The study attempts to assess the decision-making abilities of the knowledge-based system model based on classic fuzzy Petri nets and their subtypes depending on the mode of their operation. In addition, the relationship between the quantity and quality of the proposed decisions was investigated using additional knowledge of the structural and dynamic properties of the net used in the model. The change in the dynamics of the net model was influenced by the appropriate selection of the admissible triples of operators assigned to net transitions in accordance with the knowledge about the partial order between the triples. The theoretical considerations were supported by the analysis and evaluation of the results of the experiments carried out on the net model of the exemplary knowledge-based system for train traffic control. According to the authors, this work fits into the list of challenges formulated in the review article on the state of research on the theory and applications of fuzzy Petri nets, prepared by authors Zhou and Zain and published in Artificial Intelligence Review, 45, 405–446, 2016.

The paper attempts to answer the question of whether there are, and if so, what, relationships between the selected properties of generalized fuzzy Petri nets and the features expected by designers of knowledge-based systems models they construct. The search for such relationships is carried out in the area of selected structural and dynamic properties, methods of marking changes and operating modes of such a net class and their optimized versions. Looking for the desired features of the designed models, the subject of research is their quality, efficiency, numerical stability and determinism. The research trend proposed in this work seems to fall within the scope of challenges presented in the review article on the state of research in the field of fuzzy Petri net theory and applications, developed by the authors Zhou & Zain and published in “Artificial Intelligence Review”, 45, 405–446, 2016.

In this paper, we analyze selected structural and dynamic properties of uninorm Petri nets in terms of their use in modeling knowledge-based systems operating in an uncertain environment. The uninorm Petri nets use uninorms to describe their behavior. Uninorms are a special type of aggregation functions that generalize both t-norms and s-norms. This generalization is that in the case of a uninorm, the neutral element can take any value in the unit interval, in contrast to triangular norms, for which the neutral element is equal to 1 or 0 depending on whether the triangular norm is a t-norm or an s-norm. Thanks to this, by manipulating the neutral element in the unit interval, it is possible to better match the behavior of the used net to the requirements of the modeled system. When modeling systems using uninorm Petri nets, as well as nets using triangular norms, the following questions are important for the designer of such models: (1) What properties of the net affect the uniqueness of the model's decisions? (2) How to choose uninorms assigned to net transitions so that the behavior of the net model is deterministic? This work provides answers to these two questions above. The subject of this paper is a continuation of the author's earlier research on generalized fuzzy Petri nets based on triangular norms. This also falls within the range of challenges outlined in a review article on the state of research on the theory and applications of fuzzy Petri nets, developed by Zhou & Zain authors and published in Artificial Intelligence Review, 45, 405–446, 2016.

The paper presents a comparison of classical (ZtN, GtN, ZsN) and optimized (ZtN, ZtN, LsN) triples of functions for solving the hierarchical structure of the problem of passenger transport logistics. It covers the description of the subject area and its hierarchical scheme, the creation of production rules based on the knowledge of the experts, the creation of a weighted fuzzy Petri nets model with different triples, and the following analysis of the results. In order to illustrate the obtained results, a simulation was used in special software - PNeS®. The results of the experiment showed the development of the hierarchy and the following observation on calculations: the optimized triple of functions achieves higher output values, but at the same time, it can lead to an alternative decision.

In this paper, we present an approach to construct a concurrent algorithm that supports real-time decision making based on the knowledge extracted from empirical data. The data is represented by a decision table in the Pawlak sense, while the concurrent algorithm is represented as a weighted priority fuzzy Petri net. This idea overcomes the difficulties that arise when field experts are entrusted with determining the values of net parameters. In the proposed approach, we assume that the decision tables contain conditional attribute values that are obtained from measurements made by sensors in real time. The Petri net built within the presented conception allows for the fastest possible identification of objects in decision tables in order to make the right decision. The sensor output values are transmitted over the net at the maximum possible speed. We achieve this effect thanks to the appropriate implementation of all true and acceptable rules generated from a given decision table.

