SOHEYB Milles

Atmani djelloul

Espaces topologiques flous

BAHACHE Habiba

Idéaux flous dans un anneau

Moussai Nadjat

Etude sur les ensembles ordonnés flous

Samiha MERZOUG , Warda SAOUDI

Théorèmes de points fixes dans des structures ordonnées

In this paper, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of intuitionistic fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal intuitionistic fuzzy ideal (resp. filter) coincides with an intuitionistic fuzzy down-set (resp. up-set) generated by an intuitionistic fuzzy singleton. Afterwards, for a given intuitionistic fuzzy set, we introduce two intuitionistic fuzzy sets: its intuitionistic fuzzy down-set and up-set, and we investigate their interesting properties.

Citation

Soheyb MILLES , , (2020), PRINCIPAL INTUITIONISTIC FUZZY IDEALS AND FILTERS ON A LATTICE, Discussiones Mathematicae, Vol:40, Issue:1, pages:17, Faculty of Mathematics Computer Science and Econometrics University of Zielona Góra

Tarski and Davis [5, 6] were the first who have studied the fixed point property for certain classes of ordered sets. In applications as point of view, partially ordered sets evolved the fixed point theory to generalize and solve many results and problems in linear and non-linear analysis. In this paper, we characterize the fixed point property for certain classes of intuitionistic fuzzy ordered sets previously introduced by Bustince and Burillo [3, 4]. The class of intuitionistic fuzzy lattice recently proposed by Tripathy et al. [7] and the class of intuitionistic fuzzy chain-complete poset, which we will introduce later in this paper.

Citation

Soheyb MILLES , ,(2019), Tarski-Davis's fixed point theorem for certain classes of intuitionistic fuzzy ordered sets,Journée de Mathématiques Appliquées JMA2019.,Mila University

In this presentation, we characterize the fixed point property for certain classes of intuitionistic fuzzy ordered sets previously introduced by Bustince and Burillo. The class of intuitionistic fuzzy lattice recently proposed by Tripathy et al. and the class of intuitionistic fuzzy chain-complete poset, which we will introduce later in this paper.

Citation

Soheyb MILLES , ,(2019), Fixed point theorems on intuitionistic fuzzy ordered sets.,International Conference on Advances in Applied Mathematics ICAAM.,Tunis

In this paper, based on the concept of intuitionistic fuzzy lattice previously introduced by Tripathy and his colleagues, a class of intuitionistic fuzzy complete lattices is proposed with some interesting characterizations given. In particular, we show the fixed point property for this proposed class. Conversely, we show that any intuitionistic fuzzy lattice is complete having its fixed point property. These results establish a criterion for completeness of intuitionistic fuzzy lattices in terms of the fixed points of their intuitionistic fuzzy monotone mappings. Keywords: Atanassov's intuitionistic fuzzy set, Intuitionistic fuzzy relation, Intuitionistic fuzzy lattice, Fixed point property

Citation

Lemnaouar ZEDAM , Soheyb MILLES , Ewa Rak, , (2017), The fixed point property for intuitionistic fuzzy lattices, Fuzzy Information and Engineering, Vol:9, Issue:3, pages:359-380, Taylor and Francis