Entropy of fuzzy events

Criado, Francisco; Gachechiladze, T.

doi:10.1016/s0165-0114(96)00073-5

Cited by 15 publications

(5 citation statements)

References 8 publications

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“…The splitting of a set, which corresponds to the indicator splitting, as seen, is represented as (13) Here, is the operation of set synthesis.…”

Section: The Splitting Of a Setmentioning

confidence: 99%

“…One can also obtain the existence conditions for expressions , etc. Considering that such a condition holds for the aforementioned expressions, one can easily prove that (14) For example, to prove the last two formulas, one can write Let it be assumed that in these formulas the following relations hold: (15) which are evident because of (4), (6), and (13).…”

Section: The Splitting Of a Setmentioning

confidence: 99%

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Fuzzy models of language structures

Torralba

Gachechiladze

Meladze

et al. 2002

IEEE Trans. Fuzzy Syst.

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Statistical distribution of language structures reflect important regularities controlling informational and psycho-physiological processes, which accompany the generation of verbal language or printed texts. In this paper, fuzzy quantitative models of language statistics are constructed. The suggested models are based on the assumption about a super-position of two kinds of uncertainties: probabilistic and possibilistic. The realization of this super-position in statistical distributions is achieved by the splitting procedure of the probability measure. In this way, the fuzzy versions of generalized binomial, Fucks', and Zipf-Mandelbrot's distributions are constructed describing the probabilistic and possibilistic organization of language at any level: morphological, syntactic, or phonological.

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“…The splitting of a set, which corresponds to the indicator splitting, as seen, is represented as (13) Here, is the operation of set synthesis.…”

Section: The Splitting Of a Setmentioning

confidence: 99%

Section: The Splitting Of a Setmentioning

confidence: 99%

Fuzzy models of language structures

Torralba

Gachechiladze

Meladze

et al. 2002

IEEE Trans. Fuzzy Syst.

Self Cite

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“…Zadeh [ 12 ] further defined the entropy as a weighted Shannon entropy to quantify the fuzziness of an event. Moreover, Criadoa and Gachechiladzeb [ 13 ] considered the uncertainty of possibility to describe Zadeh’s general formula for the entropy. Meanwhile, there exist many applications of entropy under the possibility theory.…”

Section: Introductionmentioning

confidence: 99%

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Shen¹,

Zhou²

2019

Entropy

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Entropy has continuously arisen as one of the pivotal issues in optimization, mainly in portfolios, as an indicator of risk measurement. Aiming to simplify operations and extending applications of entropy in the field of LR fuzzy interval theory, this paper first proposes calculation formulas for the entropy of function via the inverse credibility distribution to directly calculate the entropy of linear function or simple nonlinear function of LR fuzzy intervals. Subsequently, to deal with the entropy of complicated nonlinear function, two novel simulation algorithms are separately designed by combining the uniform discretization process and the numerical integration process with the proposed calculation formulas. Compared to the existing simulation algorithms, the numerical results show that the advantage of the algorithms is well displayed in terms of stability, accuracy, and speed. On the whole, the simplified calculation formulas and the effective simulation algorithms proposed in this paper provide a powerful tool for the LR fuzzy interval theory, especially in entropy optimization.

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“…Since the seminal publication [18], fuzzy set theory has advanced in various mathematical disciplines and it has also found many significant practical applications-for example, in control theory, data analysis, artificial intelligence, and computational intelligence. Of course, many publications (see e.g., [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]) are devoted to the study of entropy in the fuzzy case. In our work [9], we introduced the concept of logical entropy of fuzzy dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Tsallis Entropy of Fuzzy Dynamical Systems

Markechová

2018

Mathematics

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This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order where is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov–Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by Markechová and Riečan in Entropy, 2016, 18, 157, which are particularized to the case of logical entropy.

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Entropy of fuzzy events

Cited by 15 publications

References 8 publications

Fuzzy models of language structures

Fuzzy models of language structures

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Tsallis Entropy of Fuzzy Dynamical Systems

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