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Doretta Vivona (1996)
Mathware and Soft Computing
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After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.
Manuel Jorge Bolaños, Luis Daniel Hernández, Antonio Salmerón (1996)
Mathware and Soft Computing
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Sugeno and Choquet integrals have been widely studied in the literature from a theoretical viewpoint. However, the behavior of these functionals is known in a general way, but not in practical applications and in particular cases. This paper presents the results of a numerical comparison that attempts to be a basis for a better comprehension and usefulness of both integrals.
Sridevi, B., Nadarajan, R. (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Aldo Ventre, Siegfried Weber (1987)
Stochastica
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Total orderings in the range of fuzzy sets can serve as choice criteria for fuzzy sets, a wide class of orderings based on functions is proposed (section 2). Decomposable measures are taken to measure the items on which the fuzzy sets are given (section 3). Combining the two levels of measurement by means of the integral introduced by the second author we obtain evaluations of fuzzy sets as functionals with appropriate properties, the concepts of energy and fuzziness are included (section...
Guha, Debashree, Chakraborty, Debjani (2010)
International Journal of Mathematics and Mathematical Sciences
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Doretta Vivona, Maria Divari (2002)
Kybernetika
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In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.
Enric Trillas, Claudi Alsina (1999)
Mathware and Soft Computing
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This paper is just a first approach to the idea that the membership function μ of a fuzzy set labelled P is, basically, a measure on the set of linguistic expressions x is P for each x in the corresponding universe of discourse X. Estimating that the meaning of P (relatively to X) is nothing else than the use of P on X, these measures seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary...