• The Journal of the Convergence on Culture Technology
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• v.5 no.1
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• pp.27-36
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• 2019

The industrialization theory that industry and economic development of country has an important influence on the development of the welfare state had become a major theory explaining the development of the welfare state. However, the theory of industrialization faced criticism that the size of public welfare was relatively weak even in advanced industrial countries where industrialization developed. To complement and explain these limitations, The theory of democracy that the welfare state could be expanded as a strategy for election competition, and the theory of power-resources theory that welfare states could develop when the power of unions and left parties demanding welfare states were strengthened. This study uses Fuzzy-set analysis for the data of OECD countries adding industrial structure variables to existing theory of the development of welfare state. The result suggests that the proportion of manufacture such as industry structure of country is important for the development of welfare state.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.263-271
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• 2010

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, such as the Reidemeister set does in Nielsen fixed point theory. In this paper, using Heath and You's methods on Nielsen type numbers, we show that these numbers can be evaluated by the set of essential orbit classes under suitable hypotheses, and obtain some formulas in some special cases.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.123-129
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• 2010

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft BL-algebras by using the soft set theory. The notion of filteristic soft BL-algebras is introduced and some related properties are investigated.

• East Asian mathematical journal
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• v.24 no.4
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• pp.369-375
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• 2008

In this paper, we first introduce inwards set valued maps in hyperconvex metric spaces. Then we present fixed point theory for continuous condensing inward set valued maps.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.733-746
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• 2023

Let (X, d) be a semimetric space. A permutation Φ of the set X is a combinatorial self similarity of (X, d) if there is a bijective function f : d(X × X) → d(X × X) such that d(x, y) = f(d(Φ(x), Φ(y))) for all x, y ∈ X. We describe the set of all semimetrics ρ on an arbitrary nonempty set Y for which every permutation of Y is a combinatorial self similarity of (Y, ρ).

• Journal of the Korean Society for Library and Information Science
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• v.21
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• pp.249-290
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• 1991

Theoretical developments in the information retrieval have offered a number of alternatives to traditional Boolean retrieval. Probability theory and fuzzy set theory have played prominent roles here. Fuzzy set theory is an attempt to generalize traditional set theory by permitting partial membership in a set and this means recognizing different degrees to which a document can match a request. In this study, an experimentation of a document retrieval system using the fuzzy relation matrix of the keywords is described and the results are offered. The queries composed of keywords and Boolean operaters AND, OR, NOT were processed in the retrieval method, and the method was implemented on the PC of 32bit level (30 MHz) in an experimental system. The measurement of the recall ratio and precision ratio verified the effectiveness of the proposed fuzzy relation matrix of keywords and retrieval method. Compared to traditional crisp method in the same document database, the recall ratio increased $10\%$ high although the precision ratio decreased slightly. The problems, in this experiment, to be resolved are first, the design of the automatic data input and fuzzy indexing modules, through which the system . can have the ability of competition and usefulness. Second, devising a systematic procedure for assigning fuzzy weights to keywords in documents and in queries.

• Journal of the Korean Geotechnical Society
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• v.23 no.11
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• pp.109-117
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• 2007

Uncertainty is pervasive in rock slope stability analysis due to various reasons and subsequently it may cause serious rock slope failures. Therefore, the importance of uncertainty has been recognized and subsequently the probability theory has been used to quantify the uncertainty since 1980's. However, some uncertainties, due to incomplete information, cannot be handled satisfactorily in the probability theory and the fuzzy set theory is more appropriate for those uncertainties. In this study the random variable is considered as fuzzy number and the fuzzy set theory is employed in rock slope stability analysis. However, the previous fuzzy analysis employed the approximate method, which is first order second moment method and point estimate method. Since previous studies used only the representative values from membership function to evaluate the stability of rock slope, the approximated analysis results have been obtained in previous studies. Therefore, the Monte Carlo simulation technique is utilized to evaluate the probability of failure for rock slope in the current study. This overcomes the shortcomings of previous studies, which are employed vertex method. With Monte Carlo simulation technique, more complete analysis results can be secured in the proposed method. The proposed method has been applied to the practical example. According to the analysis results, the probabilities of failure obtained from the fuzzy Monte Carlo simulation coincide with the probabilities of failure from the probabilistic analysis.

• Tunnel and Underground Space
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• v.11 no.4
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• pp.289-300
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• 2001

In the design of tunnel, it contains inaccuracy of data, fuzziness of evaluation, observer error and so on. The face observation during tunnel excavation, therefore, plays an important role to raise stability and to reduce supporting cost. This study is carried out to minimize the subjectiveness of observer and to exactly evaluate the natural properties of ground during the face observation. For these purpose, fuzzy set theory and neuro-fuzzy techniques in artificial intelligent techniques are applied to the inference of the RMR value from the observation data. The correlation between original RMR vague and inferred RM $R_{_FU}$ and RM $R_{_NF}$ values from fuzzy set theory and neuro-fuzzy techniques is investigated using 46 data. The results show that good correlation between original RMR value and infected RM $R_{_FU}$ and RM $R_{_NF}$ value is observed when the correlation coefficients are ｜R｜=0.96 and ｜R｜=0.95 respectively. From these results, applicability of fuzzy set theory and neuro-fuzzy techniques to rock mats classification is proved to be sufficiently high enough. enough.

• Nuclear Engineering and Technology
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• v.23 no.3
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• pp.285-298
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• 1991

An example application of the fuzzy set theory is first made to a simple portion of a given accident progression event tree with typical qualitative fuzzy input data, and thereby computational algorithms suitable for application of the fuzzy set theory to the accident progression event tree analysis are identified and illustrated with example applications. Then the procedure used in the simple example is extended to extremely complex accident progression event trees with a number of phenomenological uncertainty issues, i.e., a typical plant damage state‘SEC’of the Zion Nuclear Power Plant risk assessment. The results show that the fuzzy averages of the fuzzy outcomes are very close to the mean values obtained by current methods. The main purpose of this paper is to provide a formal procedure for application of the fuzzy set theory to accident progression event trees with imprecise and qualitative branch probabilities and/or with a number of phenomenological uncertainty issues.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.413-423
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• 2021

This study investigated the empty set which is one of the mathematical objects. We inquired some misconceptions about empty set and the background of imposing empty set. Also we studied historical background of the introduction of empty set and the axiomatic system of Set theory. We investigated the nature of mathematical object through studying empty set, pure conceptual entity. In this study we study about the existence of empty set by investigating Alian Badiou's ontology known as based on the axiomatic set theory. we attempted to explain the relation between simultaneous equations and sets. Thus we pondered the meaning of the existence of empty set. Finally we commented about the thoughts of sets from a different standpoint and presented the meaning of axiomatic and philosophical aspect of mathematics.