Zbigniew Suraj

A parallel algorithm for real-time decision making: a rough set approach

We consider decision tables with the values of conditional attributes (conditions) measured by sensors. These sensors produce outputs after an unknown but finite number of time units. We construct an algorithm for computing a highly parallel program represented by a Petri net from a given decision table. The constructed net allows to identify objects in decision tables to an extent which makes appropriate decisions possible. The outputs from sensors are propagated through the net with maximal speed. This is done by an appropriate implementation of all rules true in a given decision table. Our approach is based on rough set theory (Pawlak, 1991). It also seems to have some significance for theoretical foundations of real-time systems.

Some Remarks on Extensions and Restrictions of Information Systems

Information systems (data tables) are often used to represent experimental data [4],[5],[8]. In [16] it has been pointed out that notions of extension and restriction of information system are crucial for solving different class of problems [6],[7],[10]-[11],[12]-[15]. The intent of this paper is to present some properties of an information system extension (restriction) and methods of their verification.

Rough Computing: Theories, Technologies and Applications

Rough set theory is a new soft computing tool which deals with vagueness and uncertainty. It has attracted the attention of researchers and practitioners worldwide, and has been successfully applied to many fields such as knowledge discovery, decision support, pattern recognition, and machine learning. Rough Computing: Theories, Technologies and Applications offers the most comprehensive coverage of key rough computing research, surveying a full range of topics from granular computing to pansystems theory. With its unique coverage of the defining issues of the field, this commanding research collection provides libraries with a single, authoritative reference to this highly advanced technological topic.

Rough set methods for the synthesis and analysis of concurrent processes

Abstract. In this Chapter rough set methods for the modeling of concurrent processes are considered. The research is motivated by the problems coming from the domains such as, for example: knowledge discovery systems, data mining, control design, decomposition of information systems, object identification in real-time. this Chapter includes, in particular, the description of automatic methods for the modeling and analysis of concurrent systems specified by information systems. In this Chapter the following problems are considered: 1. The synthesis problem of concurrent systems specified by information systems. 2. The problem of discovering concurrent data models from experimental tables. 3. The re-engineering problem for cooperative information systems. 4. The real-time decision making problem. 5. The control design problem for discrete event systems.

An application of rough set methods in control design

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].

Approximate real-time decision making: Concepts and rough fuzzy Petri net models

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 Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems

We discuss the synthesis problem of concurrent systems from observations or specification encoded in data table (information system) [Pawlak,1991]. In the paper we first introduce a new notion of a so-called dynamic information system, and then we apply this notion as a tool for specification of concurrent systems behaviour [Pawlak,1992], [Pawlak,1997]. Finally, we present two methods of construction from any dynamic information system DS with its underlying system S, and transition system TS describing the behaviour of DS, a concurrent model in the form of an elementary net system N [Thiagarajan,1987] with the following property: a given transition system TS is isomorphic to the transition system associated with the constructed net system N. In the first method we assume that the data table representing a given dynamic information system DS contains the whole knowledge about the observed or specified behaviour of the system. For this setting, we adopt a method of construction a solution of the synthesis problem of concurrent system models suggested by [Desel and Reisig,1996]. A solution of the synthesis problem is any net which is constructed using the concept of regions of transition systems, introduced in [Ehrenfeucht and Rozenberg,1990]. The second method presented in the paper is based on approach that a given data table consists of only partial knowledge about the system behaviour. Thus, we at first compute an extension DS′ of the dynamic information system DS, i.e. the system in which the set of all global states of DS′ is consistent with all rules true in the underlying information system S of DS, and the set of all global states of DS′ represents the largest extension of S consistent with the knowledge represented by S. Next, for finding a solution of the synthesis problem considered here we use the first method. This approach is based on rough set theory [Pawlak,1991] and Boolean reasoning [Brown,1990]. We have implemented program on IBM PC generating a net model from a dynamic information system.

Discovery of Concurrent Data Models from Experimental Tables: A Rough Set Approach

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 consists in a determination of rules which yield a decomposition of experimental data tables; the components are then used to define fragments of the global system corresponding to a table. The method has been applied for automatic data models discovery from experimental tables with Petri nets as models for concurrency.

Design of Rough Neurons: Rough Set Foundation and Petri Net Model

This paper introduces the design of rough neurons based on rough sets. Rough neurons instantiate approximate reasoning in assessing knowledge gleaned from input data. Each neuron constructs upper and lower approximations as an aid to classifying inputs. The particular form of rough neuron considered in this paper relies on what is known as a rough membership function in assessing the accuracy of a classification of input signals. The architecture of a rough neuron includes one or more input ports which filter inputs relative to selected bands of values and one or more output ports which produce measurements of the degree of overlap between an approximation set and a reference set of values in classifying neural stimuli. A class of Petri nets called rough Petri nets with guarded transitions is used to model a rough neuron. An application of rough neural computing is briefly considered in classifying the waveforms of power system faults. The contribution of this article is the presentation of a Petri net model which can be used to simulate and analyze rough neural computations.

Reconstruction of cooperative information systems under cost constraints: a rough set approach

Abstract Bazan et al. have proposed a method for synthesis of cooperative information systems specified by data tables (information systems). The basic idea of the method concerns a decomposition of data table into functional components (modules) linked by communication lines (communications). On the basis of this method Suraj elaborated a strategy for reconstruction of the synthetized cooperative information system when the specification for the system is changing e.g. by adding new requirements. The strategy allows us to produce a plan of reconstruction of a given system by specifying which parts (modules and communications) can remain unchanged and which must be changed to satisfy new requirements. The aim of the paper is to present an approach for the reconstruction of the synthetized system under cost constraints. The cost of the reconstruction is treated as the cost of adding new functional modules, communication lines or their modifications. It is estimated with respect to any reduct and any covering in both systems i.e. in a given system and a reconstructed one. In fact, we define a new concept concerning the cost of a rule mentioned as the sum of the costs of attributes on the left-hand side of the rule. We assume that an information system representing data table together with a vector of attribute costs are given. The attribute cost can be interpreted e.g. the time of the measurement of its concrete value. We give also a simple example illustrating our approach as well as some information about a computer system for supporting the process of construction and/or reconstruction of a given cooperative information system specified by an information system. Our approach is based on rough set theory and it can be applied in the system technology domain to adaptive reorganization of existing cooperative information systems.