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Measurement-theoretic justification of connectives in fuzzy set theory
Fuzzy Sets and Systems, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Taner Bilgiç, I. Burhan Türksen
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Measure theory on granular fuzzy sets
18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397), 2003A granular fuzzy set theory is modeled on fuzzy sets whose membership functions are defined on sets of sets (granules). The grade is interpreted literally; for example, that the grade of x is 1/2 means one half of the granule x belongs to the fuzzy set. By taking the union of these subgranules, one get a crisp set representation of a fuzzy set.
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Measure Theory, Metrology and Fuzzy Sets
Śląski Przegląd StatystycznyMathematical models of physical objects customarily rely on idealised Euclidean geometries, representing boundaries as crisp, continuous lines or surfaces. However, physical reality – ranging from the surface of a rubber ball to biological membranes – is characterised by microscopic roughness, textural undulations, and measurement ambiguity. This paper
Reinhard Viertl, Jan Schneider
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A measure of the satisfaction by Fuzzy set theory
2013In this paper the fuzzy set theory is applied to define a measure of subject satisfaction relating to every social aspect (quality of life, job, a service, etc.). This theory is based on the construction of a membership function to a fuzzy set.
De Battista, F +2 more
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A THEORY OF FUZZY MEASURES: INTEGRATION AND ITS ADDITIVITY
International Journal of General Systems, 1994Fuzzy measures and their corresponding Choquet integrals introduced by Murofushi and Sugeno [1989, 1991] are included in the theory of pre-measures and the corresponding integral developed by Sipos [1979a, 1979b]. The additivity of Sipos integral is studied. As a corollary, the additivity of the Choquet integral is obtained.
RADKO MESIAR, JÁN ŠIPOŠ
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A new method for measuring uncertainty and fuzziness in rough set theory
International Journal of General Systems, 2002Based on the complement behavior of information gain, a new definition of information entropy is proposed along with its justification in rough set theory. Some properties of this definition imply those of Shannon's entropy. Based on the new information entropy, conditional entropy and mutual information are then introduced and applied to knowledge ...
Jiye Liang +3 more
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Characterizing isometries on the order polytope with an application to the theory of fuzzy measures
Information Sciences, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elías F. Combarro, Pedro Miranda 0002
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Hasse Diagrams, Poset Theory and Fuzzy Poverty Measures
Rivista internazionale di scienze sociali : 1, 2008, 2008It is generally agreed that poverty cannot be faithfully represented by a single monetary measure. Poverty involves many different aspects of life and people can be poor in different ways, to different degrees and from several points of view. For this reason, fuzzy multidimensional indicators have been proposed to measure material deprivation. However,
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FOUNDATIONS OF O-THEORY: MEASUREMENTS AND RELATION TO FUZZY SET THEORY
International Journal of General Systems, 1988Abstract A measurement framework for O-theory, an algebra of random sets, is presented. The framework is probabilistic and derived from experimental measurements of evidential support. It is used to quantify the probabilistic masses needed in O-theory.
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Toward a Fuzzy Theory of Performance Measurement
1992Abstract : This report offers an alternative method for evaluating military unit performance. Fuzzy set theory is presented as a formal model of language expressions used in value judgments made by military experts. Further, it is suggested that fuzzy set theory may be used to connect the automated or instrumented physical measures taken from unit ...
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