The set of fuzzy rational numbers and flexible querying

Rocacher, Daniel; Bosc, Patrick

doi:10.1016/j.fss.2005.04.005

Cited by 31 publications

(24 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Given a fuzzy subset ¥ i ) $ to the natural integers, hence its inverse can be (mis)interpreted as a membership function. Rocacher [21] then constructs a relative fuzzy integer as the difference between two fuzzy integers and then construct the set of fuzzy rational numbers just as rationals are constructed from relative integers. Gradual real numbers can then be viewed as limits of fuzzy rational numbers.…”

Section: B Related Workmentioning

confidence: 99%

“…Interestingly, for such gradual numbers, genuine opposite exists and the sum of a gradual number and its opposite is zero. The notion of "gradual element" did not receive lot af attention in fuzzy set theory, even if they can be found in the literature other than purely mathematical (for instance the fuzzy integers of Rocacher [21] are gradual elements on the sets of natural integers).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gradual Numbers and Their Application to Fuzzy Interval Analysis

Fortin

Dubois

Fargier

2008

IEEE Trans. Fuzzy Syst.

172

121

View full text Add to dashboard Cite

Abstract-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 to ¢ -cuts, 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.

show abstract

Section: B Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gradual Numbers and Their Application to Fuzzy Interval Analysis

Fortin

Dubois

Fargier

2008

IEEE Trans. Fuzzy Syst.

172

121

View full text Add to dashboard Cite

show abstract

“…Several authors [4], [15], [16] have pointed out that the possible cardinalities of a fuzzy set are the cardinalities of its α-cuts, since these are the possible crisp representatives of the fuzzy set. In our previous example the possible cardinalities of A are 1 or 3 since its possible α-cuts are {x 1 } and {x 1 , x 2 , x 3 }.…”

Section: A Fuzzy Cardinalitymentioning

confidence: 99%

A novel histogram definition for fuzzy color spaces

Chamorro-Martı́nez

Sánchez

Soto-Hidalgo

2008

2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence)

View full text Add to dashboard Cite

Abstract-In this paper we introduce fuzzy naturals-based 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 (non-scalar) cardinality of a fuzzy set. This approach to histograms avoids the well-known disadvantages of the ordinary sigma-count as an estimation of the probability. We illustrate the potential application of the proposal by applying it to the problem of dominant color selection.

show abstract

“…The same principle can be applied to fuzzy integers: By dividing a fuzzy integer by another [57], we obtain a quotient that is again a fuzzy quantity. By the extension principle, the result of a division among fuzzy integers is a rational fuzzy number.…”

Section: Cardinality Restrictionsmentioning

confidence: 99%

Bottom-Up Extraction and Trust-Based Refinement of Ontology Metadata

Ceravolo

Damiani

Viviani

2007

IEEE Trans. Knowl. Data Eng.

View full text Add to dashboard Cite

Abstract-We present a way of building ontologies that proceeds in a bottom-up fashion, defining concepts as clusters of concrete XML objects. Our rough bottom-up 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 bottom-up ontologies can be associated with a flexible degree of trust by nonintrusively collecting user feedback in the form of implicit and explicit votes. Dynamic trust-based views on assertions automatically filter out imprecisions and substantially improve metadata quality in the long run.

show abstract

The set of fuzzy rational numbers and flexible querying

Cited by 31 publications

References 17 publications

Gradual Numbers and Their Application to Fuzzy Interval Analysis

Gradual Numbers and Their Application to Fuzzy Interval Analysis

A novel histogram definition for fuzzy color spaces

Bottom-Up Extraction and Trust-Based Refinement of Ontology Metadata

Contact Info

Product

Resources

About