Petri net is a strong mathematical modeling language that can be used to represent parallel or concurrent activities in a system. The practical use of Petri nets is strongly dependent upon the existence of adequate computer tools. For Petri nets one needs editors as well as analysis programs. Modern computers provide an opportunity to work directly with the graphical representations of Petri nets. This paper describes integrated graphical Petri net tools called PNeS for construction of nets, as well as modification and analysis. PNeS allows us to work with different classes of Petri nets. Several analysis tools are available for each of these classes. PNeS works on any computer under any operating system.

In this paper, a fuzzy Petri net model has been proposed based on generalized weighted fuzzy production rule. Generalization has been made on the basis of inclusion of the intuitionistic fuzzy set with the associated intuitionistic fuzzy weight as input values. Such complex model may often give rise to a fuzzy Petri net model based on a complex logical operator resulting in higher computational complexity. For this reason, a dual fuzzy Petri net model of the form (N,N') has been proposed based on a simple weighted logical operator which confirms lesser computational complexity. Approximate reasoning algorithms have been proposed based on this dual structure of a fuzzy Petri net. A numerical example concerning a train traffic problem justifies the relevance of the approach in a real-life problem.

In 1973 Lotfi Zadeh introduced the theory of fuzzy logic [17]. Fuzzy logic was an extension of Boolean logic so that it allowed using not only Boolean values to express reality. One kind of basic logical operations in fuzzy logic are so-called fuzzy implications. From over eight decades a number of different fuzzy implications have been described [3] - [16]. In the family of all fuzzy implications the partial order induced from [0,1] interval exists. Pairs of incomparable fuzzy implications can generate new fuzzy implications by using min(inf) and max(sup) operations. As a result the structure of lattice is created ([1], page 186). This leads to the following question: how to choose the correct functions among basic fuzzy implications and other generated as described above. In our paper, we propose a new method for choosing implications. Our method allows to compare two fuzzy implications. If the truth value of the antecedent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication consequent. In other words, we can choose the fuzzy implication, which has the greatest or the smallest truth value of the implication consequent or which has greater or smaller truth value than another implication. Primary results regarding this problem are included in the paper [14].

The aim of this paper is to present a new version of a bibliographic database system - Rough Set Database System (RSDS). The RSDS system, among others, includes bibliographic descriptions of publications on rough set theory and its applications. This system is also an experimental environment for research related to the processing of bibliographic data using the domain knowledge and the related information retrieval.

The aim of this paper is to present the methods and algorithms of information systems decomposition. In the paper, decomposition with respect to reducts and the so-called global decomposition are considered. Moreover, coverings of information systems by components are discussed. An essential difference between two kinds of decomposition can be observed. In general, global decomposition can deliver more components of a given information system. This fact can be treated as some kind of additional knowledge about the system. The proposed approach is based on rough set theory. To demonstrate the usefulness of this approach, we present an illustrative example coming from the economy domain. The discussed decomposition methods can be applied e.g. for design and analysis of concurrent systems specified by information systems, for automatic feature extraction, as well as for control design of systems represented by experimental data tables.

This paper presents a new class of Petri nets called generalised fuzzy Petri nets. The new class extends the existing fuzzy Petri nets by introducing three operators in the form of triangular norms, which are supposed to function as substitute for th

In the paper, a computer tool called ROSECON, used for modeling and analyzing systems of concurrent processes, is described. A special attention is focused on synthesis and verification of concurrent systems specified by information systems. Two kinds of models, synchronous and asynchronous, are considered. In the first approach, all processes included in the modeled system are synchronized globally whereas in the second one, each process is synchronized individually. The presented tool allows generating automatically an appropriate model of a system of concurrent processes, in the form of colored Petri nets, from the specification given by an information system. Analysis of the model behaviors enables users to verify the correctness and/or optimality of the obtained models and to provide some modification procedures to get correct and/or more optimal solutions. Examples of selected well known problems in concurrency, in the paper, emphasize usefulness of the tool in the designing systems of concurrent processes.

