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

Anna Kolesárová; Doretta Vivona

Kybernetika (2001)

  • Volume: 37, Issue: 2, page [127]-145
  • ISSN: 0023-5954

Abstract

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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 without the computation of membership functions of corresponding sums or products. Moreover, the results for some other t -norm–based sums and products are derived. Several examples are included.

How to cite

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Kolesárová, Anna, and Vivona, Doretta. "Entropy of $T$-sums and $T$-products of $L$-$R$ fuzzy numbers." Kybernetika 37.2 (2001): [127]-145. <http://eudml.org/doc/33522>.

@article{Kolesárová2001,
abstract = {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 without the computation of membership functions of corresponding sums or products. Moreover, the results for some other $t$-norm–based sums and products are derived. Several examples are included.},
author = {Kolesárová, Anna, Vivona, Doretta},
journal = {Kybernetika},
keywords = {entropy; $L$-$R$ fuzzy numbers; entropy; - fuzzy numbers},
language = {eng},
number = {2},
pages = {[127]-145},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Entropy of $T$-sums and $T$-products of $L$-$R$ fuzzy numbers},
url = {http://eudml.org/doc/33522},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Kolesárová, Anna
AU - Vivona, Doretta
TI - Entropy of $T$-sums and $T$-products of $L$-$R$ fuzzy numbers
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 2
SP - [127]
EP - 145
AB - 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 without the computation of membership functions of corresponding sums or products. Moreover, the results for some other $t$-norm–based sums and products are derived. Several examples are included.
LA - eng
KW - entropy; $L$-$R$ fuzzy numbers; entropy; - fuzzy numbers
UR - http://eudml.org/doc/33522
ER -

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