This paper is a survey of fuzzy set theory applied in cluster analysis. These fuzzy clustering algorithms have been widely studied and applied in a variety of substantive areas. They also become the major techniques in cluster analysis. In this paper, we give a survey of fuzzy clustering in three categories. The first category is the fuzzy clustering based on fuzzy relation. The second one is t...

Abstract: In this paper, similar to the extension from intuitionistic fuzzy numbers (IFNs) to neutrosophic numbers (NNs), we propose the normal neutrosophic numbers (NNNs) based on the normal intuitionistic fuzzy numbers (NIFNs) to handle the incompleteness, indeterminacy and inconsistency of the evaluation information. In addition, because Heronian mean (HM) operators can consider capture the ...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy almost weakly generalized closed mappings and intuitionistic fuzzy almost weakly generalized open mappings in intuitionistic fuzzy topological space. Some of their properties are explored.

In this paper optimal control problem of fuzzy linear time invariant systems is considered. Determining of system optimal input with minimizing quadratic integral criterion by using Pontryagin Minimum Principle will make the Fuzzy Partial Differential Equations [FPDEs] system solve the problem. The quality of obtaining system optimal input by solving the FPDEs system has been studied based on n...

In this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.