Design Of Fuzzy Cognitive Maps Research Articles

Clustering techniques for Fuzzy Cognitive Map design for time series modeling

This study presents an approach to time series modeling with Fuzzy Cognitive Maps. In the paper we focus on initial modeling phase: map nodes selection. The research objective was to introduce algorithmic means to evaluate Fuzzy Cognitive Map design before training phase. We posed a hypothesis that application of cluster validity indexes could serve us in this endeavor. In order to validate the proposed approach we have conducted a suite of experiments on various time series, both synthetic and real-world. Five cluster validity indexes turned out to be especially valuable in our study. Results show that Fuzzy Cognitive Maps designed using one of the five selected indexes have superior quality. First, they are easy to interpret, because map nodes are related with the underlying data points. Second, after we train such maps, it turns out that the numerical quality of their predictions outrivals maps with other designs.

Design of Fuzzy Cognitive Maps for Modeling Time Series

This study elaborates on a comprehensive design methodology of fuzzy cognitive maps (FCMs). Here, the maps are regarded as a modeling vehicle of time series. It is apparent that whereas time series are predominantly numeric, FCMs are abstract constructs operating at the level of abstract entities referred to as concepts and represented by the individual nodes of the map. We introduce a mechanism to represent a numeric time series in terms of information granules constructed in the space of amplitude and change of amplitude of the time series, which, in turn, gives rise to a collection of concepts forming the corresponding nodes of the FCMs. Each information granule is mapped onto a node (concept) of the map. We identify two fundamental design phases of FCMs, namely 1) formation of information granules mapping numeric data (time series) into activation levels of information granules (viz., the nodes of the map), and 2) optimization of information granules at the parametric level, viz., learning (estimating) the weights between the nodes of the map. The learning is typically realized in a supervised mode on a basis of some experimental data. A construction of information granules is realized with the aid of fuzzy clustering, namely fuzzy C-means. The optimization is realized with the use of particle swarm optimization. The proposed approach is illustrated in detail by a series of experiments using a collection of publicly available data.

A Competent Memetic Algorithm for Learning Fuzzy Cognitive Maps

Fuzzy cognitive maps (FCMs) form an important class of models for describing and simulating the behavior of dynamic systems through causal reasoning. Owing to their abilities to make the symbolic knowledge processing simple and transparent, FCMs have been successfully used to model the behavior of complex systems originating from numerous application areas, such as economy, politics, medicine, and engineering. However, the design of FCMs necessarily involves domain experts to develop a graph-based model composed of a collection of system's concepts and causal relationships among them. Consequently, since humans exhibit an intrinsic factor of subjectivity and are only able to efficiently develop small-size graph-based models, there is a legitimate need to devise methods capable of automatically learning FCM models from data. This research addresses this need by introducing a competent memetic algorithm to generate FCM models from available historical data, with no human intervention. Extensive benchmarking tests performed on both synthetic and real-world data quantify the performance of the competent memetic method and emphasize its suitability over the models obtained by conventional and noncompetent hybrid evolutionary approaches in terms of accuracy, approximation ability, and convergence speed. Moreover, the proposed approach is shown to be scalable due to its capability to efficiently learn high-dimensional FCM models.

The Application of the Fuzzy Cognitive Map among Intravenous Drug Users

This article carries on a research about spreading and imitating based on network modal of dynamic, complex and comparing various Agents. The Agent regarded as drug complex network nodes and combine Agent itself functions. Propose a dynamic complex network technology combined with Agent simulation model based on fuzzy cognitive map to study the spread of HIV. Using fuzzy cognitive map design with independent learning ability node agent based on personal emotion and cognition, agent considers the individual perception of the epidemic of surrounding environment, social discrimination, legal constraints strength, national testing and treatment, free needle exchange extrinsic and intrinsic factors in the environment of individual course, emotion, etc., Under the combined effect of individual values ​​derived drug fuzzy cognitive map. Develop individualized decision rules to circumvent virus. This article studied the impact of fuzzy cognitive and social discrimination and legal factors on HIV transmission.

