• 호남수학학술지
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• 제27권4호
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• pp.543-550
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• 2005

Some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive fuzzy matrix is given using the properties. As a special case an open problem concerning idempotent matrices is solved. Thus we have the same result in a intuitionistic fuzzy matrix theory. In our results a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix play an important role. We decompose a transitive intuitionistic fuzzy matrix into sum of a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix. Then we obtain a canonical form of the transitive intuitionistic fuzzy matrix.

• 한국시뮬레이션학회논문지
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• 제11권4호
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• pp.57-68
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• 2002

The analysis of the cyclic scheduling problem in FMS using the transitive matrix has been proposed. Since the transitive matrix may explain all the relations between the places and transitions, we propose an algorithm to get good solution after slicing off some subnets from the original net based on machines operations. For analyzing the schedule problem, we considered two time functions such as produce time and waiting time using the P-invariant. In addition, we are shown the effectiveness of proposed algorithm after comparing with unfolding algorithms.

• 한국시뮬레이션학회논문지
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• 제10권1호
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• pp.13-24
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• 2001

We propose a divide-conquer method of Petri nets under the condition of one-boundedness for all the Petri nets. We introduce the P-invariant transitive matrix of Petri nets and relationship between them. The feature of the P-invariant transitive matrix is that each element stands for the transitive relationship between input place and output place through the firing of the enable transition.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.132.3-132
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• 2001

In this paper, we focus on the analysis of the scheduling problem in FMS after slicing off some sub-nets using the transitive matrix. This class of Time Petri nets is obtained by merging subnets based on the machine's operations. We can divide original system into some subnets based on machine's operations using Time Petri nets slice and analyze the feasibility time in each schedules. In this paper, we show the usefulness of transitive matrix to slice off some subnets from the original net, and explain on an example.

• 제어로봇시스템학회논문지
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• 제8권4호
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• pp.292-298
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• 2002

We focus on the slicing off some sub-nets using the transitive matrix. Control flows in the Petri nets is done based on the token flows. One control f]ow explains the independent tokens status and if the token-in divides into several tokens after firing a transition then the control flow divides to several flows, as well. Accordingly, we define that the basic unit of concur-rency (short BUC) is a set of the executed control flows based on the behavioral properties in the net. The BUC is S-invariant which has one control flow. We show the usefulness of transitive matrix to slice off some subnets from the original net based on BUC-through on an example.

• 한국시뮬레이션학회논문지
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• 제19권4호
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• pp.67-75
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• 2010

교착이란 일반적으로 병행과 자원공유 모듈에 의한 서브 시스템에서 발생한다. 사이폰과 트랩은 패트리 넷의 교착 상태를 잘 나타낸다. 사이폰은 많은 연구자들에게 교착을 감지하고 방지하는데 사용되어진 개념이다. 그러나 모든 사이폰 서브넷을 감지하는데는 많은 시간과 노력이 필요하다. 추이적 행렬은 플레이스와 트랜지션간의 관계를 표현하므로 추이적 행렬과의 관계를 분석하여 모든 사이폰 서브 넷을 감지하는 알고리즘을 제안한다. 또한 제안한 알고리즘의 성능을 사례를 들어 검증한다.

• 한국시뮬레이션학회논문지
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• 제12권2호
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• pp.13-24
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• 2003

In this study, we propose a scheduling analysis method of the Flexible management system using the transitive matrix. The Scheduling problem is a combination-optimization problem basically, and a complexity is increased exponentially for a size of the problem. To reduce an increase of a complexity, we define that the basic unit of concurrency (short BUC) is a set of control flows based on behavioral properties in the net. And we propose an algorithm to divide original system into some BUC. To sum up, we divide a petri net model of the Flexible management system Into the basic unit of concurrency through the division algorithm using the transitive matrix. Then we apply it to the division-scheduling algorithm to find an efficient scheduling. Finally, we verify its efficiency with an example.

• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.213-227
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• 2022

We discuss the relation between units and nilpotents of a ring, concentrating on the transitivity of units on nilpotents under regular group actions. We first prove that for a ring R, if U(R) is right transitive on N(R), then Köthe's conjecture holds for R, where U(R) and N(R) are the group of all units and the set of all nilpotents in R, respectively. A ring is called right UN-transitive if it satisfies this transitivity, as a generalization, a ring is called unilpotent-IFP if aU(R) ⊆ N(R) for all a ∈ N(R). We study the structures of right UN-transitive and unilpotent-IFP rings in relation to radicals, NI rings, unit-IFP rings, matrix rings and polynomial rings.

• 한국시뮬레이션학회논문지
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• 제17권3호
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• pp.75-83
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• 2008

여러 개의 작업이 동시에 작동 할 때 서로 다른 작업에서 공유자원을 사용하기 위하여 상대방의 작업이 끝나기를 기다리는 상태를 교착상태라 하며 이는 시스템의 효율성과 경제성 제고에 가장 중요한 문제 중 하나이다. 지금까지 이러한 교착상태 확인은 도달성(reachability)기법이나 서브 넷(Subnet)으로 분리하여 분석하는 기법 등이 가장 많이 사용되었으나, 분석에 필요한 시간과 노력, 복잡성과 효율성에 있어서 효과적이지 못한 단점을 가지고 있다. 본 연구는 패트리 넷(Petri Net)에서 모든 플레이스(Place) 간의 관계를 나타내는 추이적(Transitive)행렬을 이용하여 교착상태가 나타날 가능성이 있는 자원공유 플레이스를 분석하여 교착상태를 검증하는 정책을 제시한다. 이를 위하여 교착상태를 확인할 수 있는 자원공유 플레이스의 관계를 정의하고, 유연생산시스템 모델을 이용하여 제안한 알고리즘의 성과를 검증한다.

• 제어로봇시스템학회논문지
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• 제10권1호
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• pp.87-95
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• 2004

We proposed the division algorithm that was aimed at dividing system models. It used a transitive matrix to express the relation between place and transition. And the division algorithm was applied to the scheduling problem, with the division-scheduling algorithm. The division-scheduling algorithm was able to calculate the divided subnet table. And it is able to reduce the analysis complexity. In this study, we applied the proposed division algorithm and division-scheduling algorithm to flexible manufacturing system models. We compared the efficiency and performance of the division-scheduling algorithm with the Hillion algorithm, Korbaa algorithm, and Unfolding algorithm proposed in previous researches.