Experiential knowledge representation and reasoning based on linguistic Petri nets with application to aluminum electrolysis cell condition identification
Introduction
Petri net can be simply defined as a mathematical description that can provide a visual or graphical representation of a system, however, in the real world, most experiential knowledge is fuzzy and uncertain [2]. Fuzzy Petri nets (FPNs) are typically used when modeling an imprecise environment with no well-defined measurements exists or flexible manufacturing [17]. Due to the strong capabilities of knowledge representation and reasoning (KRR), fuzzy Petri nets (FPNs) have become a promising modeling strategy for knowledge-based systems [16]. In FPNs, places represent propositions, transitions represent fuzzy rules, and directed arcs represent the relationships between places and transitions [15]. Consequently, FPNs are characterized by graphical power [5] and the ability to model rule-based experiential knowledge [18]. Recently, FPNs have attracted more attentions from researchers and engineers, being extensively used in multiple fields of study, such as risk assessment [12], production ecosystem designing [35], novel code plagiarism detection [23], sequential control [8], abnormal condition monitoring [20] and fault section identification [13].
Despite the successful implementation of FPNs, these traditional FPNs still have some deficiencies, which were pointed out in previous studies. Some researches criticized the limitations for KRR that the values of marking and thresholds were restricted to be crisp [32]. Thus, in some literatures, uncertainty theories had been incorporated into FPNs to enhance the capability of KRR. For example, picture fuzzy sets which consist of degree of positive, neutral and negative membership to represent experiential knowledge, were adopted to improve FPNs [26]. Intuitionistic FPNs (IFPNs) could provide the hesitation and uncertainty for the certainty factor [9], were developed in [33]. Cloud model theory and linguistic 2-tuples, which were used to capture more uncertainty of experiential knowledge in [19], were introduced to FPNs, respectively. In addition, FPNs with transformable weights were introduced to develop a type of adaptive fuzzy higher order Petri nets in [1]. The deficiency that only one wight of a proposition was shared by different rules, was solved in [14]. The same place shared different weights with transitions, and different threshold values were assigned to input, output places and transitions in [28]. Moreover, the certainty factor was assigned to each output arc, influencing on the truth degree of each output proposition [14]. Although the above improvements made to FPNs had enhanced the capability of knowledge representation, they could not precisely model experiential knowledge of domain experts since the cognitive inconsistency was not ‘embraced’ by the improved FPNs.
The min, max, and product operators were usually used for knowledge reasoning in earlier FPNs [17]. However, because of the increasing complexity of systems in the real world, the above operators were inefficient. To solve this problem, research attention has also focused on the enhancement of inference efficiency and reliability of FPNs. In [24], the t-norms and s-norms were introduced to FPNs, to substitute the min, max and product operators, thereby they would be useful for the design of a Petri net model for a given decision support system. The reasoning methods based on reachability tree were developed in [2]. In addition, with backwards search and forward algorithm, a decomposition algorithm was proposed to divide a large-scale FPNs into a group of sub-FPNs [36]. However, these inference methods were inefficient since all reachable paths should be enumerated, resulting in a time-consuming process [10]. Some improved reasoning algorithms, which adopted a high-level form to perform knowledge reasoning without enumerating all possible paths, were developed in [22]. But, the ordered weights of propositions were ignored in the extended inference methods, which may cause distorted inference results. In addition, there were some other relevant researches proposed to deal with some special problems, such as time delays, negation issues and so on [27].
Based on the above analyses, despite the successful improvement of conventional FPNs, little attention has been spent to model experiential knowledge, while simultaneously considering cognitive inconsistencies, fuzziness and uncertainties. In this paper, cognitive inconformity denotes that the experiential knowledge of each technician is not strictly identical. In the aluminum electrolysis process, aluminum electrolysis cell condition identification (AECCI) can be defined as knowledge-based work, due to detection blind area and complexity [29]. Therefore, linguistic terms are usually used to depict the states of characteristic variables and to express the experience of aluminum electrolysis technicians. It is important to highlight that although the experiential knowledge is different for each aluminum electrolysis expert or technician, all of this knowledge can ensure the stable and efficient operation of the system. As presented in [6], the crisp values of propositions were difficult to accurately represent the cognition, fuzziness and uncertainty discussed within the system. Accordingly, integrating different types of cognition and modeling fuzziness and uncertainty into a uniform knowledge representation model is significant for AECCI. Due to this introduction of the secondary memberships, the footprint of uncertainty can ‘embrace’ the uncertainties of different experts/technicians in expressing experiential knowledge, and the interval type-2 fuzzy set (IT2FS) will have the ability to deal with the uncertainties within an individual, as well as among multiple individuals at the same time. However, a type-1 fuzzy set can only deal with uncertainties within an individual. Therefore, in this work the interval type-2 fuzzy set (IT2FS) is utilized to capture the varied experiential knowledge of multiple aluminum electrolysis experts/technicians. In order to get a uniform knowledge representation model, linguistic Petri nets (LPNs) were proposed based on type-2 fuzzy theory, FPNs and extended TOPSIS (ETOPSIS) for KRR. The value of each proposition take the form of IT2FS. Moreover, the ETOPSIS was developed to determine the value of each linguistic term. The interval type-2 fuzzy sets (IT2FSs) ordered weighted averaging (IT2FOWA) operator was also proposed to enhance the inference capability.
