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Fuzzy Measures and Measures of Fuzziness
1985In order to prevent confusion about fuzzy measures and measures of fuzziness, we shall first briefly describe the meaning and features of fuzzy measures. In the early 1970s, Sugeno defined a fuzzy measure as follows [Sugeno 1977]: 𝓑 is a Borel field of the arbitrary set (universe) X.
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Intuitionistic fuzzy-valued fuzzy measures
2004 2nd International IEEE Conference on 'Intelligent Systems'. Proceedings (IEEE Cat. No.04EX791), 2004The concept of intuitionistic fuzzy-valued fuzzy measure, that is L -valued fuzzy measures, where L = {(/spl xi//sub /spl infin//, /spl xi//sub /spl epsi//) /spl isin/ [l, /spl infin/] /spl times/ [l, /spl infin/]; /spl xi//sub /spl infin// + /spl xi//sub /spl epsi// /spl les/ /spl infin/}, is introduced.
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Fuzziness measures for fuzzy rectangles
Fuzzy Sets and Systems, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fuzzy measures and coherent join measures
International Journal of Intelligent Systems, 2011In assigning weights and scores in a decision problem usually we assume that they are finitely additive normalized measures, i.e., from the formal point of view, finitely additive probabilities. The normalization requirement sometimes appears as an actual restriction.
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Fuzzy σ-algebras and fuzzy measurable functions
Fuzzy Sets and Systems, 1980Abstract In this paper we first give an axiomatic definition of a fuzzy σ-algebra which is a generalisation of the family of fuzzy events considered by L.A. Zadeh [13]. The relationship between classical and fuzzy σ-algebras and between topologies and σ-algebras, in both cases, classical and fuzzy, is established in the notation of commutative ...
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Measurement, 2008
Abstract Exact measurement is a mapping f0 from the structure of physical objects into the structure of real numbers R representing the results of measurement. In the framework of the fuzzy theory of measurement an inexact measurement is represented by a mapping f from a physical objects into a structure of fuzzy intervals.
Michał K. Urbański, Janusz Wa¸sowski
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Abstract Exact measurement is a mapping f0 from the structure of physical objects into the structure of real numbers R representing the results of measurement. In the framework of the fuzzy theory of measurement an inexact measurement is represented by a mapping f from a physical objects into a structure of fuzzy intervals.
Michał K. Urbański, Janusz Wa¸sowski
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Fuzzy measurement of income inequality: a class of fuzzy inequality measures
Social Choice and Welfare, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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IEEE Transactions on Fuzzy Systems, 1994
First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes.
N.R. Pal, J.C. Bezdek
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First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes.
N.R. Pal, J.C. Bezdek
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Fuzzy Sets and Systems, 1981
Abstract In [4] Hohle has defined fuzzy measures on G-fuzzy sets [2] where G stands for a regular Boolean algebra. Consequently, since the unit interval is not complemented, fuzzy sets in the sense of Zadeh [8] do not fit in this framework in a straightforward manner.
Klement, Erich Peter +2 more
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Abstract In [4] Hohle has defined fuzzy measures on G-fuzzy sets [2] where G stands for a regular Boolean algebra. Consequently, since the unit interval is not complemented, fuzzy sets in the sense of Zadeh [8] do not fit in this framework in a straightforward manner.
Klement, Erich Peter +2 more
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International Journal of Intelligent Systems, 2005
Summary: Coherence measures are a tool to compare those fuzzy sets that are sensitive to their own similarity as well as to their fuzzy nature. In this article we find three generalizations of the definition of coherence measures: a first one for any fuzzy set, a second one for any definition of strong negation, and a final one for an extension in ...
Sancho-Royo, A., Verdegay, J. L.
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Summary: Coherence measures are a tool to compare those fuzzy sets that are sensitive to their own similarity as well as to their fuzzy nature. In this article we find three generalizations of the definition of coherence measures: a first one for any fuzzy set, a second one for any definition of strong negation, and a final one for an extension in ...
Sancho-Royo, A., Verdegay, J. L.
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