Fuzzy Cognitive Maps for Applied Sciences and Engineering

The challenging problem of complex systems modeling methods with learning capabilities and characteristics that utilize existence knowledge and human experience is investigated using Fuzzy Cognitive Maps (FCMs). FCMs are ideal causal cognition tools for modeling and simulating dynamic systems. Their usefulness has been proved from their wide applicability in diverse domains. They gained momentum due to their simplicity, flexibility to model design, adaptability to different situations, and ease of use. In general, they model the behavior of a complex system utilizing experts knowledge and/or available knowledge from existing databases. They are mainly used for knowledge representation and decision support where their modeling features and their learning capabilities make them efficient to support these tasks. This chapter gathers the methods and learning algorithms of FCMs applied to modeling and decision making tasks. A comprehensive survey of the current modeling methodologies and learning algorithms of FCMs is presented. The leading methods and learning algorithms, concentrated on modeling, are described analytically and analyzed presenting experimental results of a known case study. The main features of computational methodologies are compared and future research directions are outlined.

Fuzzy Cognitive Maps (FCM) have found favor in a variety of theoretical and applied contexts that span the hard and soft sciences. Given the utility and flexibility of the method, coupled with the broad appeal of FCM to a variety of scientific disciplines, FCM have been appropriated in many different ways and, depending on the academic discipline in which it has been applied, used to draw a range of conclusions about the belief systems of individuals and groups. Although these cognitive maps have proven useful as a method to systematically collect and represent knowledge, questions about the cognitive theories which support these assumptions remain. Detailed instructions about how to interpret FCM, especially in terms of collective knowledge and the construction of FCM by non-traditional ‘experts’, are also currently lacking. Drawing from the social science literature and the recent application of FCM as a tool for collaborative decision-making, in this chapter we attempt to clarify some of these ambiguities. Specifically, we address a number of theoretical issues regarding the use of Fuzzy Cognitive Mapping to represent individual “mental models” as well as their usefulness for comparing and characterizing the aggregated beliefs and knowledge of a community.

Semantic graphs like fuzzy cognitive map (FCM) are known as powerful methodologies commonly used in control applications, as well as in relationship modeling. Besides, FCM is used as a systematic way for analyzing real-world problems with numerous known, partially known and unknown factors. This chapter discusses FCM application in relationship modeling context using some agile inference mechanisms. A sigmoid-based activation function is discussed with application in modeling hexapod locomotion gait. The activation algorithm is then added with a Hebbian weight training technique to enable automatic construction of FCMs. A numerical example case is included to show the performance of the developed model. The model is examined with perceptron learning rule as well. Finally a real-life example case is tested to evaluate the final model in terms of relationship modeling.

Fuzzy Cognitive Map (FCM) technique is broadly used for decision making and predictions by experts and scientists of a wide range of disciplines. The use of the FCMs would be even wider if a standardized representation of FCMs was developed and a system that would simulate them was constructed. Having such a system, decision makers would be able to create and examine their own developed Fuzzy Cognitive Maps, and also distribute them e.g. through Internet. In this chapter, (a) we propose a RuleML representation of FCMs and (b) we present the design and implementation of a system that assists experts to simulate their own FCMs. This system, which is developed using the Prolog programming language, makes the results of the FCM simulation directly available to other cooperative systems because it returns them in standard RuleML syntax. In the chapter, the design choices of the implemented system are discussed and the capabilities of the RuleML representation of FCM are presented. The use of the system is exhibited by a number of examples concerning an e-business company.

A social Semantic Web empowers its users to have access to collective Web knowledge in a simple manner, and for that reason, controlling online privacy and reputation becomes increasingly important, and must be taken seriously. This chapter presents Fuzzy Cognitive Maps (FCM) as a vehicle for Web knowledge aggregation, representation, and reasoning. With this in mind, a conceptual framework for Web knowledge aggregation, representation, and reasoning is introduced along with a use case, in which the importance of investigative searching for online privacy and reputation is highlighted. Thereby it is demonstrated how a user can establish a positive online presence

Fuzzy cognitive maps (FCMs) is a knowledge representation tool that can be exploited for predicting multivariate time-series. FCM model represents dependencies among data variables as a directed, weighted graph of fuzzy sets (concepts). This way, FCM can be easily interpreted or constructed by experts in contrary to black box knowledge representation methods. Since FCM is a parametric model, it can be trained using historical data. So far, the genetic algorithm has been used to solely optimize the weights of FCM leaving the rest of FCM parameters to be adjusted by experts. Previous studies have shown that the genetic algorithm can be also used not only for optimizing the weights but also for optimization of FCM transformation functions. The main idea presented in this chapter is to further extend FCM evolutionary learning process. Special focus is given on fuzzyfication and transformation function optimization, applied in each concept seperately, in order to improve the efficacy of time-series prediction. The proposed extended evolutionary optimization process was evaluated in a number of real medical data gathered from the internal care unit (ICU). Comparing this approach with other known genetic-based learning algorithms, less prediction errors were observed for this dataset.

