Fourth International Conference on Computer Science and Information Technology (CoSIT 2017) | Matrix (Mathematics)

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This work presents the use of Adaptive Coloured Petri Net (ACPN) in support of decision making. ACPN is an extension of the Coloured Petri Net (CPN) that allows you to change the network topology. Usually, experts in a particular field can establish a set of rules for the proper functioning of a business or even a manufacturing process. On the other hand, it is possible that the same specialist has difficulty in incorporating this set of rules into a CPN that describes and follows the operation of the enterprise and, at the same time, adheres to the rules of good performance. To incorporate the rules of the expert into a CPN, the set of rules from the IF - THEN format to the extended adaptive decision table format is transformed into a set of rules that are dynamically incorporated to APN. The contribution of this paper is the use of ACPN to establish a method that allows the use of proven procedures in one area of knowledge (decision tables) in another area of knowledge (Petri nets and Workflows), making possible the adaptation of techniques and paving the way for new kind of analysis.
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    Dhinaharan Nagamalai et al. (Eds) : CoSIT, SIGL, AIAPP, CYBI, CRIS, SEC, DMA - 2017 pp. 17– 27, 2017. © CS & IT-CSCP 2017 DOI : 10.5121/csit.2017.70403 U SE   OF    A  DAPTIVE   C OLOURED   P ETRI   N ETWORK    IN   S UPPORT   OF   D ECISION- M  AKING Haroldo Issao Guibu 1  and João José Neto 2 1 Instituto Federal de Educação, Ciência e Tecnologia de São Paulo, Brazil 2 Escola Politécnica da Universidade de São Paulo, Brazil  A  BSTRACT    This work presents the use of Adaptive Coloured Petri Net (ACPN) in support of decision making. ACPN is an extension of the Coloured Petri Net (CPN) that allows you to change the network topology. Usually, experts in a particular field can establish a set of rules for the  proper functioning of a business or even a manufacturing process. On the other hand, it is  possible that the same specialist has difficulty in incorporating this set of rules into a CPN that describes and follows the operation of the enterprise and, at the same time, adheres to the rules of good performance. To incorporate the rules of the expert into a CPN, the set of rules from the  IF - THEN format to the extended adaptive decision table format is transformed into a set of rules that are dynamically incorporated to APN.   The contribution of this paper is the use of  ACPN to establish a method that allows the use of proven procedures in one area of knowledge (decision tables) in another area of knowledge (Petri nets and Workflows), making possible the adaptation of techniques and paving the way for new kind of analysis.  K   EYWORDS    Adaptive Petri Nets, Coloured Petri Nets, Adaptive Decision Tables 1.   I NTRODUCTION Coloured Petri Nets are an improvement of the srcinal Petri Nets introduced by Carl Petri in the 1960s. Because of their ability to describe complex problems, their use has spread both in the engineering area and in the administrative area. Adaptive Coloured Petri Nets introduces an adaptive layer composed of several functions capable of changing the network topology, including or excluding places, transitions and arcs. In the area of decision support systems, the tools most used by specialists are the decision tables, which gave rise to several methods to help managers in their choices. Among the methods developed for decision support there are the so-called multicriteria methods, which involve the adoption of multiple, hierarchically chained decision tables. In the process of improving the decision tables, new features are observed, which, although more complex, give the specialists the ability to describe their work model in a more realistic way. This paper describes the operation mode of the decision tables and the way of transcribing the rules of the tables for extended functions of Petri nets. By embedding a decision table in a Petri net, the simulation and analysis tools available in the Petri net development environments can be used, which leads to an increase in confidence in the decision criteria adopted.  18 Computer Science & Information Technology (CS & IT) 2.   D ECISION   T ABLES The Decision Table is an auxiliary tool in describing procedures for solving complex problems [9]. A Conventional Decision Table, presented in Table 1, can be considered as a problem composed of conditions, actions and rules where conditions are variables that must be evaluated for decision making, actions are the set of operations to be performed depending on the conditions at this moment, and the rules are the set of situations that are verified in response to the conditions . . Table 1. Conventional Decision Tables. Rules column Conditions rows Condition values Actions rows Actions to be taken A rule is constituted by the association of conditions and actions in a given column. The set of rule columns should cover all possibilities that may occur depending on the observed conditions and the actions to be taken. Depending on the current conditions of a problem, we look for which table rules satisfy these conditions: ã If no rule satisfies the conditions imposed, no action is taken; ã If only one rule applies, then the actions corresponding to the rule are executed; ã If more than one rule satisfies the conditions, then the actions corresponding to the rules are applied in parallel. ã Once the rules are applied, the table can be used again. ã The rules of a decision table are pre-defined and new rules can only be added or deleted by reviewing the table. 