• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.521-538
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• 2024

In this paper, using the notion of the imprecise set, the idea of an imprecise group is introduced including some examples. The two key rules of classical set theory are obeyed by this extended version of fuzzy sets, which the existing complement definition of a fuzzy set failed to do. With the support from general group theory, the paper also provides some fundamental properties of an imprecise group here. Additionally, it includes a few characteristics of imprecise subgroups, and abelian imprecise group.

• 산업경영시스템학회지
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• 제20권43호
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• pp.321-331
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• 1997

Measurement of attributes is often highly subjective and imprecise, yet most MADM methods lack provisions for handling imprecise data. Frequently, decision makers must establish a ranking within a finite set of alternatives with respect to multiple attributes which have varying degrees of importance. The problem is more complex if the evaluations of alternatives according to each attribute are not expressed in precise numbers, but rather in fuzzy numbers. Analysis must allow for lack of precision and partial truth. The advantages of a fuzzy approach for MADM are that a decision maker can obtain efficient solutions all at once without trial and error, and that this approach provides better support for judging the interactive improvement of solutions in comparison with o decision making method. The algorithm used in this study is based on the concepts of vague set theory. Linguistic variables and vague values are used to facilitate a decision maker's subjective assessment about attribute weightings and the appropriateness of alternative versus selection attributes in order to obtain final scores which are called vague appropriateness indices. A numerical example is presented to show the practical applicability of this approach.

• 산업경영시스템학회지
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• 제38권4호
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• pp.117-131
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• 2015

Conventional data envelopment analysis (DEA) models require that inputs and outputs are given as crisp values. Very often, however, some of inputs and outputs are given as imprecise data where they are only known to lie within bounded intervals. While a typical approach to addressing this situation for optimization models such as DEA is to conduct sensitivity analysis, it provides only a limited ex-post measure against the data imprecision. Robust optimization provides a more effective ex-ante measure where the data imprecision is directly incorporated into the model. This study aims to apply robust optimization approach to DEA models with imprecise data. Based upon a recently developed robust optimization framework which allows a flexible adjustment of the level of conservatism, we propose two robust optimization DEA model formulations with imprecise data; multiplier and envelopment models. We demonstrate that the two models consider different risks regarding imprecise efficiency scores, and that the existing DEA models with imprecise data are special cases of the proposed models. We show that the robust optimization for the multiplier DEA model considers the risk that estimated efficiency scores exceed true values, while the one for the envelopment DEA model deals with the risk that estimated efficiency scores fall short of true values. We also show that efficiency scores stratified in terms of probabilistic bounds of constraint violations can be obtained from the proposed models. We finally illustrate the proposed approach using a sample data set and show how the results can be used for ranking DMUs.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권2호
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• pp.71-76
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• 2011

The problem of decision making under imprecise environments are widely spread in real life decision situations. We present a method of object recognition from imprecise multi observer data, which extends the work of Roy and Maji [J Compu. Appl. Math. 203(2007) 412-418] to generalized intuitionistic fuzzy soft set theory. The method involves the construction of a comparison table from a generalized intuitionistic fuzzy soft set in a parametric sense for decision making.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.331-347
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• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

• 한국컴퓨터산업학회논문지
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• 제2권7호
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• pp.923-932
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• 2001

본 논문에서는 멀티미디어 데이터들로 구성된 부정확한 실시간 태스크 집합들을 여러 가지 인자들을 사용하여 생성하고 생성된 부정확한 실시간 태스크 집합의 스케줄가능성을 이 태스크 집합의 실행 이전에 분석할 수 있는 알고리즘을 제안하였다. 또한 태스크 집합의 생성 시 사용된 인자들의 값의 변화에 따른 태스크 집합의 스케줄가능성도 살펴보았다. 실험결과에 의하면 태스크들의 필수적 부분들의 실행요구시간이 커질수록 그리고, 임의의 시점에서 스케줄 될 수 있는 태스크들의 개수가 많아질수록 태스크집합의 스케줄가능성은 희박해진다는 것이 입증되었다. 본 논문에서 제시된 스케줄가능성 분석 알고리즘은 멀티미디어 데이터들의 005 서비스에서 유용하게 활용될 것으로 기대된다.

• 국제학술발표논문집
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• The 4th International Conference on Construction Engineering and Project Management Organized by the University of New South Wales
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• pp.468-473
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• 2011

The goal of a project manager is generally to minimize the cost of the project and also to cope with uncertainty. This paper deals with the problem of project scheduling a set of activities satisfying precedence constraints in order to minimize the sum of the costs associated with the starting times of the activities in the network with imprecise activity durations, represented by means of interval or fuzzy numbers. So far this problem has been completely solved by several authors when the activities durations have crisp values. However, they do not consider the imprecision in activity durations in their models. Here the framework of possibility theory is proposed to solve this problem. In fuzzy arithmetic, usually, the interval calculations are used for the aim of complexity reduction and simplification. Thus the case of interval-valued durations is first addressed, and then extended to fuzzy intervals. A numerical example is used to illustrate the developed concept.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 춘계학술대회 학술발표 논문집
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• pp.81-86
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• 1997

It is proposed, for fuzzy combustion control system of refuse incinerator to find the relationship between inputs and outputs and to generate rules to control by using rough set theory. It is not easy to find out the corresponding inputs for each output and the control rules with incomplete or imprecise information consisting expert knowledge, process and manipulator values in the field, and operation manual for the given system. Most decision problems can be formulated employing decision table formalism. A decision table on fuzzy combustion control system for refuse incinerator is simplified and produces control(rules). The I/O realtions and the control rules found by rough set theory are compared with the previous result.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1991년도 추계학술대회 논문집 학회본부
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• pp.197-200
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• 1991

In this paper, a technique to reduce the computational effort of Hough Transform used to recognize digital circles is proposed. The technique, which is a version of the Hough Transform uses bisectors of circles cords to estimate the center of circles. This system which is implemented in this paper gets center, radius, thickness of circular fiducials regardless of input form. This system uses fuzzy set theory which deals with 'ambigousness', In order to recognize imprecise circular fiducial.

• Nuclear Engineering and Technology
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• 제23권3호
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• pp.285-298
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• 1991

전형적인 정성적 퍼지형태의 입력데이타를 가진, 주어진 사고진행사건수목의 일부분에 대하여 퍼지집합이론(fuzzy set theory)의 응용 예를 먼저 보여주고, 이 예를 통해서 퍼지집합이론을 사고 진행사건수목에 적용하기 위해 적절한 계산알고리즘을 찾아내고 또 예를 들어 설명하였다. 그리고, 간단한 예제에 사용한 계산절차를 많은 현상학적 불확실성 인자를 포함한 아주 복잡한 사고진행사건수목 즉, 최근 Zion 발전소 위험도평가(PRA)에 사용된 전형적인 발전소 손상군의 하나인‘SEC’에 응용해서 적용하였다. 퍼지집합이론으로 평가한 계산값들의 퍼지평균치들은 최근 통계적 PRA 평가 방법론으로 얻는 값들의 평균치와 거의 같은 결과를 보여주고 있다. 본 논문의 주요목적은 부정확하고 또 정성적인 분기점확률이나 또는 많은 현상학적 불확실성 인자들을 가진 사고진행사건수목들에 이 퍼지집합이론을 적용하기 위한 공식적 계산절차를 제공하는데 있다.