1. On the representation of L-M algebra by intuitionistic fuzzy subsets
- Author
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Amroune Abdelaziz, Zedam Lemnaouar, Laboratory of Pure and Applied Mathematics (LPAM), and Université Mohamed Boudiaf de M'sila
- Subjects
0209 industrial biotechnology ,Mathematics::General Mathematics ,Structure (category theory) ,Intuitionistic fuzzy ,02 engineering and technology ,[MATH] Mathematics [math] ,[INFO] Computer Science [cs] ,Representation theorems ,Set (abstract data type) ,020901 industrial engineering & automation ,Algèbres de Moisil-Lukasiewicz ,Computer Science::Logic in Computer Science ,Lukasiewicz-Mosil algebras ,0202 electrical engineering, electronic engineering, information engineering ,[INFO]Computer Science [cs] ,Algebra over a field ,[MATH]Mathematics [math] ,Representation (mathematics) ,théorème de représentation ,Mathematics ,Intuitionistic fuzzy subsets ,General Medicine ,Algebra ,Mathematics::Logic ,sous-ensemble flous intuitionistes ,020201 artificial intelligence & image processing ,Universe (mathematics) - Abstract
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.
- Published
- 2006