• Honam Mathematical Journal
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• v.27 no.4
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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.

• Journal of the Korea Society for Simulation
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• v.11 no.4
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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.

• Journal of the Korea Society for Simulation
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• v.10 no.1
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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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• 2001.10a
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.4
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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.

• Journal of the Korea Society for Simulation
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• v.19 no.4
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• pp.67-75
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• 2010

Deadlock usually appears in contain subsystem which is run in parallel and resources share modules. Siphons and traps have been well introduced to characterize deadlocks of Petri nets. Siphon concept be well used for proposing the detect and prevent deadlock by the pleasure researchers. But it's need many times and efforts to detect all siphon sub-nets in the Petri model. Since transitive matrix could explain all relations between the place and transitions in Petri nets, we propose an algorithm to detect all siphon sub-nets after analyzed the transitive matrix's properties. Examples are givens to illustrate the method.

• Journal of the Korea Society for Simulation
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• v.12 no.2
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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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• v.62 no.2
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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.

• Journal of the Korea Society for Simulation
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• v.17 no.3
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• pp.75-83
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• 2008

A deadlock is a condition in which the excessive demand for the resources being used by others causes activities to stop and it is one of the important problems in process control system to detect and prevent deadlocks. While the reachability analyze methods or divide subnets for analyzing methods are well used, it requires a lot of times and effects to analyze the detection of the deadlock status. Furthermore, it could not be effective if the model is complex or huge. Therefore, it is necessary to develop a new and more efficient deadlock detection algorithm. In this paper, a deadlock detection conditions after analyzed the Petri Net using the transitive matrix has been proposed to solve these problems. For presenting the results, the suggested deadlock detection algorithm was also adapted to an illustrated FMS (Flexible Manufacturing System) model.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.1
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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.