Fuzzy Petri nets (FPNs) are a useful instrument for modelling expert systems to conduct knowledge representation and reasoning. Many studies have been carried out for improving the performance of FPNs in terms of their accurate representation of knowledge and power of approximate reasoning. Nevertheless, the current representation methods with FPNs are unable to handle the uncertain linguistic knowledge given by domain experts and the reliability of their judgments. In addition, the existing reasoning algorithms have no way to capture the interrelationship of the propositions with the same output transition. Therefore, we present a new type of FPNs, called 2-dimensional uncertain linguistic Petri nets (2DULPNs). The 2-dimensional uncertain linguistic variables (2DULVs) and Choquet integral are combined for knowledge representation and reasoning for the first time. The truth degrees of propositions, thresholds and certainty values of linguistic production rules are denoted as 2DULVs. Some new aggregated operators based on Choquet integral are proposed and used in the approximate reasoning to capture the interactions among antecedent propositions. Finally, an equipment fault diagnosis example is provided to illustrate the correctness and effectiveness of the proposed 2DULPN model.

In previous studies, fuzzy Petri nets (FPNs) have been used for knowledge representation and reasoning in various areas. However, the traditional FPNs have limited abilities in representing uncertain knowledge and conducting approximate reasoning when applied in practical situations. In addition, the knowledge parameters in existing FPNs are usually given by a small number of experts. To address these issues, a grey reasoning Petri net (GRPN) model is proposed in this article for knowledge representation and reasoning under large group environment. In this model, grey production rules in an expert system are modeled by the GRPNs, where grey numbers are used to represent the truth degrees of places, certainty values, and the thresholds on output arcs of transitions. The grey weighted Bonferroni mean operator is adopted as a substitute of the classical min and max operators in the developed grey reasoning algorithm to capture the interrelationships of input places and the interrelationships between transitions. Furthermore, a large group decision-making method is introduced for obtaining the knowledge parameters of GRPNs based on the grey correlation analysis. Finally, the usefulness and effectiveness of the proposed GRPN model is demonstrated by a real-world risk evaluation example.

Fuzzy Petri nets (FPNs) are a vital modeling technique for the construction of knowledge-based systems, which have been commonly used in many fields, such as fault diagnosis, risk assessment, workflow management, and disassembly process planning. However, the conventional FPNs have been blamed for the following reasons: 1) the representation parameters in FPNs cannot precisely model experts' experience since it is difficult to manage the fuzziness and randomness of knowledge assessments simultaneously, and 2) the weight coefficients in the existing approximate reasoning algorithms are hardly enough to reflect the associated weights of reordered places. In response, we propose a new type of FPNs, called cloud reasoning Petri nets (CRPNs) based on the concept of interval clouds and the hybrid averaging operator. The cloud production rules in a knowledge-based system are modeled by CRPNs, where the truth degrees of places, the certainty factors of rules, and the thresholds of transitions are represented by interval clouds. Moreover, a matrix operation-based reasoning algorithm is proposed to improve the efficiency of calculating final truth degrees, in which both local and ordered weight coefficients are taken into consideration. Finally, a practical example concerning a power system is provided to demonstrate the usefulness and advantages of the proposed CRPN model.