• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.187-199
• /
• 2009

In this paper, we introduce the concept of fuzzy weakly (r,s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense. The relations among various kinds of fuzzy mappings on intuitionistic fuzzy topological spaces in $\check{S}ostak^{\prime}s$ sense are displayed. The characterization for the fuzzy weakly (r,s)-semicontinuous mapping is obtained. Also, we introduce the notion of fuzzy weakly (r,s)-semicontinuous mappings at a given intuitionistic fuzzy point. The relation between fuzzy weakly (r,s)- semicontinuous mappings and fuzzy weakly (r,s)-semicontinuous mappings at an intuitionistic fuzzy point is discussed.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1419-1430
• /
• 2010

Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.12 no.2
• /
• pp.149-153
• /
• 2012

In this paper, we introduce the concept of fuzzy almost strongly (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense. The relationships among fuzzy strongly (r, s)-semicontinuous, fuzzy almost (r, s)-continuous, fuzzy almost (r, s)-semicontinuous, and fuzzy almost strongly (r, s)-semicontinuous mappings are discussed. The characterization for the fuzzy almost strongly (r, s)-semicontinuous mappings is obtained.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.439-454
• /
• 2013

In this paper, we introduce the Birkho integral of fuzzy mappings in Banach spaces in terms of the Birkhoff integral of set-valued mappings and investigate some properties of the Birkho integrals of set-valued mappings and fuzzy mappings in Banach spaces.

• Korean Journal of Mathematics
• /
• v.18 no.3
• /
• pp.229-241
• /
• 2010

In this paper, we introduce the Denjoy-Pettis integral of fuzzy mappings in Banach spaces and obtain some properties of the Denjoy-Pettis integral of fuzzy mappings and the convergence theorems for Denjoy-Pettis integrable fuzzy mappings.

• Communications of the Korean Mathematical Society
• /
• v.26 no.4
• /
• pp.661-667
• /
• 2011

In this paper, we introduce the notions of fuzzy strongly (r, s)-preopen and preclosed mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense. The relationships among fuzzy (r, s)-open, fuzzy strongly (r, s)-semiopen, fuzzy (r, s)-preopen, and fuzzy strongly (r, s)-preopen mappings are discussed. The characterizations for the fuzzy strongly (r, s)-preopen and preclosed mappings are obtained.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.3
• /
• pp.190-196
• /
• 2011

In this paper, we introduce the concept of fuzzy (r, s)-semi-irresolute mappings on intuitionistic fuzzy topological spaces in Sostak's sense, which is a generalization of the concept of fuzzy semi-irresolute mappings introduced by S. Malakar. The characterizations for the fuzzy (r, s)-semi-irresolute mappings are obtained by terms of semi-interior, semi-${\theta}$-interior, semi-clopen, and regular semi-open.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.1
• /
• pp.54-58
• /
• 2010

We introduce the concepts of interval-valued fuzzy $m{\alpha}$-open sets and interval-valued fuzzy $m{\alpha}$-continuous mappings. And we study some characterizations and properties of such concepts.

• Communications of the Korean Mathematical Society
• /
• v.23 no.3
• /
• pp.427-446
• /
• 2008

In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.279-291
• /
• 2010

In this paper, we introduce the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces in terms of the Kurzweil-Henstock-Pettis integral of set-valued mappings and obtain some properties of the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces and the convergence theorem for Kurzweil-Henstock-Pettis integrable fuzzy mappings.