• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.3
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• pp.389-394
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• 2011

The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.184-189
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• 2011

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan's law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on generalized intuitionistic fuzzy soft sets. We discuss the basic properties of operations on generalized intuitionistic fuzzy soft sets such as necessity and possibility. Moreover, we illustrate their interconnections between each other.

• Proceedings of the Korea Concrete Institute Conference
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• 1992.10a
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• pp.240-244
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• 1992

The values of a linguistic variable are words, phrases, or sentences in a given language. For example, structural damage can be considered as linguistic variable with values such a 'severely damaged', 'moderately damaged', which are meaningful classifications but not clearly defined, This paper is to evaluate reasonably the correction factor of bridge capacity with the aid of fuzzy sets theory. By using the above mentioned fuzzy measure, the concept of fuzzy integral and linear membership function can be defined. It is concluded that the fuzzy sets theory cam be applied to determine reasonably the correction factor of bridge capacity.

• Honam Mathematical Journal
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• v.44 no.3
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1058-1061
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• 1993

Fuzzy set theory has been extensively researched in various fields of engineering. In nuclear science, a significant influence of fuzzy sets can be noticed. However, applications of fuzzy set theory to nuclear engineering is novel. In this paper, we start with a basic statement of the decision-making process based on fuzzy set theory, and then apply it to nuclear science with some practical applications (a fuzzy decision making in an accidental release to the atmosphere as well as in a problem of land suitability classification). We believe that the use of fuzzy set theory in nuclear science has potential advantages.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.125-129
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• 2004

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic fuzzy sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.12-15
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• 2001

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.412-415
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• 2008

In this paper, we show that the concepts of null interval-valued fuzzy and absolute interval-valued fuzzy soft sets are not reasonable. Thus we introduce the modified concepts for them and study some properties. Also we introduce an operation for the interval-valued fuzzy soft set theory and study basic properties.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.551-562
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• 2007

This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.114-118
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• 2002

As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. By using intuitionistic fuzzy sets, we introduce and study the concept of intuitionistic fuzzy filters and define the concept of Hausdorffness on intuitionistic fuzzy filters, which can not be defined in crisp theory of filters, and study their properties for some extent.