• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.371-381
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• 2004

In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 추계학술대회 논문집
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• pp.524-528
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• 1996

Quality information is known to have the characteristic of continuous distribution in many manufacturing processes. It is difficult to describe the process condition by classifying the distribution into discrete ranges which is based on the set concept. Fuzzy control chart has been developed for the control of linguistic data but it still utilizes the dichotomous notion of classical set theory. In this paper, the fuzzy sampling method is studied in order to manage the ambiguous data properly and incorporated for generating fuzzy control chart. The method is based on the fuzzy set concept and considered to be appropriate for the realization of a complete fuzzy control chart. The fuzzy control chart was compared with the conventional generalized p-chart in the sensitivity for quality distribution and robustiness against the noise. The fuzzy control chart with the fuzzy sampling method showed better characteristics.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.569-585
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• 2021

In this paper, we introduce the concept of relative co-fuzzy annihilator filters in distributive lattices. We give a set of equivalent conditions for a co-fuzzy annihilator to be a fuzzy filter and we characterize distributive lattices with the help of co-fuzzy annihilator filters. Furthermore, using the concept of relative co-fuzzy annihilators, we prove that the class of fuzzy filters of distributive lattices forms a Heyting algebra. We also study co-fuzzy annihilator filters. It is proved that the set of all co-fuzzy annihilator filters forms a complete Boolean algebra.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.485-494
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• 2023

The degree of hesitancy of a vertex in a hesitancy fuzzy graph depends on the degree of membership and non-membership of the vertex. We define a new class of hesitancy fuzzy graph, the intuitionistic hesitancy fuzzy graph in which the degree of hesitancy of a vertex is independent of the degree of its membership and non-membership. We introduce the idea of β-product of a pair of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs and prove certain results based on this product.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권3호
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• pp.182-187
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• 2007

A fuzzy modeling method is proposed to build the dynamic model of a walking-beam reheating furnace from the recorded data. In the proposed method, the number of membership function on each variable is increased individually and the modeling accuracy is evaluated iteratively. When the modeling accuracy is satisfied, the membership functions on each variable are fixed and the structure of fuzzy model is determined. Because the training data is limited, in this process, as the number of membership function increase, it is highly possible that some rules are missing, i.e., no data in the training set corresponds to the consequent part of a missing rule. To complete the rulebase, the output of the model constructed at the previous step is used to generate the consequent part of the missing rules. Finally, in the real time application, a rolling update scheme to rulebase is introduced to compensate the change of system dynamics and fine tune the rulebase. The proposed method is verified by the application to the modeling of a reheating furnace.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 ISIS 2003
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• pp.36-39
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• 2003

This paper proposes a simultaneous application of homogeneity analysis and fuzzy clustering with in complete data. Taking the similarity between the loss of homogeneity in homogeneity analysis and the least squares criterion in principal component analysis into account, the new objective function is defined in a similar formulation to the linear fuzzy clustering with missing values. Numerical experiment shows the characteristic properties of the proposed method.

• 대한수학회논문집
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• 제24권2호
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• pp.197-214
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• 2009

In this paper, we formulate the definition of compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces and prove a common fixed point theorem by using the conditions of compatible mappings of type (I) and (II) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Cho, Sedghi, and Shobe [4].

• 대한수학회논문집
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• 제23권3호
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• pp.427-446
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• 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.

• 한국지능시스템학회논문지
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• 제4권2호
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• pp.9-12
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• 1994

Let X, Y be normed linear spaces, and let p$_{1}$, p.sub 2/ be lower semi-continuous fuzzy norms on X, Y respectively, and have the bounded supports on X, Y respectively. In this paper, we prove that if Y is conplete, the set of all fuzzy continuous linear maps from X into Y is a fuzzy complete fuzzy normed linear space.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.401-408
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• 2006

Fixed point theory is one of famous theories from theoretical and numerical point of views. Banach fixed point theorem plays a main role in this theory. In this article, Grabiec's fuzzy Banach contraction theorem [3] and Vasuki's theorem [12] for a complete fuzzy metric space, in the sense of Song [11] (or George and Veeramani), is proved by an extra condition.