Displaying similar documents to “Multiplication, distributivity and fuzzy-integral. III”

Multiplication, distributivity and fuzzy-integral. II

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

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Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms...

The distribution of mathematical expectations of a randomized fuzzy variable.

V. B. Kuz'min, S. I. Travkin (1998)

Mathware and Soft Computing

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The Shaffer's definition of the upper and lower expectations of fuzzy variables is considered with respect to randomized fuzzy sets. The notion of randomized fuzzy sets is introduced in order to evaluate fuzzy statistical indices for an arbitrary chosen fuzzy variable. Provided the distribution of the mathematical expectation of a randomized fuzzy variable is known, it is possible to adopt the traditional methods of testing statistical hypotheses for fuzzy variables. We show...

General theory of the fuzzy integral.

Pietro Benvenuti, Doretta Vivona (1996)

Mathware and Soft Computing

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By means of two general operations + and x, called pan-operations'', we build a new kind of integral. This formulation contains, as particular cases, both Choquet's and Sugeno's integrals.

Numerical experimentation and comparison of fuzzy 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.

The fuzzy hyperbolic inequality index of fuzzy random variables in finite populations.

Norberto Corral, María Angeles Gil, Hortensia López-García (1996)

Mathware and Soft Computing

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This paper presents an approach to the problem of quantifying the inequality of a finite population with respect to a (social, economical, etc.) fuzzy-valued attribute. For this purpose, the fuzzy hyperbolic inequality index is introduced, and some properties extending the basic ones for real-valued attributes are examined.