A fuzzy Petri net-based expert system and its application to damageassessment of bridges

In this paper, a fuzzy Petri net approach to modeling fuzzy rule-based reasoning is proposed to bring together the possibilistic entailment and the fuzzy reasoning to handle uncertain and imprecise information. The three key components in our fuzzy rule-based reasoning-fuzzy propositions, truth-qualified fuzzy rules, and truth-qualified fuzzy facts-can be formulated as fuzzy places, uncertain transitions, and uncertain fuzzy tokens, respectively. Four types of uncertain transitions-inference, aggregation, duplication, and aggregation-duplication transitions-are introduced to fulfil the mechanism of fuzzy rule-based reasoning. A framework of integrated expert systems based on our fuzzy Petri net, called fuzzy Petri net-based expert system (FPNES), is implemented in Java. Major features of FPNES include knowledge representation through the use of hierarchical fuzzy Petri nets, a reasoning mechanism based on fuzzy Petri nets, and transformation of modularized fuzzy rule bases into hierarchical fuzzy Petri nets. An application to the damage assessment of the Da-Shi bridge in Taiwan is used as an illustrative example of FPNES.     

Inference in possibilistic network classifiers under uncertain observations

Possibilistic networks, which are compact representations of possibility distributions, are powerful tools for representing and reasoning with uncertain and incomplete information in the framework of possibility theory. They are like Bayesian networks but lie on possibility theory to deal with uncertainty, imprecision and incompleteness. While classification is a very useful task in many real world applications, possibilistic network-based classification issues are not well investigated in general and possibilistic-based classification inference with uncertain observations in particular. In this paper, we address on one hand the theoretical foundations of inference in possibilistic classifiers under uncertain inputs and propose on the other hand a novel efficient algorithm for the inference in possibilistic network-based classification under uncertain observations. We start by studying and analyzing the counterpart of Jeffrey’s rule in the framework of possibility theory. After that, we address the validity of Markov-blanket criterion in the context of possibilistic networks used for classification with uncertain inputs purposes. Finally, we propose a novel algorithm suitable for possibilistic classifiers with uncertain observations without assuming any independence relations between observations. This algorithm guarantees the same results as if classification were performed using the possibilistic counterpart of Jeffrey’s rule. Classification is achieved in polynomial time if the target variable is binary. The basic idea of our algorithm is to only search for totally plausible class instances through a series of equivalent and polynomial transformations applied on the possibilistic classifier taking into account the uncertain observations.     

基于直觉模糊Petri网的故障诊断

故障诊断经常受到多种不确定性和模糊性因素的影响,针对不确定性的故障诊断问题,利用直觉模糊集较好的表达不确定性信息的优势和Petri网较好的并行处理以及图形处理问题的能力,构建了直觉模糊Petri网模型。由于将直觉模糊推理转化为矩阵运算的过程中有非隶属度参数的参与,因此推理结果可提供更多的信息。根据实际故障诊断中的模糊推理问题,给出了带有权值、阈值等参数条件下新的直觉模糊推理算法。通过获取和处理故障诊断中的不确定性和模糊性的知识,该算法将故障诊断过程转化为利用直觉模糊Petri网的直觉模糊推理过程。实际燃气轮机故障诊断模型案例表明了所给直觉模糊推理算法的有效性。     

Binary naive possibilistic classifiers: Handling uncertain inputs

Possibilistic networks are graphical models particularly suitable for representing and reasoning with uncertain and incomplete information. According to the underlying interpretation of possibilistic scales, possibilistic networks are either quantitative (using product‐based conditioning) or qualitative (using min‐based conditioning). Among the multiple tasks, possibilitic models can be used for, classification is a very important one. In this paper, we address the problem of handling uncertain inputs in binary possibilistic‐based classification. More precisely, we propose an efficient algorithm for revising possibility distributions encoded by a naive possibilistic network. This algorithm is suitable for binary classification with uncertain inputs since it allows classification in polynomial time using several efficient transformations of initial naive possibilistic networks. © 2009 Wiley Periodicals, Inc.     

时间Petri网的随机模拟

模拟是Peri网进行系统分析的常用方法之一。由于时间Petri网采用时间区间来描述变迁实施的时间范围,因此变迁的实施时间点在区间内是不确定的。提出了时间Petri网的随机模拟方法。该方法在变迁开始使能时,根据某种随机分布确定实施区间内的实施时间点;然后基于模拟仿真的实验数据,运用统计分析方法及算法,构造时间Petri网状态类树,计算变迁实施区间及实施概率,为时间Petri网的系统模拟提供了一种新的探索途径。     

模糊Petri网在航电总线系统故障诊断中的研究

航电总线系统结构复杂,各部件相互耦合,故障传播模式多样化。因此,为了处理故障诊断中不充分和模糊的信息,提出了将模糊Petri网应用到航电总线系统的故障诊断中,构建出其故障的传播模型,并在模型的基础上,给出有效的推理算法。表明利用模糊Petri网,可以建立航电总线系统的故障传播模式的模型,清晰地反映故障的产生、发展及影响。     

