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This paper focus on the use of Rule Based Fuzzy Cognitive Maps to represent cell behaviour in Voronoi Based Cellular Automata in order to model the dynamics of temporal and spatial propagation processes. As an application example, the proposed approach is applied to modelling and simulation of forest fire propagation.
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... The nature of a problem determines the type and the number of FCM nodes; which are often specified by experts. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] As for control problems, one may use the experiences of control engineers in designing FCMs. 28 However, this approach might not be efficient since one might face the following difficulties (1) not be able to find experts for each control applications, (2) the complexity of the resulting FCM might be too high and thus might not feasible for real-time applications, and (3) the stability of the resulting FCM cannot be shown which is an essential requirement in any control system. 2 | AMIRKHANI ET AL. ...
In this paper, we provide a complete framework for the design of genetically evolved cognitive tracking controller based on interval type-2 (IT2) fuzzy cognitive map (FCM). We construct the cognitive controller based on a nonlinear controller by transforming its representation into a FCM. This representation gives the opportunity to prove the stability of the cognitive controller in the framework of nonlinear control theory. Moreover, with the deployment of IT2-fuzzy sets which are known to be capable to handle high level of uncertainty, the proposed cognitive controller has the ability to deal with uncertainty that are encountered in real-time world applications. To accomplish the design of the cognitive controller, we present a systematic approach based on genetic algorithm to optimize its parameters and learn fuzzy rules by extracting them from model space (e.g., a set of rules). Within the paper, all steps in constructing and designing the IT2-FCM-based cognitive controller are presented. We first show the performance improvements of the proposed IT2-FCM-based tracking controller with extensive and comparative simulation results and then with experimental results that were collected on real-world mobile robot. The results clearly show the superiority of proposed cognitive control systems when compared to its conventional and fuzzy controller counterparts. We believe that the proposed genetically evolved design approach of the IT2-FCM-based cognitive controller will provide a bridge between the well-developed cognitive sciences and control theory.
... However, the notion of cognitive map Meta-states, introduced in 2006 [16] [17], can implicitly model such mechanisms on a qualitative and simpler way. Such principles can be applied to implement Evolving Dynamic Cognitive Maps (Ev-DCM). ...
... It has been shown that FCM based post processing decision support, can greatly improve the overall system performance and diminish the false alarms rate. Carvalho et al. (2006) focused on the modeling and simulation of forest fire propagation using Dynamic Cognitive Map Cellular ...
Forest fires are one of the most serious natural disasters for the countries of the Mediterranean basin and especially for Greece. Studying the climate change effect on the maximization of the problem is a constant objective of the scientific community. This research initially proposes an innovative hybrid version of the statistical Chi-Square test that employs Soft Computing methods. More specifically it introduces the Fuzzy Chi Square Independence test that fuzzifies p values using proper Risk Linguistics, based on Fuzzy Membership functions. In the second stage, it proposes a new Hybrid approach that models the evolution of burned areas in Greece. First it analyzes the parameters and determines the way they affect the problem, by constructing Fuzzy cognitive maps. The system projects into the future and forecasts the evolution of the problem through the years till 2100, based on the variance of average monthly temperature and average rain height (due to climate change) for the months May–October based on various climate models. Historical data for the period 1984–2004 were used to test the system for the areas of Chania and Ilia.
... This approach, based on standard forestry maps together with expert knowledge, was shown to be an efficient way of predicting the spatial pattern of species diversity under a set of different forest management scenarios. Carvalho et al. (2006) have combined FCM with voronoi cellular automata to simulate the propagation of forest fires. They used rulebased FCM to model the dynamic behavior of individual forest fire cells. ...
