• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.551-562
• /
• 2007

This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

• Kyungpook Mathematical Journal
• /
• v.50 no.4
• /
• pp.465-472
• /
• 2010

In this paper, we consider two extreme sets of zero-term rank sum of fuzzy matrix pairs: $$\cal{z}_1(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=min\{z(X),z(Y)\}\};$$ $$\cal{z}_2(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=0\}$$. We characterize the linear operators that preserve these two extreme sets of zero-term rank sum of fuzzy matrix pairs.

• Korean Journal of Mathematics
• /
• v.25 no.2
• /
• pp.261-278
• /
• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized closed and open sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized continuous mappings and then investigate some of their properties.

• Communications of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.117-134
• /
• 2005

We introduce the notion of (r,s)-connected sets in intuitionistic fuzzy topological spaces and investigate some properties of them. In particular, we show that every (r,s)-component in an intuitionistic fuzzy topological space is (r,s)-component in the stratification of it.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.111-123
• /
• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.161-170
• /
• 2009

For various fuzzy numbers, many operations have been calculated. We generalize about triangular fuzzy number and calculate four operations based on the Zadeh's extension principle, addition A(+)B, subtraction A(-)B, multiplication A(${\cdot}$)B and division A(/)B for two generalized triangular fuzzy sets.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.383-399
• /
• 2013

In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.10 no.6
• /
• pp.557-563
• /
• 2000

We introduce r-fuzzy $\delta$-cluster ($\theta$-cluster) points and r-fuzzy $\delta$-closure ($\theta$-closure) sets in smooth fuzzy topological spaces in a view of the definition of A.P. Sostak [13]. We study some properties of them.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.341-355
• /
• 2003

The fuzzification of ${\bigotimes}-closed$ set is considered, and its basic properties we investigated. Characterizations of fuazzy ${\bigotimes}-closed$ set we given. Using a collection of ${\bigotimes}-closed$ sets with additional conditions, a fuzzy ${\bigotimes}-closed$ set is stated. The theory of fuzzy topological ${\bigotimes}-closed$ sets is discussed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.63-66
• /
• 2002

As a generalization of fuzzy sets, the concept of interval-valued fuzzy sets was introduced by Gorzalczany(GO). In this paper, we shall extend the concept of "fuzzy inclusion", introduced by Sostak[SO1], to the interval-valued fuzzy setting and study its fundamental properties for some extent.