A reasoning algorithm for high-level fuzzy Petri nets

We introduce an automated procedure for extracting information from knowledge bases that contain fuzzy production rules. The knowledge bases considered here are modeled using the high-level fuzzy Petri nets proposed by the authors in the past. Extensions to the high-level fuzzy Petri net model are given to include the representation of partial sources of information. The case of rules with more than one variable in the consequent is also discussed. A reasoning algorithm based on the high-level fuzzy Petri net model is presented. The algorithm consists of the extraction of a subnet and an evaluation process. In the evaluation process, several fuzzy inference methods can be applied. The proposed algorithm is similar to another procedure suggested by Yager (1983), with advantages concerning the knowledge-base searching when gathering the relevant information to answer a particular kind of query     

A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system

A fuzzy reasoning and verification Petri nets (FRVPNs) model is established for an error detection and diagnosis mechanism applied to a complex fault-tolerant PC-controlled system. The inference accuracy can be improved through the hierarchical design of a two-level fuzzy rule decision tree and a Petri nets technique to transform the fuzzy rule into the FRVPNs model. Several simulation examples of the assumed failure events were carried out by using the FRVPNs and the Mamdani fuzzy method with MATLAB tools. The reasoning performance of the developed FRVPNs was verified by comparing the inference outcome to that of the Mamdani method. Both methods result in the same conclusions. Thus, the present study demonstrates that the proposed FRVPNs model is able to achieve the purpose of reasoning, and furthermore, determining of the failure event of the monitored application program.     

基于知识Petri网的确定性和不确定性联合推理

知识推理是人工智能的核心领域,旨在研究如何从已知(知识库和推理规则)推理出未知,以帮助智能体做出科学决策.而智能体所处的环境存在不可观性和不确定性,因此知识库通常不仅包含确定性知识,还包含不确定性知识,而且推理过程需要两类知识紧密协作.然而,目前的推理方法无法将两类知识统一表示,常常将两者对应的推理过程割裂进行.基于此,为了实现在统一的模型架构下完成确定性和不确定性联合推理,给出了一种知识Petri网推理方法.首先,定义了一种新的知识Petri网,使其不仅能够描述确定性的知识规范,也可以描述先验概率知识;其次,根据知识Petri网的网结构,给出了一种知识Petri网概率独立剪枝算法,能够指数级地降低不确定性推理的计算复杂性;最后,利用知识Petri网及其概率独立剪枝算法,给出了一种新型推理算法,实现了确定性和不确定性的联合推理,并利用Wumpus世界进行了演示和验证.     

Fuzzy set-based methods in instance-based reasoning

A formal framework of instance-based prediction is presented in which the generalization beyond experience is founded on the concepts of similarity and possibility. The underlying extrapolation principle is formalized within the framework of fuzzy rules. Thus, instance-based reasoning can be realized as fuzzy set-based approximate reasoning. More precisely, our model makes use of so-called possibility rules. These rules establish a relation between the concepts of similarity and possibility, which takes the uncertain character of similarity-based inference into account: inductive inference is possibilistic in the sense that predictions take the form of possibility distributions on the set of outcomes, rather than precise (deterministic) estimations. The basic model is extended by means of fuzzy set-based modeling techniques. This extension provides the basis for incorporating domain-specific (expert) knowledge. Thus, our approach favors a view of instance-based reasoning according to which the user interacts closely with the system     

On the composition of time Petri nets

Complex systems are often designed and built from smaller pieces, called components. Components are open sub-systems meant to be combined (or composed) to form other components or closed systems. It is well known that Petri nets allow such a component based modeling, relying on parallel composition and transition synchronization. However, synchronizing transitions that carry temporal constraints does not yield a compositional method for assembling components, a highly desirable property. The paper addresses this particular problem: how to build complex systems in a compositional manner from components specified by Time Petri nets (TPN). A first solution is proposed, adequate for a particular subclass of Time Petri nets but significantly increasing the complexity of components. Then an improved solution is developed, relying on an extension of Time Petri nets with two relations added on transitions. This latter solution requires a much simpler transformation of nets, does not significantly increase their complexity, and is applicable to a larger class of TPN.     

Dealing with explicit preferences and uncertainty in answer set programming

In this paper, we show how the formalism of Logic Programs with Ordered Disjunction (LPODs) and Possibilistic Answer Set Programming (PASP) can be merged into the single framework of Logic Programs with Possibilistic Ordered Disjunction (LPPODs). The LPPODs framework embeds in a unified way several aspects of common-sense reasoning, nonmonotonocity, preferences, and uncertainty, where each part is underpinned by a well established formalism. On one hand, from LPODs it inherits the distinctive feature of expressing context-dependent qualitative preferences among different alternatives (modeled as the atoms of a logic program). On the other hand, PASP allows for qualitative certainty statements about the rules themselves (modeled as necessity values according to possibilistic logic) to be captured. In this way, the LPPODs framework supports a reasoning which is nonmonotonic, preference- and uncertainty-aware. The LPPODs syntax allows for the specification of (1) preferences among the exceptions to default rules, and (2)?necessity values about the certainty of program rules. As a result, preferences and uncertainty can be used to select the preferred uncertain default rules of an LPPOD and, consequently, to order its possibilistic answer sets. Furthermore, we describe the implementation of an ASP-based solver able to compute the LPPODs semantics.     

