• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.461-472
• /
• 2022

In optimization theory, hypo-convergence is considered as an effective tool by providing the convergence of supremum values under some conditions. This feature makes it different from other types of convergence. Therefore, we have defined the hypo-convergence of a sequence of fuzzy sets due to the increasing interest in fuzzy set theory in recent years. After giving a theoretical framework, we deal with the optimization process by using a sequential characterization of hypo-convergence of sequence of fuzzy sets. Since the maximization process in optimization theory is beyond the presence of hypo-convergence, we give some conditions to satisfy the convergence of supremum values. Furthermore, we show how sequence of fuzzy sets and fuzzy numbers differ in the convergence of the supremum values.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10a
• /
• pp.28-31
• /
• 1996

A bag is a set-like entity which can contain repeated elements. Fuzzy bags have been studied by Yager, who defined their basic relations and operations. However, his definitions of the basic relations and operations are inconsistent with the corresponding relations and operations for ordinary fuzzy sets. The present paper presents new basic relations and operations of fuzzy bags using a grade sequence for each element of the universal set. Moreover the .alpha.-cut, t-norms, the extension principle, and the composition of fuzzy bag relations are described.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.291-308
• /
• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.3 no.2
• /
• pp.157-160
• /
• 2003

In this paper, we describe how to represent lower case hand-written English alphabets by a sequence of two to seven fuzzy sets. Each fuzzy set represents an arc segment of the character and each arc segment is assumed to be a part of an ellipse. The part of an ellipse is defined by five quantities; its short and long radii, its orientation angle, whether it is a part of the lower half or the upper half, and whether it is the full half or a part of a half. Hence, we use the Cartesian product of five fuzzy sets to represent each arc segment. We show that this representation is a translation, rotation, and scaling invariant and that it can be used to generate the hand-written English alphabets. The representation we describe is different from the one proposed earlier by the author and when compared with the previous representation, the one described in this paper simulates more closely the behavior of how one writes English characters.

• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.349-361
• /
• 2023

In this article, we construct lacunary ∆^m-statistical convergence for triple sequences within the context of intuitionistic fuzzy n-normed spaces (IFnNS). For lacunary ∆^m-statistical convergence of triple sequence in IFnNS, we demonstrate numerous results. For this innovative notion of convergence, we further built lacunary ∆^m-statistical Cauchy sequences and offered the Cauchy convergence criterion.

• Journal of Intelligence and Information Systems
• /
• v.13 no.2
• /
• pp.55-68
• /
• 2007

DNA sequence alignment algorithms in computational molecular biology have been improved by diverse methods. In this paper, we proposed a DNA sequence alignment algorithm utilizing quality information and a fuzzy inference method utilizing characteristics of DNA sequence fragments and a fuzzy logic system in order to improve conventional DNA sequence alignment methods using DNA sequence quality information. In conventional algorithms, DNA sequence alignment scores were calculated by the global sequence alignment algorithm proposed by Needleman-Wunsch applying quality information of each DNA fragment. However, there may be errors in the process for calculating DNA sequence alignment scores in case of low quality of DNA fragment tips, because overall DNA sequence quality information are used. In the proposed method, exact DNA sequence alignment can be achieved in spite of low quality of DNA fragment tips by improvement of conventional algorithms using quality information. And also, mapping score parameters used to calculate DNA sequence alignment scores, are dynamically adjusted by the fuzzy logic system utilizing lengths of DNA fragments and frequencies of low quality DNA bases in the fragments. From the experiments by applying real genome data of NCBI (National Center for Biotechnology Information), we could see that the proposed method was more efficient than conventional algorithms using quality information in DNA sequence alignment.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.171-189
• /
• 2005

In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^P$. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.597-606
• /
• 2009

In this paper, we introduce the notion of the statistically complete fuzzy norm on a linear space. And we consider some relations between the fuzzy statistical completeness and ordinary completeness on a linear space.

• Kyungpook Mathematical Journal
• /
• v.52 no.2
• /
• pp.189-200
• /
• 2012

In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.

• The Pure and Applied Mathematics
• /
• v.12 no.1
• /
• pp.17-31
• /
• 2005

In this paper we prove common fixed point theorems for three mappings under the condition of weak compatible mappings, without taking any function continuous in fuzzy metric space and then extend this result to fuzzy 2-metric space and fuzzy 3-metric space.