This chapter is devoted to the synthesis and some analysis of multi-step learning algorithms for fuzzy cognitive maps (FCM). Multi-step supervised learning based on gradient method and unsupervised learning type of differential Hebbian learning (DHL) algorithm were described. Comparative analysis of these methods to one-step algorithms, from the point of view of the influence on the work of the medical prediction system (average percentage prediction error) was performed. FCM learning and testing was based on historical data. Simulation research together with the analysis results were done on prepared software tool ISEMK (Intelligent Expert System based on Cognitive Maps). Selected results of this analysis were presented.

This chapter deals with certain aspects of the design of fuzzy cognitive maps, which operations are based not on a set of causal rules but on mathematically defined relationships between the model key concepts. In such a model, which can be called a relational fuzzy cognitive map, the key concepts are described by fuzzy numbers, and the relationships between concepts take the form of specially shaped fuzzy relations. As a result, the operation of the model is described mathematically by the system of special equations operating on fuzzy numbers and relations. This approach introduces formal and technical difficulties but on the other hand, it allows to apply certain automation of the process of creating and modifying the relational model of a fuzzy cognitive map. It also enables detachment from the rigidly defined linguistic values in relation to their abstract equivalents, which number can be easily changed depending on the current needs of the modeling process. The chapter describes the results of work up until today by authors of design of fuzzy relational models of cognitive maps.

This work presents an architecture for cooperative autonomous agents based on dynamic fuzzy cognitive maps (DFCM) that are an evolution of fuzzy cognitive maps. This architecture is used to build an autonomous navigation system for mobile robotics that presents learning capacity, on line tuning, self-adaptation abilities and behaviors management. The developed navigation system adopts a multi-agent approach, inspired on the Brooks’ subsumption architecture due to its hierarchical management functions, parallel processing and direct mapping from situation to action. In this paper, a DFCM is hierarchically developed, from low-level describing reactive actions to the highest level that comprises management actions. A multi-agent scheme to share experiences among robots is also implemented at the last hierarchy level based on pheromone exchange by ant colony algorithm. The proposed architecture is validated on a simple example of swarm robotics.

Modeling of complex dynamic systems, for which establishing mathematical models is very complicated, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. On one hand, Fuzzy Cognitive Maps (FCMs) are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. On the other hand, human experts are subjective and can handle only relatively simple FCMs; therefore, there is a need of developing novel approaches for an automated generation of FCMs using historical data. Although, many novel learning algorithms are published in literature, there is no software existing that especially focuses on a learning method for FCMs. In order to fill this gap, and to help researchers and developers in social sciences, medicine and engineering, a graphical user interface (GUI) is designed. Since the interest of developing software or a GUI in Matlab is increasing within the last years, the proposed FCM-GUI is developed using Matlab. In this study, a new optimization algorithm, which is called Big Bang-Big Crunch (BB-BC), is proposed for an automated generation of FCMs from data. Two real-world examples; namely an ERM maintenance risk model and a synthetic model generated by the proposed FCI-GUI are used to emphasize the effectiveness and usefulness of the proposed methodology. The results of the studied examples show the efficiency of the developed FCM-GUI for design, simulation and learning of FCMs.

Java Fuzzy Cognitive Maps (JFCM) [1] is an open source library by Dimitri De Franciscis [2] that implements fuzzy cognitive maps using the Java™  programming language. In this chapter we will introduce the library and its main features, along with many code examples and experiments that show how to effectively use it in your projects.

A halt in loss of biodiversity is an important issue in conservation management across Europe. As landscapes tend to be perceived as a combination of natural and social elements, and people’s values and attitudes, research supporting conservation management is dealing with landscapes as socio-ecological systems. As part of ALTER-Net, we applied FCM to five cases and subsequently evaluated the approach by means of a SWOT framework. This examined the strengths and weaknesses of, and the opportunities and threats to FCM when applied as a tool in conservation management.

Recently, Fuzzy Grey Cognitive Maps (FGCM) has been proposed as a Grey System theory-based FCM extension. Grey systems have become a very effective theory for solving problems within environments with high uncertainty, under discrete small and incomplete data sets. The benefits of FGCMs over conventional FCMs make evident the significance of developing a greyness-based cognitive model such as FGCM. In this chapter, the FGCM model and the proposed NHL learning algorithm were applied within an industrial problem, concerning a chemical process control process with two tanks, three valves, one heating element and two thermometers for each tank. The proposed mathematical formulation of FGCMs and the implementation of the NHL algorithm have been successfully applied. This type of learning rule accompanied with the good knowledge of the given system, guarantee the successful implementation of the proposed technique in industrial process control problems.

