• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.491-503
• /
• 2011

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

• Korean Journal of Mathematics
• /
• v.17 no.3
• /
• pp.315-330
• /
• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.89-108
• /
• 1996

In this paper we obtain common fixed point theorems for sequences of fuzzy mappings on Menger probabilistic metric spaces, including common fixed point theorems for sequences of multi-valued mappings, which generalize and improve some results of Lee et al. [8] and Chang [2].

• Honam Mathematical Journal
• /
• v.27 no.2
• /
• pp.251-265
• /
• 2005

In this paper, we introduce a generalized vector quasivariational like inequality for fuzzy mappings and show the existence of solutions under compact assumption.

• Honam Mathematical Journal
• /
• v.27 no.3
• /
• pp.445-463
• /
• 2005

In this paper, we introduce a Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings and consider the existence of solutions to them under non-compact assumption.

• East Asian mathematical journal
• /
• v.18 no.2
• /
• pp.225-233
• /
• 2002

In this paper, we obtain the common fixed point for fuzzy mappings satisfying an implicit relation. We improve earlier results of this line.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.485-492
• /
• 2005

In this paper, we obtain some common fixed point theorems for fuzzy mappings in complete metric linear spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.207-220
• /
• 2008

We introduce and study the notions of supra fuzzy convergence of fuzzy filters, $s{\gamma}$-fuzzy open (closed) sets, $s{\gamma}(/TEX>$s{\gamma}^*)$-fuzzy continuous and $s{\gamma}$-fuzzy open mapping. Also. we investigate some of fundamental properties of these notions.

• Journal of Information Processing Systems
• /
• v.13 no.3
• /
• pp.435-447
• /
• 2017

Associative and bidirectional associative memories are examples of associative structures studied intensively in the literature. The underlying idea is to realize associative mapping so that the recall processes (one-directional and bidirectional ones) are realized with minimal recall errors. Associative and fuzzy associative memories have been studied in numerous areas yielding efficient applications for image recall and enhancements and fuzzy controllers, which can be regarded as one-directional associative memories. In this study, we revisit and augment the concept of associative memories by offering some new design insights where the corresponding mappings are realized on the basis of a related collection of landmarks (prototypes) over which an associative mapping becomes spanned. In light of the bidirectional character of mappings, we have developed an augmentation of the existing fuzzy clustering (fuzzy c-means, FCM) in the form of a so-called collaborative fuzzy clustering. Here, an interaction in the formation of prototypes is optimized so that the bidirectional recall errors can be minimized. Furthermore, we generalized the mapping into its granular version in which numeric prototypes that are formed through the clustering process are made granular so that the quality of the recall can be quantified. We propose several scenarios in which the allocation of information granularity is aimed at the optimization of the characteristics of recalled results (information granules) that are quantified in terms of coverage and specificity. We also introduce various architectural augmentations of the associative structures.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.4
• /
• pp.312-315
• /
• 2008

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