## 1 Introduction  
In expert systems, fuzzy Petri nets (FPNs) are often utilized as a potential modeling tool for knowledge representation and reasoning [1; 2]. The combination of the graphical power of Petri nets and ability of fuzzy sets to express vague information makes FPNs suitable for modeling uncertain rule-based expert systems [3; 4]. An FPN is a marked graphical system containing places and transitions [5]. Due to the capacity to depict imprecise knowledge and support inference processes, FPNs have garnered an increasing interest in both academics and practitioners and have been used in a lot of fields, such as fault diagnosis [6; 7], adaptive software systems modeling [8], reliability optimization design [9], genetic regulatory network design [10], and DNA sequencing prediction [11; 12]. However, the conventional FPNs have many deficiencies, as pointed out in previous studies [13; 14]. Some scholars criticized the limitation of FPNs in knowledge representation when the knowledge parameter values are restricted to be crisp values between 0 and 1. To address this issue, some uncertainty methods have been incorporated into FPNs. For example, [PERSON] [1] represented the truth values of propositions, the weights of propositions, and the certainty factors of rules by fuzzy numbers in a weighted FPN model. Linguistic interval 2-tuples were adopted by [PERSON] et al. [15] to acquire and represent tacit knowledge in the interval-valued intuitionistic FPNs. [PERSON] et al. [16] proposed a new type of FPN for knowledge representation based on intuitionistic fuzzy set (IFS) theory. A generalized weighted FPN model, where the truth values and the weights of places were represented by intuitionistic fuzzy numbers, was proposed by [PERSON] [17]. However, due to the complexity and uncertainty involved, there exist many circumstances in which it is improper to use fuzzy sets or IFSs to accurately express experts' knowledge. Recently, the concept of picture fuzzy sets (PFSs) was proposed by [PERSON] [18] to describe uncertain phenomena and information. The PFSs, characterized by three membership degrees: positive, neutral, and negative, are more appropriate to deal with human expert evaluation information. Since its introduction, the PFS has received widespread attention in academia and has been applied in many practical fields [19; 20; 21; 22]. Knowledge acquisition plays a significant role in the development of a rule-based expert system. But there are few studies considering the acquisition of knowledge parameters of FPNs in the literature. With the increasing complexity of expert systems, difficulties arise during development, particularly when acquiring knowledge from human experts. It is an even much more difficult problem to fine-tune the knowledge parameters of fuzzy production rules (FPRs) during the knowledge base update stage [23; 24]. Consequently, the traditional process to extract FPRs from experts can be a bottleneck, causing delay in establishing an expert system [25; 26]. In this respect, [PERSON] et al. [24] suggested a knowledge acquisition approach using a fuzzy evidential reasoning approach. [PERSON] et al. [27] proposed a group decision-making approach using hesitant 2-tuple linguistic term sets to derive the initial truth values of FPNs. [PERSON] et al. [15] developed a theoretical model based on linguistic interval 2-tuples and interval-valued intuitionistic FPNs (IVIFPNs) for acquiring and representing tacit knowledge in a healthcare organization. On the other hand, domain experts can have many differences in terms of their backgrounds, attitudes, and organizations, and conflicts are inevitable. Consequently, it is important to develop methods to effectively handle conflicts, which will lead to efficiency improvements in knowledge acquisition processes. Based on the above analyses, the objective of this paper is to propose a new type of FPN, called picture fuzzy Petri nets (PFPNs), to represent and acquire imprecise and uncertain expert knowledge.