Displaying similar documents to “The uncertainty measure of hierarchical quotient space structure.”

Information Measure for Vague Symbols

Milan Mareš (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The structures of the fuzzy information theory are focused on the concept of fuzzy entropy, where the individual information of symbols is considered only implicitely. This paper aims to fill this gap and to study the concepts of fuzzy information. Special attention is paid to the typical fuzzy set theoretical paradigma of monotonicity of operations.

Entropy of T -sums and T -products of L - R fuzzy numbers

Anna Kolesárová, Doretta Vivona (2001)

Kybernetika

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In the paper the entropy of L – R fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of L – R fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of T M –sums and T M –products of L – R fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters...

Fundamentals of a mathematical theory of fuzzy sets

Jindřich Spal (1982)

Aplikace matematiky

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Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.

Entropies of vague information sources

Milan Mareš (2011)

Kybernetika

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The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entropy - the main of them regard the formal aspects of the fundamental concepts. Namely their...

A Method to Construct an Extension of Fuzzy Information Granularity Based on Fuzzy Distance

Thien, Nguyen Van, Demetrovics, Janos, Thi, Vu Duc, Giang, Nguyen Long, Son, Nguyen Nhu (2016)

Serdica Journal of Computing

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In fuzzy granular computing, a fuzzy granular structure is the collection of fuzzy information granules and fuzzy information granularity is used to measure the granulation degree of a fuzzy granular structure. In general, the fuzzy information granularity characterizes discernibility ability among fuzzy information granules in a fuzzy granular structure. In recent years, researchers have proposed some concepts of fuzzy information granularity based on partial order relations. However,...

Interpretability of linguistic variables: a formal account

Ulrich Bodenhofer, Peter Bauer (2005)

Kybernetika

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This contribution is concerned with the interpretability of fuzzy rule-based systems. While this property is widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what “interpretability” actually means is not available. So far, interpretability has most often been associated with rather heuristic assumptions about shape and mutual overlapping of fuzzy membership functions. In this paper, we attempt to approach this problem from a...