Lack of information and large uncertainties can constrain the effectiveness and acceptability of environmental models. Fuzzy-logic cognitive mapping (FCM) is an approach that deals with these limitations by incorporating existing knowledge and experience. It is a soft-knowledge approach for system modeling, where components of a system and their relationships are identified and semi-quantified in a participatory way. Its usefulness has been manifested through applications in a variety of disciplines, including engineering, information technology, business, and medicine. This chapter introduces FCM as a simple, transparent, and flexible participatory method to model complex social-ecological systems based on expert and stakeholder knowledge. It describes the evolution of FCM to environmental modeling due to its ability to facilitate public participation, data generation, and systems thinking. Numerous actors can be involved when studying environmental issues: experts, scientists, decision makers, and other stakeholders. Thus, a wide range of opinions and perceptions can be taken into account, providing a platform for discussion and negotiation among different actors. Moreover, data that is otherwise inaccessible can be gathered through FCM. Finally, one of the most significant characteristics of the method is the possibility to study causal relationships and feedback loops. In this way, FCM supports decision-making by simulation and scenario studies.
... Application examples can be found in political science [8], [9], economics [10], [11], representing social scientific knowledge, and describing decision-making methods [12]- [14]. Other applications include geographical information systems [15]- [17], cellular automata [18], pattern-recognition applications [19], [20], and numerical and linguistic prediction of time-series functions [21]. FCMs have also been used to model the behavior and reactions of virtual worlds [22]- [26] as a generic system for decision analysis [14], [27] and coordinator of distributed cooperative agents. ...
In this chapter, we present a study for the existence of equilibrium points of FCNs equipped with continuous differentiable sigmoid functions that have contractive or at least nonexpansive properties. The study is done by using an appropriately defined contraction mapping theorem and the nonexpansive mapping theorem. It is proved that, when the weight interconnections fulfill certain conditions, related to the size of the FCN and the inclination of the sigmoid functions, the concept values will converge to a unique solution regardless of their initial states, or in some cases a solution exists that may not necessarily be unique.
Otherwise the existence or the uniqueness of equilibria may or may not exist, it may depend on the initial states, but it cannot be assured. In case the FCN has also input nodes (that is nodes that influence but are not influenced by other nodes), the unique equilibrium does not depend solely on the weight set, as in the case of FCNs with no input nodes; it depends also on the values of the input nodes. Numerical examples explore the results and a thorough discussion interprets them.
... This approach has been tested in medical applications [16]. Rule based FCMs are another extension which provides greater versatility [17]. Timed automata based FCMs have been proposed for applications where dynamic behavior is needed [18]. ...
Autonomous polygeneration microgrids (APM) are a relatively new approach in covering specific needs like power, potable water and fuel for transportation, in remote areas. This approach has been proved to be technically feasible nowadays and even present itself as an economically viable investment. The initial management system built for this approach is a simple ON/OFF supervisor which can make the APM operate, but not in an optimal way. The devices cannot be operated in part load and as a consequence there is little room for optimization. A combined fuzzy cognitive maps (FCMs)–petri nets (PN) approach has been developed for the energy management of such a system. The PN is used as an activator in the fuzzy cognitive map structure so as to enable different FCMs to be activated depending on the state of the microgrid. This combination forms an integrated approach to the energy management of the microgrid. Using this approach considerable optimization in the design and operation of the microgrid is possible. A methodology for simultaneous and interactive optimization of the energy management system along with the sizing of the various devices of the actual microgrid is implemented. A software platform consisting of TRNSYS, TRNOPT and GenOPT software packages was used for simulation and optimization. Particle swarm optimization is applied both for the sizing of the system and the optimization of the FCM weights and PN parameters. Two microgrids were designed, one based on the FCM–PN energy management system (FPEMS) and one on the ON/OFF approach. The results show that FPEMS manages the energy flows more effectively throughout the year which leads to a considerable decrease in the sizing of the various components of the microgrid.
... Besides Btime, RB-FCMs introduced the idea of meta-states that models complex temporal and spatial propagation processes. RB-FCMs augmented with meta-states [35] provide several benefits by the usage of simple state diagrams, where each meta-state contains the most suitable RB-FCM that is capable of modeling a system under certain conditions. This idea seems similar to TAFCMs' proposal but significant differences characterize the two approaches. ...
