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.
Susana Montes, J. Jiménez, Pedro Gil (1998)
Mathware and Soft Computing
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The aim of this paper is to study a special type of fuzzy relations, the α-equivalences, as well as to consider the relation that connects these with the family of ε-partitions of the referential. Some classic equivalences between set, partitions and fuzzy relations are also studied.
Sridevi, B., Nadarajan, R. (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Ľubica Valášková, Peter Struk (2005)
Kybernetika
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Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.
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.
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...
Vicenç Torra (1995)
Mathware and Soft Computing
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In this work we study the synthesis of membership functions when they have been calculated from a set of observations according to the definition of (Zhang, 1993). The results obtained have been used to determine the radius of influence of a tramp for Podarcis lilfordi (a kind of saurians) in the island of Cabrera (Balearic Islands). The measure of this radius was used in a later work to estimate the density of these saurians in the island.
Domenico Candeloro, Sabrina Pucci (1987)
Stochastica
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In the last twenty years many papers have appeared dealing with fuzzy theory. In particular, fuzzy integration theory had its origin in the well-known Thesis of Sugeno [7]. More recently, some authors faced this topic by means of some binary operations (see for instance [3], [8] and references): a fuzzy measure must be additive with respect to one of them, an the integral is to define in a way, which is very similar to the construction of the Lebesgue integral. On the contrary, we are...