• 호남수학학술지
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• 제44권3호
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• pp.461-472
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• 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
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.28-31
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• 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.

• 대한수학회보
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• 제44권2호
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• pp.291-308
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• 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
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• 제3권2호
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• pp.157-160
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• 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
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• 제31권3호
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• pp.349-361
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• 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.

• 지능정보연구
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• 제13권2호
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• pp.55-68
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• 2007

분자 생물학(computational molecular biology) 분야에서 DNA 염기 서열 배치 알고리즘은 다양한 방법으로 개선되어 왔다. 본 논문에서는 기존의 DNA 염기의 품질 정보(quality information)를 이용한 DNA 염기 서열 배치 방법을 개선하기 위하여 퍼지 논리 시스템(fuzzy logic system)과 DNA 염기 서열 단편의 특징을 적용한 품질 정보와 퍼지 추론 기법을 이용한 DNA 염기 서열 배치 알고리즘을 제안한다. 기존의 알고리즘은 Needleman-Wunsch가 제안한 전역 배치 알고리즘에 각 DNA 염기의 품질 정보를 적용하여 DNA 염기 서열 배치 점수를 계산하였다. 그러나 전체 DNA 염기의 품질 정보를 이용하여 계산하기 때문에 DNA 염기 말단 부분의 품질이 낮은 경우에는 DNA 염기 서열 배치 점수를 계산하는 과정에서 오차가 발생한다. 본 논문에서는 기존의 품질 정보를 이용한 알고리즘을 개선하여 DNA 염기 서열의 말단 부위의 품질이 낮은 경우에도 정확히 서열을 배치할 수 있도록 한다. 또한 DNA 염기 서열 단편의 길이와 낮은 품질의 DNA 염기 빈도를 퍼지 논리 시스템에 적용하여 DNA 염기 서열 배치 점수를 계산하는데 적용되는 매핑 점수 인자(parameter)를 동적으로 조정한다. 제안된 알고리즘의 성능 평가를 위해 NCBI(National Center for Biotechnology Information)의 실체 유전체 데이터를 받아 성능을 분석한 결과, 제안된 알고리즘이 기존의 품질 정보만을 이용한 알고리즘 보다 DNA 염기 서열 배치에 있어서 효율적임을 확인하였다.

• 대한수학회지
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• 제42권1호
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• pp.171-189
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• 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.

• 충청수학회지
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• 제22권3호
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• pp.597-606
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• 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
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• 제52권2호
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• pp.189-200
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• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권1호
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• pp.17-31
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• 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.