RuleML representation and simulation of Fuzzy Cognitive Maps

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Abstract

Fuzzy Cognitive Map (FCM) technique is a combination of Fuzzy Logic and Artificial Neural Networks that is extensively used by experts and scientists of a diversity of disciplines, for strategic planning, decision making and predictions. A standardized representation of FCMs accompanied by a system that would assist decision makers to simulate their own developed Fuzzy Cognitive Maps would be highly appreciated by them, and would help the dissemination of FCMs. In this paper, (a) a RuleML representation of FCM is proposed and (b) a system is designed and implemented in Prolog programming language to assist experts to simulate their own FCMs. This system returns results in valid RuleML syntax, making them readily available to other cooperative systems. The representation capabilities and the design choices of the implemented system are discussed and a variety of examples are given to demonstrate the use of the system.

Highlights

► A RuleML representation of FCM is proposed that assists their dissemination. ► A system is designed and implemented to assist experts to simulate their own FCMs. ► System returns results in RuleML syntax, making them available to other systems. ► System’s design and implementation choices are discussed. ► Illustrative examples exhibit system’s capabilities.

Introduction

Fuzzy Cognitive Map (FCM) is a formal method for making predictions and taking decisions, that is used by scientists from various disciplines. The success of the construction of an FCM is heavily depended on the degree of expertise of the domain experts involved in the FCM construction. Making decisions through FCM, requires the simulation of the FCM model, which is a hard task especially from those scientists that do not possess the necessary computer skills.

Some of the major problems that concern nowadays FCMs are the following:

  • (a)

    Although many scientists create their own FCMs there is no solid and standard representation of them that would make them easily reusable and transportable.

  • (b)

    There is not any standard software that would simulate these FCMs, so every scientist has to create his own software system.

  • (c)

    No repository of FCMs exists to assist their dissemination.

In this paper these problems are handled by developing an XML representation of FCMs, which is based on a popular rule interchange format for the web, namely RuleML (Boley, 2006), accompanied by a Prolog-based simulation system that can assist FCM authors to both create syntactically correct FCMs and simulate their scenarios in FCMs. The basic assumption that we make in this paper is that FCMs closely resemble rules, since they represent causality relations between concepts, something that matches with the logical implication semantics of rules.

This study can provide additional dissemination of the use of FCMs because:

  • (a)

    FCMs authors will have a tool to create and simulate FCM,

  • (b)

    a RuleML repository of FCMs can be created that will help the concentration and distribution of FCMs and

  • (c)

    FCMs represented in RuleML will be able to be used in RuleML projects. Additionally, the results of the FCM simulation are stored in RuleML format, making easy their use by other systems.

In this paper, a short introduction to FCMs and related literature is given in Section 2. The representation capabilities of RuleML are presented and discussed in Section 3. In Section 4, the proposed extensions to RuleML in order to be able to represent FCMs are presented. The design of the Prolog-based simulation system that simulates FCMs represented in RuleML is discussed in Section 5, followed by a section concerning the implementation and demonstration of the system’s capabilities. Finally, in Section 7, a summary is presented, accompanied by a number of conclusions and recommendations for further research.

Section snippets

Fuzzy Cognitive Maps and related literature

Based on Axelord’s work on Cognitive Maps (Axelrod, 1976), Kosko introduced in 1986, Fuzzy Cognitive Maps (FCMs) (Kosko, 1986, Kosko, 1992). FCMs are considered a combination of fuzzy logic and artificial neural networks and many researchers have made extensive studies on their capabilities (see for example Khan et al., 2000, Khan and Quaddus, 2004, Stach et al., 2005, Taber et al., 2006, Tsadiras and Margaritis, 1997a, Tsadiras and Margaritis, 1997b). An example of an FCM, concerning a car

Representation capabilities of rules and RuleML

Rule-based systems have been extensively used in several applications and domains, both in academia and industry, such as e-commerce, personalization, games, medicine, etc. They offer a simplistic model for knowledge representation for both domain experts and programmers; experts usually find it easier to express knowledge in a rule-like format and programmers usually find rule-based programming easier to understand and manipulate, decoupling computation from control. The first is performed by

RuleML representation of FCMs

As it is discussed in Section 2, an FCM contains a number of arcs that represent causal relationships between the concepts of the FCM. All these relationships are of the following form:Concept1influencesConcept2withweightW.

Having justified the isomorphism between causal relationships and rules in the previous section, in this section we detail how FCM causal relationships are being represented in RuleML as rules. The above abstract relationship is represented as follows (in RuleML 1.0,

Design of the RuleML-FCM simulation system

Having represented the FCM in RuleML, the next step is that of simulating the represented FCM. The stages for the simulation of scenarios imposed to FCMs, are shown in Fig. 4.

In stage 1 of the simulation system (a) the RuleML file that represents the FCM and (b) the XSLT file of Fig. 5, are inputted to an XSLT processor which performs an XSL transformation and produces at the output an FCM text file having statements of the forms shown in Fig. 6.

Using the above transformation in stage 1, the

Implementation and demonstration of the RuleML-FCM simulation system

The RuleML-FCM simulation system is implemented in SWI-Prolog (http://www.swi-prolog.org/), following the design described in Section 5. To demonstrate its implementation, the FCM of Fig. 1 will be used, that imposes scenario #1. According to this scenario, “lower price is set to 0.3” so it attempts to predict the consequences of a small decrease at the prices of the cars, by the car industry. To examine this scenario, the RuleML representation of FCM of Fig. 1(as shown in Fig. 2) is saved to a

Summary – Conclusions

After a short introduction to Fuzzy Cognitive Maps and RuleML, a RuleML representation of FCMs is proposed that make:

  • (a)

    FCMs easily transferable and reusable.

  • (b)

    FCMs ready to interact with other systems that interact with RuleML.

  • (c)

    Easy the creation of a repository of FCMs, that is important for FCM researchers and practitioners.

A system for simulating RuleML representation of FCMs is designed and implemented in order to:

  • (a)

    Simulate the scenario written in the form of the RuleML representation of FCM.

  • (b)

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