The theory of fuzzy cognitive maps (FCMs) is a powerful approach to modeling human knowledge that is based on causal reasoning. Taking advantage of fuzzy logic and cognitive map theories, FCMs enable system designers to model complex frameworks by defining degrees of causality between causal objects. They can be used to model and represent the behavior of simple and complex systems by capturing and emulating the human being to describe and present systems in terms of tolerance, imprecision, and granulation of information. However, FCMs lack the temporal concept that is crucial in many real-world applications, and they do not offer formal mechanisms to verify the behavior of systems being represented, which limit conventional FCMs in knowledge representation. In this paper, we present an extension to FCMs by exploiting a theory from formal languages, namely, the timed automata, which bridges the aforementioned inadequacies. Indeed, the theory of timed automata enables FCMs to effectively deal with a double-layered temporal granularity, extending the standard idea of B-time that characterizes the iterative nature of a cognitive inference engine and offering model checking techniques to test the cognitive and dynamic comportment of the framework being designed.
... Nevertheless, a non-uniform grid may be used based on attributes of the tessellated space i.e. Voronoi polygons (Carvalho 2006) or even a dynamic grid (Vilet et al. 2008). The choice of the grid, and hence of the cells, depends on the nature of the phenomenon under study, the requirements and the limitations of its mathematical description. ...
... Application examples can be found in political science [8], [9], in economic field [10]- [15], in representing social scientific knowledge and describing decision making methods [16] - [18]. Other applications include geographical information systems [19] - [21], cellular automata [22], pattern recognition applications [23], [24] and numerical and linguistic prediction of time series functions [25]. Fuzzy cognitive maps have also been used to model the behavior and reactions of virtual worlds [26] - [30], as a generic system for decision analysis [18], [31] and as coordinator of distributed cooperative agents. ...
Fuzzy Cognitive Networks (FCN) constitutes an operational extension of Fuzzy Cognitive Maps (FCM), which assume that they
always reach equilibrium points during their operation. Moreover, they are in continuous interaction with the system they
describe and may be used to control it. FCN are capable of capturing steady state operational conditions of the system they
describe and associate them with input values and appropriate weight sets. In the sequence they store the acquired knowledge
in fuzzy rule based data bases, which can be used in determining subsequent control actions. This chapter presents basic theoretical
results related to the existence and uniqueness of equilibrium points in FCN, the adaptive weight estimation based on system
operation data, the fuzzy rule storage mechanism and the use of the entire framework to control unknown plants. The results
are validated using well known control benchmarks.
... Application examples can be found in political science [8], [9], economics [10], [11], representing social scientific knowledge, and describing decision-making methods [12]- [14]. Other applications include geographical information systems [15]- [17], cellular automata [18], pattern-recognition applications [19], [20], and numerical and linguistic prediction of time-series functions [21]. FCMs have also been used to model the behavior and reactions of virtual worlds [22]- [26] as a generic system for decision analysis [14], [27] and coordinator of distributed cooperative agents. ...
Fuzzy cognitive maps (FCMs) have been introduced by Kosko to model complex behavioral systems in various scientific areas. One issue that has not been adequately studied so far is the conditions under which they reach a certain equilibrium point after an initial perturbation. This is equivalent to studying the existence and uniqueness of solutions for their concept values. In this paper, we study the existence of solutions of FCMs equipped with continuous differentiable sigmoid functions having contractive or, at least, non-expansive properties. This is done by using an appropriately defined contraction mapping theorem and the non-expansive mapping theorem. It is proved that when the weight interconnections fulfill certain conditions, the concept values will converge to a unique solution, regardless of the exact values of the initial concept values perturbations, or in some cases, a solution exists that may not necessarily be unique; otherwise, the existence or the uniqueness of equilibrium cannot be assured. Based on these results, an adaptive weight-estimation algorithm is proposed that employs appropriate weight projection criteria to assure that the uniqueness of FCM solution is not compromised. In view of these results, recently proposed extensions of FCM, which are the fuzzy cognitive networks (FCN), are invoked.
