A study on compactness in intuitionistic fuzzy topological spaces

The purpose of this paper is to introduce and study the compactness in intuitionistic fuzzy topological spaces. Here we define two new notions of intuitionistic fuzzy compactness in intuitionistic fuzzy topological space and find their relation. Also we find the relationship between intuitionistic general compactness and intuitionistic fuzzy compactness. Here we see that our notions satisfy hereditary and productive property.

(3, 2)-Fuzzy Sets and Their Applications to Topology and Optimal Choices

The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

Unsupervised Change Detection Using Fuzzy Topology-Based Majority Voting

Remote sensing change detection (CD) plays an important role in Earth observation. In this paper, we propose a novel fusion approach for unsupervised CD of multispectral remote sensing images, by introducing majority voting (MV) into fuzzy topological space (FTMV). The proposed FTMV approach consists of three principal stages: (1) the CD results of different difference images produced by the fuzzy C-means algorithm are combined using a modified MV, and an initial fusion CD map is obtained; (2) by using fuzzy topology theory, the initial fusion CD map is automatically partitioned into two parts: a weakly conflicting part and strongly conflicting part; (3) the weakly conflicting pixels that possess little or no conflict are assigned to the current class, while the pixel patterns with strong conflicts often misclassified are relabeled using the supported connectivity of fuzzy topology. FTMV can integrate the merits of different CD results and largely solve the conflicting problem during fusion. Experimental results on three real remote sensing images confirm the effectiveness and efficiency of the proposed method.

More on Fuzzy Topological Spaces on Fuzzy Space

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip’s approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip’s article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces

On Fuzzy L-paracompact Topological Spaces

The aim of this paper is to study fuzzy extensions of some covering properties defined by L. Kalantan as a modification of some kinds of paracompactness-type properties due to A.V.Arhangels'skii and studied later by other authors. In fact, we obtain that: if (X,T) is a topological space and A is a subset of X, then A is Lindelöf in (X,T) if and only if its characteristic map χ_{A} is a Lindelöf subset in (X,ω(T)). If (X,τ) is a fuzzy topological space, then, (X,τ) is fuzzy Lparacompact if and only if (X,ι(τ)) is L-paracompact, i.e. fuzzy L-paracompactness is a good extension of L-paracompactness. Fuzzy L₂-paracompactness is a good extension of L₂- paracompactness. Every fuzzy Hausdorff topological space (in the Srivastava, Lal and Srivastava' or in the Wagner and McLean' sense) which is fuzzy locally compact (in the Kudri and Wagner' sense) is fuzzy L₂-paracompact

Connectedness concept in intuitionistic fuzzy topological spaces

The purpose of this paper is to establish the connectedness in intuitionistic fuzzy topological space. In this paper we give six notions of separatedness, connectedness and total connectedness and one notion of T1-space in intuitionistic fuzzy topological space. Also, we find a relation between classical topology and intuitionistic fuzzy topology. Further, we show that connectedness in intuitionistic fuzzy topological spaces are productive and we demonstrate some of its features.

Notes on Bipolar Interval Valued Intuitionistic Fuzzy Topological Space

In this paper we have introduced Bipolar Interval Valued Intuitionistic Fuzzy Point, Bipolar Interval Valued Intuitionistic Fuzzy Neighbourhood,Bipolar Interval Valued Intuitionistic Fuzzy Interior and Bipolar Interval Valued Intuitionistic Fuzzy Closurein Bipolar Interval Valued Intuitionistic Fuzzy topological space and have verifiedsome of its properties.