The aim of this paper is to present a new methodology for knowledge representation and reasoning based on generalised fuzzy Petri nets. Recently, this net model has been proposed as a new class of fuzzy Petri nets. The new class extends the existing fuzzy Petri nets by introducing two operators: t-norms and s-norms, which are supposed to function as substitute for the min and max operators. This model is more flexible than the traditional one as in the former class the user has the chance to define the input/output operators. The choice of suitable operators for a given reasoning process and the speed of reasoning process are very important, especially in real-time decision support systems. The advantages of the proposed methodology are shown in an application in train traffic control decision support.

The main goal of this paper is to give the outline of some approach to intelligent searching the Rough Set Database System (RSDS). RSDS is a bibliographical system containing bibliographical descriptions of publications connected with methodology of rough sets and its applications. The presented approach bases on created ontologies which are models for the considered domain (rough set theory, its applications and related fields) and for information about publications coming from, for example, abstracts.

The minimal inhibitory rules for information systems can be used for construction of classifiers. We show that almost all information systems from a certain large class of information systems have relatively short minimal inhibitory rules. However, the number of such rules is not polynomial in the number of attributes and the number of objects. This class consists of all k-valued information systems, k ⩾ 2, with the number of objects polynomial in the number of attributes. Hence, for efficient construction of classifiers some filtration techniques in rule generation are necessary. Another way is to work with lazy classification algorithms based on inhibitory rules.

Summary form only given. This paper presents an overview of algorithms for automated discovering concurrent models from data tables. Constructed models have the form of coloured Petri nets and can be used to determine different properties concerning structures and behaviours of modeled systems; extract new knowledge about systems or verify their descriptions or specifications. We consider a description of concurrent systems by information systems as well as dynamic information systems.

The aim of this paper is to present some remarks on computing maximal consistent extensions of dynamic information systems. Dynamic information systems can be used as a tool for description of concurrent systems. In this case, they include the knowledge about global states and transitions between them observed in given concurrent systems. The task of creating a maximal consistent extension is to find all global states and all transitions between them which are consistent with the knowledge included in data tables representing a dynamic information system. A method for computing such an extension is given. The method presented here seems to be more efficient than methods presented earlier in the literature. Our approach is based on the rough set theory.

The paper presents an approach to the synthesis problem. The approach is based on the rough set philosophy, Boolean reasoning and Petri nets. Information systems as a tool for specification of concurrent systems are treated. However colored Petri nets as a model for concurrency are used. The proposed approach in the ROSECON computer system has been implemented. It can be used to deal with various problems arising from the process design domain.

The paper deals with an automatic concurrent control design method derived from the specification of a discrete event control system represented in the form of a decision table. The main stages of our approach are: the control specification by decision tables, generation of rules from the specification of the system behavior, and converting rules set into a concurrent program represented in the form of a Petri net. Our approach is based on rough set theory [17].

This paper considers the construction of Petri nets to simulate the computation performed by decision systems. Algorithms are given to construct Petri nets which correspond to decision rules, information systems, and real-time decision systems. Rough as well as rough fuzzy Petri net extensions of colored and generalized fuzzy Petri nets are used to create highly parallel programs to simulate reasoning system computations. Constructed nets make it possible to evaluate the design of decision system tables, and to trace computations in rules derived from decision tables. Start places of nets are connected to Dill process receptors which await input from the environment. Time consumption during the propagation of outputs from sensors in a decision system is monitored with timers called approximate time windows, which measure durations between firings of decision transitions relative to time granules with names such as early, ontime, and late. Guards on decision transitions are propositional functions which permit a rule to fire for some sensor values and not for others. In addition, the design of guards makes allowance for multivalued logic, where conditional sensor readings are assessed in terms of their degree of membership in sensor measurement granules. In some cases, a rule can fire if the degree of truth of its guard (premise) is above some threshold. Through simulation, designers can arrive at reasonable estimates of the period of timers on decision transitions. The approach to simulating computations by decision systems presented in this paper results in fast, massively parallel programs implementable on a multiprocessor. © 1999 John Wiley & Sons, Inc.

The main objective of machine discovery is the determination of relations between data and of data models. In the paper we describe a method for discovery of data models represented by concurrent systems from experimental tables. The basic step consi