2.1. Adaptive Decision Tables In 2001 Neto introduces the Adaptive Decision Table (ADT) [7] from a rule-driven adaptive device. In addition to rule lookup, an ADT allows you to include or exclude a rule from the rule set during device operation. As an example of its potential, Neto simulates an adaptive automaton to recognize sentences from context-dependent languages. In the ADT a conventional decision table is the underlying device to which a set of lines will be added to define the adaptive functions. Adaptive functions constitute the adaptive layer of the adaptive device governed by rules. Modifying the rule set implies increasing the number of columns in the case of rule insertion, or decreasing the number of columns in the case of rule deletion. In both cases the amount of lines remains fixed. The Adaptive Decision Table (ADT) is capable to change its set of rules as a response to an external stimulus through the action of adaptive functions [7]. However, the implementation of more complex actions is not a simple task due to the limitation of the three elementary operations supported by ADT [9]. When a typical adaptive device is in operation and does not find applicable rules, it stops executing, indicating that this situation was not foreseen. For continuous operation devices, which do not have accepting or rejecting terminal states, stopping their execution would recognize an unforeseen situation and constitutes an error.  Computer Science & Information Technology (CS & IT) 19 2.2. Extended Adaptive Decision Tables To overcome this problem faced by continuous operation devices, Tchemra [9] created a variant of ADT and called it Extended Adaptive Decision Table (EADT), shown in Table 2 . Table 2. Extended Adaptive Decision Table. Adaptive Actions Rules Conventional Criteria Criteria values Decision Alternative Actions to be Table Set of elementary applied Set of Auxiliary auxiliary Auxiliary Adaptive actions Functions to be functions functions called Adaptive Adaptive Adaptive actions to be layer functions performed In EADT, adaptability does not apply only during the application of a rule, but also in the absence of applicable rules. A modifier helper device is queried and the solution produced by the modifier device is incorporated into the table in the form of a new rule, that is, in the repetition of the conditions that called the modifier device, the new rule will be executed and the modifier device will not need to be called. 3.   P ETRI N ETS   3.1. Ordinary Petri Nets Petri nets (PN) were created by Carl Petri in the 1960s to model communication between automata, which at that time also encompassed Discrete Event Systems (DES). Formally, a Petri net is a quadruple PN= [P, T, I, O] where P is a finite set of places; T is a finite set of transitions; I: (P x T) → N is the input application, where N is the set of natural numbers;  O: (T x P) →  N is the output application, where N is the set of natural numbers A marked network is a double MPN = [PN, M], where PN is a Petri net and M is a set with the same dimension of P such that M (p) contains the number of marks or tokens of place p. At the initial moment, M represents the initial marking of the MPN and it varies over time as the transitions succeed. In addition to the matrix form indicated in the formal definition of the Petri nets, it is possible to interpret the Petri nets as a graph with two types of nodes interconnected by arcs that presents a dynamic behaviour, and also as a system of rules of the type condition →  action which represent a knowledge base. Figure 1 shows a Petri net in the form of a graph, in which the circles are the Places , the rectangles are the Transitions . The Places and the Transitions constitute the nodes of the graph and they are interconnected through the oriented arcs  20 Computer Science & Information Technology (CS & IT) Figure 1. Example of a Petri Net 3.2. Reconfigurable Petri Nets Several extensions of the Petri Nets were developed with the objective of simplifying the modelling of Discrete Events Systems, even for distributed environments. However, m Several extensions of the Petri Nets were developed with the objective of simplifying the modelling of Systems to Discrete Events, even for distributed environments. However, most extensions are not designed to model systems that change during their operation. One group of Petri Nets extensions that attempts to tackle the problem of modelling systems that change during their operation is composed by the Self-Modifying Petri Nets [10], by the Reconfigurable Petri Nets via graph rewriting [6], by the Adaptive Petri Nets [1] and the Adaptive Fuzzy Petri Nets [5]. Each of these extensions has its own characteristics, but they share the fact that they can modify, during execution, the firing rules of the transitions or the topology of the network. With the same name, the same acronym, but of different srcins, we find in the literature Reconfigurable Petri Nets (RPN) introduced in [3] and in [6]. The work of Llorens and Oliver is an evolution of the work of Badouel and Oliver [1] and combines the techniques of graph grammars with the idea of Valk's Self-Modifying Petri Net, creating a system of rewriting of the network. In their work, Llorens and Oliver demonstrated the equivalence between the RPN and the PN in terms of properties and also that the RPN are equivalent to the Turing machines regarding the power of expression. In Figure 2 we have schematized a Reconfigurable Petri Net according to Guan [3]. There are two interdependent layers, the control layer and the presentation layer. The places of the control layer are different in their nature from the places of the presentation layer. Each place of the control layer has associated a set of functions that is capable to change the topology of the presentation layer, that is, they reconfigure the presentation layer. The tokens of the places are actually functions designed to modify the topology of the presentation layer.
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