Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

Deng, Weilin; Qiu, Daowen

doi:10.1109/tfuzz.2014.2310466

Cited by 58 publications

(5 citation statements)

References 41 publications

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“…That is, ∼ FB,gbg is the transitive closure of the union of all group-by-group fuzzy bisimulations. [2,5,7,9,10,11,16,17,18,19]. All these notions can be divided into two classes.…”

Section: Example 1 Consider Thementioning

confidence: 99%

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Bisimulations for fuzzy transition systems revisited

Chen

Han

et al. 2018

International Journal of Approximate Reasoning

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Bisimulation is a well-known behavioral equivalence for discrete event systems, and has recently been adopted and developed in fuzzy systems. In this paper, we propose a new bisimulation, i.e., the group-by-group fuzzy bisimulation, for fuzzy transition systems. It relaxes the fully matching requirement of the bisimulation definition proposed by Cao et al. [IEEE Transaction on Fuzzy Systems, 19:540-552], and can equate more pairs of states which are deemed to be equivalent intuitively, but which cannot be equated in previous definitions. We carry out a systematic investigation on this new notion of bisimulation. In particular, a fixed point characterization of the group-by-group fuzzy bisimilarity is given, based on which, we provide a polynomial-time algorithm to check whether two states in a fuzzy transition system are group-by-group fuzzy bisimilar. Moreover, a modal logic, which is an extension of the Hennessy-Milner logic, is presented to completely characterize the group-by-group fuzzy bisimilarity.

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“…That is, ∼ FB,gbg is the transitive closure of the union of all group-by-group fuzzy bisimulations. [2,5,7,9,10,11,16,17,18,19]. All these notions can be divided into two classes.…”

Section: Example 1 Consider Thementioning

confidence: 99%

“…Ćirić et al [5] investigated bisimulations for fuzzy automata. Qiu and Deng [9], and Xing et al [19] studied (bi)simulations for fuzzy discrete event systems. Fan [10] discussed fuzzy bisimulations for Gödel logic.…”

Section: Introductionmentioning

confidence: 99%

Bisimulations for fuzzy transition systems revisited

Chen

Han

et al. 2018

International Journal of Approximate Reasoning

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“…Recently, Deng and Wu [13] provided a modal characterisations of fuzzy bisimulation. As an application of fuzzy bisimulation theory, Deng and Qiu [11] developed the supervisory control of fuzzy discrete-event systems based on simulation equivalence. To the best of our knowledge, this is the first paper to study (polynomial) algorithms of computing the distances between two fuzzy transition systems.…”

Section: Related Workmentioning

confidence: 99%

Polynomial-time algorithms for computing distances of fuzzy transition systems

Chen

Han

Cao

2018

Theoretical Computer Science

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Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature. Such a distance, defined as a pseudo-ultrametric over the state space of the model, provides a quantitative analogue of bisimilarity. In this paper, we focus on the problem of computing these distances. We first extend the definition of the pseudo-ultrametric by introducing discount such that the discounting factor being equal to 1 captures the original definition. We then provide polynomial-time algorithms to calculate the behavioural distances, in both the non-discounted and the discounted setting. The algorithm is strongly polynomial in the former case. Furthermore, we give a polynomial-time algorithm to compute bisimulation over fuzzy transition systems which captures the distance being equal to 0.

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“…Simulation is more and more widely used in evaluating discrete event dynamic systems due to the increasing complexity of these systems. Examples of using simulation can be found in supervisory control (Deng & Qiu, 2015), logistics and supply chain (Tako & Robinson, 2012), and virtual reality (Turner et al, 2016). Although computing power has improved significantly in recent years due to the rapid development of information technology, efficiency is still the bottleneck in using simulation.…”

Section: Introductionmentioning

confidence: 99%

Ranking and selection for pairwise comparison

Xiao

Zhang

Kou

et al. 2023

Naval Research Logistics

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In many real-world applications, designs can only be evaluated pairwise, relative to each other. Nevertheless, in the simulation literature, almost all the ranking and selection procedures are developed based on the individual performances of each design. This research considers the statistical ranking and selection problem when the design performance can only be simulated pairwise. We formulate this new problem using the optimal computing budget allocation approach and derive the asymptotic optimality condition based on some approximations. The numerical study indicates that our approach can reduce the number of simulations required to confidently identify the best design.

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Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

Cited by 58 publications

References 41 publications

Bisimulations for fuzzy transition systems revisited

Bisimulations for fuzzy transition systems revisited

Polynomial-time algorithms for computing distances of fuzzy transition systems

Ranking and selection for pairwise comparison

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