A CURIOUS LEARNING MODEL WITH ELM FOR FUZZY COGNITIVE MAPS

The design of fuzzy cognitive maps (FCMs) mainly relies on human knowledge, which implies subjectivity of the developed model. This affects the accuracy of an FCM significantly. In order to address this issue, we propose a novel learning model for FCMs in this paper. It achieves efficient learning by automatically adjusting the system parameters according to the environment. The learning model consists of extreme learning machine (ELM) and a curious model, where ELM learns from the modeled system and the curious model helps to further improve the performance of ELM. We use an example to illustrate the effectiveness of our model. The simulation results show that our model helps to improve the accuracy of FCMs.

Design of fuzzy cognitive maps using neural networks for predicting chaotic time series

As a powerful paradigm for knowledge representation and a simulation mechanism applicable to numerous research and application fields, Fuzzy Cognitive Maps (FCMs) have attracted a great deal of attention from various research communities. However, the traditional FCMs do not provide efficient methods to determine the states of the investigated system and to quantify causalities which are the very foundation of the FCM theory. Therefore in many cases, constructing FCMs for complex causal systems greatly depends on expert knowledge. The manually developed models have a substantial shortcoming due to model subjectivity and difficulties with accessing its reliability. In this paper, we propose a fuzzy neural network to enhance the learning ability of FCMs so that the automatic determination of membership functions and quantification of causalities can be incorporated with the inference mechanism of conventional FCMs. In this manner, FCM models of the investigated systems can be automatically constructed from data, and therefore are independent of the experts. Furthermore, we employ mutual subsethood to define and describe the causalities in FCMs. It provides more explicit interpretation for causalities in FCMs and makes the inference process easier to understand. To validate the performance, the proposed approach is tested in predicting chaotic time series. The simulation studies show the effectiveness of the proposed approach.

Learning fuzzy cognitive maps with required precision using genetic algorithm approach

Fuzzy cognitive maps (FCMs) are a powerful and convenient tool for describing and analysing dynamic systems. Their generic design is performed manually, exploits expert knowledge and is quite tedious, especially in the case of larger systems. This shortcoming is alleviated by completing the design of FCMs through learning carried out on experimental data. Comprehensive experiments reveal that this approach helps design models of required accuracy in an automated manner.

Interrogating the structure of fuzzy cognitive maps

Causal algebra in fuzzy cognitive maps (FCMs) plays a critical role in the analysis and design of FCMs. Improving causal algebra in FCMs to model complicated situations has been one of the major research topics in this area. In this paper we propose a dynamic causal algebra in FCMs which can improve FCMs' inference and representation capability. The dynamic causal algebra shows that the indirect, strongest, weakest and total effects a vertex influences another in the FCM not only depend on the weights along all directed paths between the two vertices but also the states of the vertices on the directed paths. Therefore, these effects are nonlinear dynamic processes determined by initial conditions and propagated in the FCM to reach a static or cyclic pattern. We test our theory with a simple example.

On causal inference in fuzzy cognitive maps

Fuzzy cognitive maps (FCM) is a powerful paradigm for representing human knowledge and causal inference. This paper formally analyzes the causal inference mechanism of FCM. We focus on binary concept states. It is known that given initial conditions, FCM is able to reach only certain states in its state space. We prove that the problem of finding whether a state is reachable in the FCM is nondeterministic polynomial (NP) hard, that we can divide fuzzy cognitive maps containing circles into basic FCM modules. The inference patterns in these basic modules can be studied individually in a hierarchical fashion. This paper also presents a recursive formula for computing FCM's inference patterns in terms of key vertices. The theoretical results presented in this paper provide a feasible and effective framework for the analysis and design of fuzzy cognitive maps in real-world large-scale applications.