On fuzzinesstic measures of entropy on Kleene algebras

I. Z. Batyrshin

doi:10.1016/0165-0114(90)90126-Q

On fuzzinesstic measures of entropy on Kleene algebras

I. Z. Batyrshin

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12 Citas (Scopus)

Resumen

The concept of measure of fuzziness is generalized to the arbitrary Kleene algebras. It is shown that these measures characterize Kleene algebras in the class of De Morgan algebras. The algebra of fuzzy sets of Zadeh belongs to the class of Kleene algebras with central element. In these algebras one-to-one correspondence between the measures of entropy and metrics is established.

Idioma original	Inglés
Páginas (desde-hasta)	47-60
Número de páginas	14
Publicación	Fuzzy Sets and Systems
Volumen	34
N.º	1
DOI	https://doi.org/10.1016/0165-0114(90)90126-Q
Estado	Publicada - 10 ene. 1990
Publicado de forma externa	Sí

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10.1016/0165-0114(90)90126-Q

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title = "On fuzzinesstic measures of entropy on Kleene algebras",

abstract = "The concept of measure of fuzziness is generalized to the arbitrary Kleene algebras. It is shown that these measures characterize Kleene algebras in the class of De Morgan algebras. The algebra of fuzzy sets of Zadeh belongs to the class of Kleene algebras with central element. In these algebras one-to-one correspondence between the measures of entropy and metrics is established.",

keywords = "De Morgan algebra, Kleene algebra, distributive lattice, measure of entropy, measure of fuzziness, metric, valuation",

author = "Batyrshin, {I. Z.}",

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doi = "10.1016/0165-0114(90)90126-Q",

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AU - Batyrshin, I. Z.

PY - 1990/1/10

Y1 - 1990/1/10

N2 - The concept of measure of fuzziness is generalized to the arbitrary Kleene algebras. It is shown that these measures characterize Kleene algebras in the class of De Morgan algebras. The algebra of fuzzy sets of Zadeh belongs to the class of Kleene algebras with central element. In these algebras one-to-one correspondence between the measures of entropy and metrics is established.

AB - The concept of measure of fuzziness is generalized to the arbitrary Kleene algebras. It is shown that these measures characterize Kleene algebras in the class of De Morgan algebras. The algebra of fuzzy sets of Zadeh belongs to the class of Kleene algebras with central element. In these algebras one-to-one correspondence between the measures of entropy and metrics is established.

KW - De Morgan algebra

KW - Kleene algebra

KW - distributive lattice

KW - measure of entropy

KW - measure of fuzziness

KW - metric

KW - valuation

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U2 - 10.1016/0165-0114(90)90126-Q

DO - 10.1016/0165-0114(90)90126-Q

M3 - Artículo

SN - 0165-0114

VL - 34

SP - 47

EP - 60

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 1

ER -

On fuzzinesstic measures of entropy on Kleene algebras

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