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Start Over Subject fuzzy entropy

2. Entropies of vague information sources

Creator:
Mareš, Milan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
information source, message, uncertainty, fuzzy set, fuzzy entropy, and fuzzy information
Language:
English
Description:
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 rather additive (i. e., probability-like) than monotonous (typical for fuzzy set theoretical models) structure. The main goal of this paper is to describe briefly the existing state of art, and to suggest and analyze alternative, more fuzzy set theoretical, approaches to the fuzzy entropy developed as a significant characteristic of the information sources, in the information-theoretical sense.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Exponential entropy on intuitionistic fuzzy sets

Creator:
Verma, Rajkumar and Sharma, Bhu Dev
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fuzzy seat, fuzzy entropy, Atanassov´s intuitionistic fuzzy set, intuitionistic fuzzy entropy, and exponential entropy
Language:
English
Description:
In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that the proposed entropy measure for Atanassov's intuitionistic fuzzy set is consistent by comparing it with other existing entropies.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Fuzzy entropy from weak fuzzy subsethood measures

Creator:
Galar, M., Bustince, H., Fernandez, J., Sanz, J., and Beliakov, G.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Implication operator, fuzzy subsethood measures, weak fuzzy subsethood measures, and fuzzy entropy
Language:
English
Description:
In this paper, we propose a new construction method for fuzzy and weak fuzzy subsethood measures based on the aggregation of implication operators. We study the desired properties of the implication operators in order to construct these measures. We also show the relationship between fuzzy entropy and weak fuzzy subsethood measures constructed by our method.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. On continuity of the entropy-based differently implicational algorithm

Creator:
Tang , Yiming and Pedrycz, Witold
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
continuity, fuzzy entropy, fuzzy inference, and compositional rule of inference
Language:
English
Description:
Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm. Finally, in the entropy-based differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

6. Symmetric implicational restriction method of fuzzy inference

Creator:
Tang, Yiming, Wu, Wenbin, Zhang, Youcheng, Pedrycz, Witold, Ren, Fuji, and Liu, Jun
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
continuity, fuzzy entropy, fuzzy inference, and compositional rule of inference
Language:
English
Description:
The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public