its contribution is a new approach based on the arithmetic on fuzzy numbers (ℕf, ℤf, ℚf) expressing wellknown but gradual numbers. The advantage of this proposition is that no particular a ..."
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This paper is devoted to the evaluation of quantified statements in flexible querying of relational databases. Its contribution is a new approach based on the arithmetic on fuzzy numbers (ℕf, ℤf, ℚf) expressing wellknown but gradual numbers. The advantage of this proposition is that no particular assumption is made on the monotonicity of the linguistic quantifier. In addition, this approach is a generalization of the OWAbased evaluation.
Lattice properties of discrete fuzzy numbers under extended min and max
"... Abstract — This paper proposes to study the lattice properties of two closed binary operations in the set of discrete fuzzy numbers. Using these operations to represent the meet and the join, we prove that the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers is a d ..."
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Abstract — This paper proposes to study the lattice properties of two closed binary operations in the set of discrete fuzzy numbers. Using these operations to represent the meet and the join, we prove that the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers is a distributive lattice. Finally, we demonstrate that the subsets of discrete fuzzy numbers, which have the same support, are distributive lattices too.
Control and Cybernetics
"... Conditions with aggregates evaluated using gradual numbers ∗ by ..."
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Evolutionary ANNs for improving accuracy and efficiency in Document Classification Methods
"... Abstract. Approaches to document classification belong to two major families: similaritybased (crisp) classification methods and neural networks (gradual) ones. For gradual techniques, a major open issue is controlling search space dimension. While similaritybased methods identify clusters based o ..."
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Abstract. Approaches to document classification belong to two major families: similaritybased (crisp) classification methods and neural networks (gradual) ones. For gradual techniques, a major open issue is controlling search space dimension. While similaritybased methods identify clusters based on the same number of variables used for document encoding, neural networks automatically identify variables that cause distinctions among clusters. Therefore, the variables ’ number may vary depending on the documents structure and content, and is difficult to estimate it a priori. This paper proposes a hybrid classification method suitable for heterogeneous document bases like the ones commonly encountered in business and knowledge management applications. Our method is based on an evolutionary algorithm for tuning both neural network’s structure and weights. While searching the optimal neural network’s configuration it is possible to determine the minimal number of variables to be used in order to classify the given set of documents.
ACCEPTED MANUSCRIPT Database Design and Querying within the Fuzzy Semantic Model
"... This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. ..."
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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.