Suitable interval-valued intuitionistic fuzzy topological spaces

2021 ◽  
pp. 1-11
Author(s):  
O.R. Sayed ◽  
N.H. Sayed ◽  
Gui-Xiu Chen
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Set Operations ◽  
The Family ◽  
Fuzzy Topological Spaces ◽  
Interval Valued

In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.

scholarly journals Quasicoincidence for intuitionistic fuzzy points

2005 ◽  
Vol 2005 (10) ◽  
pp. 1539-1542 ◽  
Author(s):  
Francisco Gallego Lupiáñez
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Spaces

The introduction of intuitionistic fuzzy sets is due to K. T. Atanassov, who also proposed some problems about this subject. D. Çoker defined the intuitionistic fuzzy topological spaces and, with some coworkers, studied these spaces. In this paper, we define and study the notion of quasicoincidence for intuitionistic fuzzy points and obtain a characterization of continuity for maps between intuitionistic fuzzy topological spaces

Intuitionistic Fuzzy γ-Continuity

2009 ◽  
Vol 52 (4) ◽  
pp. 544-554 ◽  
Author(s):  
I. M. Hanafy
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Spaces

AbstractThis paper introduces the concepts of fuzzy γ-open sets and fuzzy γ-continuity in intuitionistic fuzzy topological spaces. After defining the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy γ-open sets and intuitionistic fuzzy γ-continuity and other results related topological concepts.

Interval-Valued Intuitionistic Fuzzy Subnear Rings

2020 ◽  
pp. 213-224
Author(s):  
Amal Kumar Adak
Keyword(s):  
Fuzzy Sets ◽  
Level Set ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Family ◽  
Interval Valued

The theory of interval-valued intuitionistic fuzzy sets is a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this chapter, the notion of interval-valued intuitionistic fuzzy subnear-ring is introduced, and some interesting properties are discussed. Some relations on the family of all interval-valued intuitionistic fuzzy subnear-ring are presented, and some related properties are investigated. Also, the authors represent upper and lower level set of interval-valued intuitionistic fuzzy set.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

scholarly journals A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

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