• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.781-799
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• 2023

For any bipolar multi Q-fuzzy set δ of an universe set G, we redefined a normal, conjugate concepts, union and product operations of a bipolar M - N-multi Q-fuzzy subgroups and we discuss some of its properties. On the other hand, we introduce and define the level subsets positive β-cut and negative α-cut of bipolar M - N- multi Q- fuzzy subgroup and discuss some of its related properties.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.26
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• pp.13-19
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• 1992

MODM(multiobjective decision-making)problem is very complex system for the analysist and decision maker. Therefore, it requires suitable MODM method to solve multiobjective decision-making problem. This paper presents an interactive fuzzy decision making method for solving multiobjective nonlinear programming problems with fuzzy goals and $\alpha$-cut set of fuzzy numbers. In our interactive method, if the decision maker specifies the degree $\alpha$of the objective value and the imprecise goals, λ-mux problem is solved. To examplify the proposed method, an interactive computer programming written in FORTRAN and an illustrate numerical example along with computer outputs are presented.

• Proceedings of the KIPE Conference
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• 2000.07a
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• pp.38-40
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• 2000

In this paper we propose a calculation method for fuzzy control based on quantized $\alpha$-cut decomposition of fuzzy sets. This method is easy to be implemented in analog hardware. The effect of quantization levels on defuzzified fuzzy inference results is investigated. A few quantization levels are sufficient for fuzzy control. The hardware implementation of this calculation method and the defuzzification by gravity center method by PWM are also presented.

• 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 Korea Water Resources Association
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• v.46 no.10
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• pp.977-987
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• 2013

This study aims to develop a multiple criteria decision making (MCDM) approach for flood vulnerability assessment which considers uncertainty. The flood vulnerability assessment procedure consists of three steps: (1) use the Delphi process to determine the criteria and their corresponding weights-the adopted criteria represent the social, economic, and environmental circumstances related to floods, (2) construct a fuzzy data matrix for the flood vulnerability criteria using fuzzification and standardization, and (3) set priorities based on the number of assessed vulnerabilities. This study uses a modified fuzzy TOPSIS method based on ${\alpha}$-level sets which considers various uncertainties related to weight derivation and crisp data aggregation. Further, Spearman's rank correlation analysis is used to compare the rankings obtained using the proposed method with those obtained using fuzzy TOPSIS with fuzzy data, TOPSIS, and WSM methods with crisp data. The fuzzy TOPSIS method based on ${\alpha}$-cut level sets is found to have a higher correlation rate than the other methods, and thus, it can reduce the difference of the rankings which uses crisp and fuzzy data. Thus, the proposed flood vulnerability assessment method can effectively support flood management policies.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.37-41
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• 2009

We would like to propose Dirichlet-Jordan theorem on the space of summable in measure(SIM). Surely, this is a kind of extension of bounded variation([1, 4]), and considered as an application of fuzzy set such that ${\alpha}$-cut is 0.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1266-1269
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• 1993

The paper introduces a new method for fuzzy processing. The method allows handing a piece of information lost in the classic fuzzification process, and thus neglected by other methods. Processing the result after fuzzification is sustained by the interpretation that the input-output set mapping, specified by the IF-THEN rules, can be regarded as a direct mapping of their corresponding alpha-cuts. Processing involves just singletons as intermediary results, the final result being a combination of singletons obtained from fired rules.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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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.

• International Journal of Reliability and Applications
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• v.16 no.1
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• pp.15-26
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• 2015

Present study investigates the fuzzy reliability of some systems using intuitionistic fuzzy Weibull lifetime distribution, in which the lifetime parameters are assumed to be fuzzy parameter due to uncertainty and inaccuracy of data. Expressions for fuzzy reliability, fuzzy mean time to failure, fuzzy hazard function and their ${\alpha}$-cut have been discussed when systems follow intuitionistic fuzzy Weibull lifetime distribution. A numerical example is also taken to illustrate the methodology to calculate the fuzzy reliability characteristics of systems.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.5
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• pp.1050-1057
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• 2004

The purpose of study is development of a fuzzy controller which independent of a computer and its software for fuzzy control of servo system. This paper describes a method of approximate reasoning for fuzzy control of servo system, based on decomposition of $\alpha$-level fuzzy sets, It is propose that fuzzy logic algorithm is a body from fuzzy inference to defuzzificaion in cases where the output variable u directly is generated PWM. The effectiveness of quantified $\alpha$-levels on input/output characteristics of fuzzy controller and output response of DC servo system is investigated. It is concluded that $\alpha$-cut 4 levels give a sufficient result for fuzzy control performance of DC servo system. The experimental results shows that the proposed hardware method is effective for practical applications of DC servo system.