Fuzzy Cognitive Maps (FCM) started in the last decade to penetrate to areas as decision-making and control systems including robotics, which is characterized by its distributiveness, need for parallelism and heterogeneity of used means. This chapter deals with specification of needs for a robot control system and divides defined tasks into three basic decision levels dependent on their specification of use as well as applied means. Concretely, examples of several FCMs applications from the low and middle decision levels are described, mainly in the area of navigation, movement stabilization, action selection and path cost evaluation. Finally, some outlooks for future development of FCMs are outlined.

Fuzzy cognitive map (FCM) is applied to the problem of structural damage detection. Structures are important parts of infrastructure and engineering systems and include buildings, bridges, aircraft, rockets, helicopters, wind turbines, gas turbines and nuclear power plants, for example. Structural health monitoring (SHM) is the field which evaluates the condition of structures and locates, quantifies and suggests remedial action in case of damage. Damage is caused in structures due to loading, fatigue, fracture, environmental degradation, impact etc. In this chapter, the damage is modeled in a cantilever beam using the continuum damage and natural frequencies are used as damage indicators. Finite element analysis, which is a procedure for numerically solving partial differential equations, is used to solve the mathematical physics problem of finding the natural frequencies. The measurement deviations due to damage are fuzzified. Then they are mapped to a set of damage locations using FCM. An improvement in performance of the FCM is obtained using an unsupervised neural network approach based on Hebbian learning.

This paper presents the application of a Fuzzy Cognitive Map (FCM) based theoretical framework and its associated modeling and simulation tool to Strategy Maps (SMs). Existing limitations of SMs are presented in a literature survey. The need for scenario based SMs with inherited ability to change scenarios dynamically as well as the missing element of time are highlighted and discussed upon. FCMs are presented as an alternative to overcome these shortfalls with the introduction of fuzziness in their weights and the robust calculation mechanism. An FCM tool is presented that allows simulation of SMs as well as interconnection of nodes (performance measures) in different SMs which enable the creation of SM hierarchies. An augmented FCM calculation mechanism that allows this type of interlinking is also presented. The resulting methodology and tool are applied to two Banks and the results of these case studies are presented.

Turkey has experienced a major wave of migration since the early 1950s. Although many studies have tried to investigate how social dynamics and identities play a role in the migration phenomenon in urban areas, none of them have analysed this through a model that allows to present perception of migrants and the phenomenon of migration from the point of view of social groups at a conceptual and relational level. This study conducted in Gebze proposes to analyse FCMs based on modelling position and perception that shows how migrants locate one another in the city and the migration phenomenon. The findings of this study suggest that since experiences and perceptions differ according to social categories, social inequalities caused by and/or leading to migration become visible and more comprehensive from the perspective of different social categories of migrants.

Community needs ask for local management approaches as a response to the structure and evolution of a specific environment. The importance of managerial ethics in individualizing operational entities in terms of sustainable development of increasingly tense spaces stands for an efficient design of socio-ecological systems, such as Danube Delta Biosphere Reserve (DDBR). Such an approach helps people gain knowledge, values and the awareness they need to manage efficiently environmental resources and to take responsibility for maintaining environmental quality. This study examines the perceptions of local stakeholders in Sfantu Gheorghe, DDBR, Romania, with the aim of developing key concepts that will be used in future information and communication strategies regarding economic characteristics, sustainable development and biodiversity conservation in the area. For this 30 cognitive maps were developed together with stakeholders. Analysis reveals that DDBR Administration, county authorities and local authorities are substantially worried about the pollution and overfishing, while other social groups care more about touristic activities, accessibility degree, health system or financial resources. The lack of coordination and effective policies for the management of different sectors of activities were also identified as a common problem and have accentuated both environmental and socio-economic problems.

Periodontal disease is a chronic bacterial infection that affects the gums and bone supporting the teeth. This research work aims to assess the severity level of periodontal disease in dental patients. The presence or absence of sign-symptoms and risk factors make it a complicated diagnostic task. Dentist usually relies on his knowledge, expertise and experiences to design the treatment(s). Therefore, it is found that there is a variation among treatments administered by different dentists. The methodology of Fuzzy Cognitive Maps (FCM) was used to model this problem and then to calculate the severity of the periodontal disease. The relationships between different sign-symptoms have been defined using easily understandable linguistic terms following the construction process of FCM and then converted to numeric values using Mamdani inference method. For convenience, a graphical interface of the system has been designed based on FCM modeling and reasoning.