The remainder of this paper is organized as follows. In Section 2, IT2FSs and aggregation operators are introduced. In Section 3, the ETOPSIS, LPNs model and parallel reasoning algorithm are presented. In Section 4, two numerical examples are used, demonstrating the effectiveness of the proposed ETOPSIS and LPNs model, respectively. To illustrate the validity and advantages of the proposed methods, the ETOPSIS and LPNs are used for AECCI. Finally, the conclusion is discussed in Section 5.
Section snippets
IT2FSs and aggregation operators
In this section, we introduce the basic definitions and aggregation operators of IT2FSs to facilitate the study.
Definition of LPNs
As a result of the cognitive inconsistency of experts/technicians, linguistic fuzziness and uncertainty, some parameters of FPNs will take the form of IT2FS in this study. Considering the limitations that information loss is based on min, max and product, the IT2FOWA operator was introduced to improve the capacity of knowledge reasoning. Definition 7 LPNs structure is defined as an 12-tuplewhere is a finite set of places; is a finite set of
AECCI Based on LPNs and extended TOPSIS
In this section, the proposed LPNs and extended TOPSIS were used for AECCI. Firstly, examples were utilized to verify the validity and effectiveness of the proposed methods [3], [14], respectively. Then, they are used for AECCI to demonstrate the advantages of the proposed methods.
Conclusions
In this paper, an LPNs model was proposed to enhance the KRR ability of conventional FPNs, with potential applications for AECCI. In contrast to existing FPNs, LPNs took advantage of IT2FSs, FPNs and extended TOPSIS to model experiential knowledge. The truth degrees of places, input thresholds, output thresholds, certainty factors and so on all took the form of IT2FSs. The IT2FOWA operator was used for knowledge reasoning, while considering the limitation of min, max, and product operators. Two
Declaration of Competing Interest
Authors have no conflict of interest to declare.
Acknowledgements
This project is supported by the National Natural Science Foundation of China (61773405, 61533020, 61751312 and 61725306).
References (36)
- et al.
Reasoning dynamic fuzzy systems based on adaptive fuzzy higher order petri nets
Inf. Sci.
(2014) - et al.
Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method
Expert Syst. Appl.
(2010) - et al.
Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number
Knowl. Based Syst.
(2013) - et al.
Fuzzy petri nets for knowledge representation and reasoning: a literature review
Eng. Appl. Artif. Intell.
(2017) - et al.
Towards timed fuzzy petri net algorithms for chemical abnormality monitoring
Expert Syst. Appl.
(2011) - et al.
Uncertainty measures for interval type-2 fuzzy sets
Inf. Sci.
(2007) - et al.
A novel dynamic timed fuzzy petri nets modeling method with applications to industrial processes
Expert Syst. Appl.
(2018) - et al.
A data and knowledge collaboration strategy for decision-making on the amount of aluminum fluoride addition based on augmented fuzzy cognitive maps
Engineering
(2019) - et al.
A decomposition algorithm of fuzzy petri net using an index function and incidence matrix
Expert Syst. Appl.
(2015) Fuzzy backward reasoning using fuzzy petri nets
IEEE Trans. Syst. Man. Cybern.Part B (Cybernetics)
(2000)
Semantic network based on intuitionistic fuzzy directed hyper-graphs and application to aluminum electrolysis cell condition identification
IEEE Access
Tradeoffs between trust and survivability for mission effectiveness in tactical networks
IEEE Trans. Cybern.
Modeling self-adaptive software systems by fuzzy rules and petri nets
IEEE Trans. Fuzzy Syst.
Multiple attribute group decision making based on interval type-2 fuzzy cross-entropy and ranking value
Automation
Sequential control algorithm in the form of fuzzy interpreted petri net
IEEE Trans. Syst. Man Cybern.Part B
A new method for intuitionistic fuzzy multi-attribute decision making
IEEE Trans. Syst. Man Cybern.Syst.
Fuzzy knowledge representation and reasoning using a generalized fuzzy petri net and a similarity measure
Soft Comput.
The simulation-fuzzy method of assessing the risk of air traffic accidents using the fuzzy risk matrix
Saf. Sci.
Cited by (22)
Multicriteria requirement ranking based on uncertain knowledge representation and reasoning
2024, Advanced Engineering InformaticsFailure mode and effect analysis with ORESTE method under large group probabilistic free double hierarchy hesitant linguistic environment
2024, Advanced Engineering InformaticsConsensus-based probabilistic hesitant intuitionistic linguistic Petri nets for knowledge-intensive work of superheat degree identification
2024, Advanced Engineering InformaticsA dynamic spatial distributed information clustering method for aluminum electrolysis cell
2023, Engineering Applications of Artificial Intelligence