Intuitionistic Fuzzy Topological Research Articles

On neutrosophic paraconsistent topology

PurposeRecently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets (NSs). Also, this author introduced a general definition of neutrosophic topology. On the other hand, there exist various kinds of paraconsistent logics, where some contradiction is admissible. The purpose of this paper is to show that a Smarandache's definition of neutrosophic paraconsistent topology is not a generalization of Çoker's intuitionistic fuzzy topology (IFT) or Smarandache's general neutrosophic topology.Design/methodology/approachThe possible relations between the IFT and the neutrosophic paraconsistent topology are studied.FindingsRelations on IFT and neutrosophic paraconsistent topology are shown.Research limitations/implicationsClearly, the paper is confined to IFSs and NSs.Practical implicationsThe main applications are in the mathematical field.Originality/valueThe paper shows original results on fuzzy sets and topology.

On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations

Topologies and rough set theory are widely used in the research field of machine learning and cybernetics. An intuitionistic fuzzy rough set, which is the result of approximation of an intuitionistic fuzzy set with respect to an intuitionistic fuzzy approximation space, is an extension of fuzzy rough sets. For further studying the theories and applications of intuitionistic fuzzy rough sets, in this paper, we investigate the topological structures of intuitionistic fuzzy rough sets. We show that an intuitionistic fuzzy rough approximation space can induce an intuitionistic fuzzy topological space in the sense of Lowen if and only if the intuitionistic fuzzy relation in the approximation space is reflexive and transitive. We also examine the sufficient and necessary conditions that an intuitionistic fuzzy topological space can be associated with an intuitionistic fuzzy reflexive and transitive relation such that the induced lower and upper intuitionistic fuzzy rough approximation operators are, respectively, the intuitionistic fuzzy interior and closure operators of the given topology.

On intuitionistic fuzzy rough sets and their topological structures

In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.

On various neutrosophic topologies

PurposeRecently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs) and also defined various notions of neutrosophic topologies on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and neutrosophic topologies on the non‐standard interval. The purpose of this paper is to show that this is false.Design/methodology/approachThe possible relations between the intuitionistic fuzzzy topology and neutrosophic topologies are studied.FindingsRelations on IFT and neutrosophic topologies.Research limitations/implicationsClearly, the paper is confined to IFSs and NSs.Practical implicationsThe main applications are in the mathematical field.Originality/valueThe paper shows original results on fuzzy sets and topology.

IF-topologies and IF-automata

The purpose of this work is to indicate that a study of IF-automata (also called, intuitionistic fuzzy automata) can be carried out much on the same lines as the one done for fuzzy automata in Srivastava and Tiwari (Proceedings of 2002 AFSS international conference on fuzzy systems. Lecture notes in artificial intelligence, vol 2275. Springer, Berlin, pp 485–490, 2002). It is also shown that two IF-topologies (also called, intuitionistic fuzzy topologies) can be associated with the state-sets of IF-fuzzy automata whose level topologies have interesting relationships with the topologies introduced by Srivastava and Tiwari (above mentioned) for fuzzy automata.

Results on Fuzzy Weakly (r, s)-Continuous Mappings on the Intuitionistic Fuzzy Topological Spaces in Šostak's Sense

In this paper, we investigate some characterizations for fuzzy weakly (r, s)-continuous mapping on an intuitionistic fuzzy topological space in ?ostak's sense.

On neutrosophic topology

PurposeRecently, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false.Design/methodology/approachThe possible relation between the IFT and the neutrosophic topology is studied.FindingsRelations on neutrosophic topology and IFT are found.Research limitations/implicationsClearly, this paper is confined to IFSs and NSs.Practical implicationsThe main applications are in the mathematical field.Originality/valueThe paper shows original results on fuzzy sets and topology.

On intuitionistic fuzzy topological spaces

PurposeIn 2000, Wang and He published an important result on the theory of intuitionistic fuzzy sets (IFSs). Indeed, they showed that every IFS may be regarded as an L‐fuzzy set for some appropriate lattice L. This paper aims to show that, nevertheless, the results obtained by various authors on intuitionistic fuzzy topological spaces (IFTSs), are not redundant with others for the ordinary fuzzy sense.Design/methodology/approachThe most important definitions and results on intuitionistic fuzzy topology (IFT) one compared with the result obtained by Wang and He.FindingsThat these results are not redundant.Research limitations/implicationsClearly, this paper is devoted to IFTSs.Practical implicationsThe main applications are in the mathematical field.Originality/valueThe originality and value of IFT are here demonstrated.

INTUITIONISTIC FUZZY RETRACTS

The concept of a intuitionistic fuzzy topology (IFT) was introduced by Coker 1997. The concept of a fuzzy retract was introduced by Rodabaugh in 1981. The aim of this paper is to introduce a new concepts of fuzzy continuity and fuzzy retracts in an intuitionistic fuzzy topological spaces and establish some of their properties. Also, the relations between these new concepts are discussed.

Intuitionistic fuzzy proximity spaces

We introduce the concept of the intuitionistic fuzzy proximity as a generalization of fuzzy proximity, and investigate its properties. Also we investigate the relationship among intuitionistic fuzzy proximity and fuzzy proximity, and intuitionistic fuzzy topology.

Completely Continuous Functions in Intuitionistic Fuzzy Topological Spaces

In this paper, after giving the basic results related to the product of functions and the graph of functions in intuitionistic fuzzy topological spaces, we introduce and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.

A Tychonoff theorem in intuitionistic fuzzy topological spaces

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.