可能性理论与不相容知识处理

Ｄ．Ｄｕｂｏｉｓ和Ｈ．Ｐｒａｄｅ提出的可能性逻辑是一种基于可能性理论的非经典逻辑，主要和于不确定证据推理。可能性逻辑不同于模糊逻辑，因为模糊逻辑处理非布尔公式，其命题中包模糊谓词，而可能性逻辑处理布尔公式，其中只包含经典命题的和谓词。本文尝试在可能性理论的框架下进行不相容知识库的维护和问题求解。这里的知识表示是基于可能性逻辑的。为此，我们提出了两种不同的方法：第一种方法在计算命题可信度时，要考虑所     

Petri net models for the semi-automatic construction of large scale biological networks

For the implementation of the virtual cell, the fundamental question is how to model and simulate complex biological networks. During the last 15 years, Petri nets have attracted more and more attention to help to solve this key problem. Regarding the published papers, it seems clear that hybrid functional Petri nets are the adequate method to model complex biological networks. Today, a Petri net model of biological networks is built manually by drawing places, transitions and arcs with mouse events. Therefore, based on relevant molecular database and information systems biological data integration is an essential step in constructing biological networks. In this paper, we will motivate the application of Petri nets for modeling and simulation of biological networks. Furthermore, we will present a type of access to relevant metabolic databases such as KEGG, BRENDA, etc. Based on this integration process, the system supports semi-automatic generation of the correlated hybrid Petri net model. A case study of the cardio-disease related gene-regulated biological network is also presented. MoVisPP is available at .     

基于知识Petri网和归结规则的推理方法

本文提出了一种基于知识Petri网和归结规则的推理方法.通过知识Petri网描述命题逻辑知识库,将归结规则映射到知识Petri网上,根据库所和变迁的连接关系,定义了知识Petri网中的归结结构.利用归结结构,给出了基于知识Petri网的归结推理算法和扩展知识库的推理算法,并利用Wumpus实例验证了推理算法.该推理方法是可靠且完备的,能够利用知识Petri网的网络结构降低计算复杂性.     

模糊时间Petri网的时间推理及其在过程监测中的应用

针对传统分析方法的不足,提出用线性逻辑给出模糊时间Petri网描述和时间推理的方法。该方法能清楚地分析模糊时间Petri网的运行行为,具体例子说明了其在系统过程监测和诊断中的应用。     

T-组合Petri网的活性和公平性分析

同步合成是研究复杂Ｐｅｔｒｉ网系统性质的有效途径．文中通过引入可引发变迁序偶的概念,研究了Ｔ－组合（同步合成）Ｐｅｔｒｉ网对子网的活性和公平性继承关系,给出了一组Ｔ－组合Ｐｅｔｒｉ网活或公平的充要条件和充分条件．这些结果对网组合同步设计具有重要的指导意义     

Structuring Acyclic Petri Nets for Reachability Analysis and Control

The incidence matrices—from places to transitions and vice versa—of an acyclic Petri net can obtain a block-triangular structure by reordering their rows and columns. This allows the efficient solution of some reachability problems for acyclic Petri nets. This result is further used in supervisory control of Petri nets; supervisors for Petri nets with uncontrollable transitions are constructed by extending the method of Yamalidou et al. (1996) to Petri nets where transitions can be executed simultaneously. A large class of Petri nets with uncontrollable transitions is given for which the maximally permissive supervisor can be realized by a Petri net. The original specification is algorithmically transformed—by using the results for acyclic Petri nets—into a new specification to take the presence of uncontrollable transitions into account. The supervisor is obtained by simple matrix multiplications and no linear integer programs need to be solved. Furthermore, a class of Petri nets is given for which the supervisor can be realized by extending the enabling rule with OR-logic.     

基于工作流网的实时协同系统模拟技术

基于Petri网和工作流的概念，提出一种实时协同系统的形式化模拟与分析技术——逻辑工作流网，逻辑工作流网是抑制弧Petri网和高级Petri网的抽象和扩展，其变迁的输入／输出受逻辑表达式的约束，它与一般工作流网相比，能够在一定程度上缓解状态空间爆炸问题，且便于系统设计人员掌握和使用，该文分析了逻辑工作流网的若干性质及组合网的性质继承问题，并以网上企业销售系统为例，说明逻辑工作流网在实时协同系统模拟分析中的应用。