• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.4
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• pp.592-594
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• 2009

In this paper we consider voting analysis in the political science in connection with $B_n$(or $M_n${0, 1}), the semigroup of the binary relations on X with n elements. We also consider it in connection with $M_n$(F) (or $B_n$(F)), the semigroup of all fuzzy binary relations on X. Also we establish a possibility theorem and an impossibility theorem in voting analysis based on preferences in $B_n$ and $M_n$(F).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.7-16
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• 2007

First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${\rho}\;o\;{\sigma}{\in}$ FC(S) for any two fuzzy congruences ${\rho}\;and\;{\sigma}$ on a fuzzy groupoid ($S,{\odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.240-245
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• 1998

Fuzzy information retrieval which uses the concept of fuzzy relation is able to retrieve documents in the way based on not morphology but semantics, dissimilar to traditional information retrieval theories. Fuzzy information retrieval logically consists of three sets : the set of documents, the set of terms and the set of queries. It maintains a fuzzy relational matrix which describes the relationship between documents and terms and creates a thesaurus with fuzzy relational product. It also provides the user with documents which are relevant to his query. However, there are some problems on building a thesaurus with fuzzy relational product such that it has big time complexity and it uses fuzzy values to be processed with flating-point. Actually, fuzzy values have to be expressed and processed with floating-point. However, floating-point operations have complex logics and make the system be slow. If it is possible to exchange fuzzy values with binary values, we could expect sp eding up building the thesaurus. In addition, binary value expressions require just a bit of memory space, but floating -point expression needs couple of bytes. In this study, we suggest a new method of building a thesaurus, which accelerates the operation of the system by pre-applying an ${\alpha}$-cut. The experiments show the improvement of performance and reliability of the system.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.47
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• pp.219-232
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• 1998

A lot of difficulties exist in analyzing the structure of a system owing to the complex and organic relations in the systems we face in reality. Focuses have been put on the research of optimal solution in a defined structure, however, on the assumption that the structure of the system has been already defined. With the grasping of the structure as the most prior condition, ISM(Interpretive Structural Modeling) and FSM(Fuzzy Structural Modeling) are suggested as solutions in this paper. ISM uses the systematic application of some elementary notions of graph theory and boolean algebra, FSM uses Fuzzy conception for representing relationship between elements. In FSM, the entries in the relation matrix are taken to value on the interval [0,1] by virtue of a fuzzy binary relation. Numeric examples are used as the actual application as follows.

• Journal of Intelligence and Information Systems
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• v.16 no.4
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• pp.67-84
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• 2010

In terms of business, forecasting is a work of what is expected to happen in the future to make managerial decisions and plans. Therefore, the accurate forecasting is very important for major managerial decision making and is the basis for making various strategies of business. But it is very difficult to make an unbiased and consistent estimate because of uncertainty and complexity in the future business environment. That is why we should use scientific forecasting model to support business decision making, and make an effort to minimize the model's forecasting error which is difference between observation and estimator. Nevertheless, minimizing the error is not an easy task. Case-based reasoning is a problem solving method that utilizes the past similar case to solve the current problem. To build the successful case-based reasoning models, retrieving the case not only the most similar case but also the most relevant case is very important. To retrieve the similar and relevant case from past cases, the measurement of similarities between cases is an important key factor. Especially, if the cases contain symbolic data, it is more difficult to measure the distances. The purpose of this study is to improve the forecasting accuracy of case-based reasoning approach using fuzzy relation and composition. Especially, two methods are adopted to measure the similarity between cases containing symbolic data. One is to deduct the similarity matrix following binary logic(the judgment of sameness between two symbolic data), the other is to deduct the similarity matrix following fuzzy relation and composition. This study is conducted in the following order; data gathering and preprocessing, model building and analysis, validation analysis, conclusion. First, in the progress of data gathering and preprocessing we collect data set including categorical dependent variables. Also, the data set gathered is cross-section data and independent variables of the data set include several qualitative variables expressed symbolic data. The research data consists of many financial ratios and the corresponding bond ratings of Korean companies. The ratings we employ in this study cover all bonds rated by one of the bond rating agencies in Korea. Our total sample includes 1,816 companies whose commercial papers have been rated in the period 1997~2000. Credit grades are defined as outputs and classified into 5 rating categories(A1, A2, A3, B, C) according to credit levels. Second, in the progress of model building and analysis we deduct the similarity matrix following binary logic and fuzzy composition to measure the similarity between cases containing symbolic data. In this process, the used types of fuzzy composition are max-min, max-product, max-average. And then, the analysis is carried out by case-based reasoning approach with the deducted similarity matrix. Third, in the progress of validation analysis we verify the validation of model through McNemar test based on hit ratio. Finally, we draw a conclusion from the study. As a result, the similarity measuring method using fuzzy relation and composition shows good forecasting performance compared to the similarity measuring method using binary logic for similarity measurement between two symbolic data. But the results of the analysis are not statistically significant in forecasting performance among the types of fuzzy composition. The contributions of this study are as follows. We propose another methodology that fuzzy relation and fuzzy composition could be applied for the similarity measurement between two symbolic data. That is the most important factor to build case-based reasoning model.