Dissertation for Master's Degree in Computer Engineering - Artificial Intelligence
Abstract
Due to the rapid growth of complexity and size of simulation systems, designing efficient structures for evaluation and validation is an important issue. Today, Petri net is used for validation and verification. Petri nets are used to model systems of discrete events that may occur concurrently or with precedence and delay. However, accurate data does not always have accurate mathematical modeling, and sometimes these data are fuzzy data, which due to the application and capabilities of the Petri net, good results are expected to be obtained in the field of validity and validation of such systems. During this thesis, in order to create a knowledge base, a questionnaire related to the sales department of a commercial complex was designed. The purpose of this questionnaire is to study and check the level of customer satisfaction with this business unit. Then, for the purpose of validity and verification, first the knowledge base is mapped to the fuzzy Petri net, and then graphs are produced to check the structural errors of the law base. Then, based on the validation reference, fuzzy Petri nets are searched to check semantic errors. Key words: validation, correctness, fuzzy logic and Petri net Chapter 1: Introduction Considering that knowledge-based systems technology is expanding, there is a greater need to validate knowledge-based systems than It feels like the past. At the static evaluation level, only errors such as repetition, conflict, and cycle can be detected. And any semantic error such as inconsistency in the specification level of the system requirements provided by the knowledge base is not investigated. In this section, we discuss the process of modeling human model systems using Petri nets and static evaluation of Petri nets. Then, in the dynamic evaluation stage, we examine the connection between the network nodes and examine the structure of fuzzy rules to detect semantic incompleteness at the level of system inputs and environmental knowledge and provide a method to resolve this incompleteness. Validation is a process that is applied after production or during it to ensure the correctness and efficiency of the desired system. Validation means that the results obtained after the implementation of the system match the results that the system was designed for (it does the right thing). However, validation is the concept of complete compliance of the system with the description of the system (does the job correctly).
The purpose of validity and validation is twofold: 1) reducing errors 2) determining the correctness of the system. [1]
1-3 Description of human behavioral models
In order to describe the human behavioral model and also map it to the Petri net, a method is presented in [1] is:
Definition 1: It is a 5-way human behavior model, where Na is the name of the control and command model, IPS is the set of input features, InPS is the set of internal features, OPS is the set of output features, and RS is also the set of rules. For a command and control model, features can be divided into 3 types: where IP is an input feature, Inp is an internal feature, and OP is an external feature. Definition 3: A rule is a 4, where Na is the name of the rule, AntS is the set of antecedents of the rule, ConS is the set of tuples of the rule, and CF is the certainty factor of the rule. Definition 4: An antecedent of a rule is defined in the form A(F) where A is an input feature and F is a linguistic value. It is fuzzy. Definition 5: A sequence of a rule is defined in the form C(G) where C is an output feature and G is a fuzzy linguistic value. Definition 6: A degree of certainty of a sequence or antecedent is defined as ?(p) where p represents a sequence or an antecedent. Now, with this description, the human behavior model can be easily mapped to the Petri net.. With this description, the command and control model can be defined as follows:
1-4 Petri net [2]
(Images and relationships are available in the main file)
Today, the use of modeling methods in industrial applications, especially with the expansion of computer science and the increase in the speed of processors, has found a wide application. One of the modeling methods is the use of Petri nets, which is discussed in this section [2].
Simulation means a structure similar to a system in any possible way or form, which can be different from the reference system in some ways. The purpose of simulation is to study and check the reference system. The basis and pillar of modeling is choosing the right model. Choosing the right model is a decisive parameter, so you should know the model well at first. Any type of presentation or expression of a system is called a model. The model expresses the behavior of the system and one of the properties of modeling is simplification and creating uniformity and unity. One of the modeling methods is using a Petri net. Petri net was invented in 1962 by the claim of Mr. Carl Adam Petri[3]. He put most of his work on information system. Petri net is used in modeling and analyzing systems. The systems are first modeled as a Petri net, then the model is analyzed. A correct understanding of the system from the results will lead us to a useful system.
1-5 Petri net components[2]
1. Location[4]: To store tokens temporarily. 2. Transfer [5]: the activity center that affects the token and maybe creates a new token. 3. Kaman [6]: the movement path of tokens in the Petri net graph. 4. Token: Token or bead.
In Petri nets, places and transitions are considered as two separate sets of nodes, and arcs are their connecting edges, one end of which is connected to places and the other end to transitions. Petri net graph is a way to present the structure of Petri nets in which there are two types of nodes. There are nodes in the form of circles (O) and lines (?), where circles indicate locations and lines indicate transitions. These places and transitions are connected by arcs. When an arc is connected from a transition to a location, it indicates that that location will be the output of the aforementioned transition, and if an arc is drawn from a location to a transition, it indicates that that location will be the input of the aforementioned transition. Figure 1-1 is a simple example of a Petri net.
Formal definition of a Petri net
A Petri net is a 5-item that:
is a finite set of locations.
is a finite set of transitions.
is a set of arcs.
is a weight function.
The original symbol is [7].
(images are available in the main file)
1-6 Fuzzy Petri Net
Fuzzy Petri Net (FPN[8]) is a combination of Petri nets and knowledge representation. If used correctly, it is an effective tool for validating and validating human behavioral models. FPN is defined as an octet[1]:
(images and relations are available in the original file)
which is a finite set of locations.
is a finite set of transitions.
is a finite set of transitions.
(images and relations are available in the original file)
is an input function that represents a Mapping from location to transition.
It is an output function that represents a mapping from transition to location.
It is a continuity function that represents a mapping from transition to [0,1] such as confidence coefficient [9].
It is a continuity function that represents a mapping from location to [0,1] such as degree of accuracy[10].
It is a continuity function that represents a Mapping from location to transitions.
This section shows how to map human behavioral models to FPN. First consider the simple rule. To map it to an FPN, one must first map it to input locations, tails to output locations, and its name to transitions in the FPN. Furthermore, these mappings can be formally described as follows which means mapping.
which is an input location of a transition.
which is an output location of a transition.
Now the composite rules are mapped to FPN. Fuzzy rules can be classified into three types [13]. (Relations are available in the main file) which is the degree of correctness that precedes and follows the fuzzy rule and is the confidence factor.