Representation of Łukasiewicz' many-valued algebras

“…In [17] Ponasse has also studied the representability of involutive many-valued Lukasiewicz-Moisil algebra as an algebra of fuzzy subsets equipped with an order-reversing involution. This problem was also investigated in [1,9,10,18]. In another direction, Atanassov [2,5] introduced another fuzzy object, called intuitionistic fuzzy subset (briefly IFS) as a generalization of the concept of fuzzy subset.…”

Section: Introductionmentioning

confidence: 99%

Many Valued Logic and Intuitionistic Fuzzy Sets: A Stone Theorem Generalization

Amroune¹,

Davvaz²

2015

Honam Mathematical Journal

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“…In [17] Ponasse has also studied the representability of involutive θ-valued Lukasiewicz-Moisil algebra as an algebra of fuzzy subsets equipped with an order-reversing involution. This problem was also investigated in [1,9,10,18].…”

Section: Introductionmentioning

confidence: 99%

On the representation of L-M algebra by intuitionistic fuzzy subsets

Zedam

Amroune

2006

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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International audience In this paper we introduce the notions of intuitionistic weak alpha-cut and untuitionistic strong alpha-cut of intuitionistic fuzzy subsets of a universe X. These notions lead us to show that the set IF(X) of all intuitionistic fuzzy subsets on a universe X can be equipped with a structure of involutive theta-valued Lukasiewicz-Moisil algebra. Conversely, we show that every involutive theta-valued Lukasiewicz-Moisil algebra can be embedded into an algebra of intuitionistic fuzzy subsets. Dans ce travail nous introduisons les notions de alpha-coupes et de alpha-coupes strictes d'un ensemble flou intuitionsiste d'un référentiel X. A l'aide de ces notions, nous montrons que l'ensemble IF(X) des sous-ensembles flous intuitionistes d'un référentiel X admet une structure d'algèbre de Moisil-Lukasiewicz. theta-valente involutive. Réciproquement, nous montrons que toute algèbre de Moisil-Lukasiewicz theta-valente involutive se plonge dans une algèbre des sous-ensembles flous intuitionistes.

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Representation of Łukasiewicz' many-valued algebras

Cited by 6 publications

References 12 publications

Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras

Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras

Many Valued Logic and Intuitionistic Fuzzy Sets: A Stone Theorem Generalization

On the representation of L-M algebra by intuitionistic fuzzy subsets

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