Fuzzy cognitive maps are signed directed graphs used to model the evolution of scenarios with time. FCMs can be useful in decision support for predicting future states given an initial state. Genetic algorithms (GA) are well-established tools for optimization. This paper concerns the use of FCMs in goal-directed analysis of scenarios for aiding decision making. A methodology for GA-based goal-directed analysis is presented. The search for the initial stimulus state, that over time leads to a target state of interest, is optimized using GA. This initial state found can be used to answer the question – what course of events leads to a certain state in a given scenario?
Fuzzy Cognitive Maps (FCM), as defined originally, are limited in their capacity to model real-world scenarios, due to the rather simple representation of causal relationships between interrelated concepts. They can model a world that has only monotonic cause-effect relationships. Unlike this traditional FCM, which uses a linear function to represent the strength of relationship between two concepts, and a non-linear transfer function, to update the value of a concept during simulation, the FCM proposed by us uses fuzzy rules based on membership functions, and an aggregation operator respectively to serve these two purposes. This allows representation of non-monotonic causality, which is typical of many scenarios. Architecture and Operation of a Fuzzy Cognitive MapAn FCM, represented by a directed graph, is used to model a scenario as a collection of concepts or events (shown as nodes), and the causal relations between them (shown by directed edges). A node that has a causal influence on another node is called a cause node, and a node that is subject to that influence is called the effect node. The direction of the edges indicates the direction of causality. Edges are labelled with
The ever growing popularity of the Internet as a source of information, coupled with the accompanying growth in the number of documents made available through the World Wide Web, is leading to an increasing demand for more efficient and accurate information retrieval tools. Numerous techniques have been proposed and tried for improving the effectiveness of searching the World Wide Web for documents relevant to a given topic of interest. The specification of appropriate keywords and phrases by the user is crucial for the successful execution of a query as measured by the relevance of documents retrieved. Lack of users' knowledge on the search topic and their changing information needs often make it difficult for them to find suitable keywords or phrases for a query.This results in searches that fail to cover all likely aspects of the topic of interest. We describe a scheme that attempts to remedy this situation by automatically expanding the user query through the analysis of initially retrieved documents. Experimental results to demonstrate the effectiveness of the query expansion scheme are presented.
dbsfruct-Transparency and complexity are two major concerns of fumy rule-based systems. To improve accuracy and precision of the outputs, we need to increase the partitioning of the input space. However, this increases the number of rules exponentially, thereby increasing the complexity of the system and decreasing its transparency. The main factor behind these t w o issues is the conjunctive canonical form of the fuzzy rules. We prment a novel method for replacing these rules with their singleton forms, and using aggregation operators to provide the mechanism for combining the crisp outputs.Keywords-Fuuy comiraint aggregation uperatur, fuziy ino&liing, singleton fuzzy rule 1NTRODUCTtONUntil recently, it has generally been perceived that systems implementing fuzzy modclling [ 13 provide better transparency than the black box models such as artificial neural networks. By transparency, we mean interpretability of rules and outputs. The main reason for this perception is that most conventional rule-based fuzzy systems are abstracted from human experts or heuristics, and they are usually easy to comprehend. This providcs the transparency enabling one to gain insights into the system and acquire important knowledge. However, as more and more fuzzy rules are automatically generated using training or experimenta1 data, fuzzy modelling becomes less easily understood by humans because of the increase in complexity of these rules. Another issue is that the number of inputs has to be kept low because the dimension of the input space and complexity grows exponentially in terms of the number of input variables [2, 3j. So we have a dilemma:' On one hand, the requirement of accuracy calls for the use of dense ruIe bases with Iarge numbers of antecedent variables and linguistic terms, on the other hand, exponential growth in the size of rule base creates problems with computational time and storage space requirements. Reduction of rules is dcsirable but limiting the number of rules may destroy the property of the model as a universal approximator [4].Many techniques have been proposed for rule reduction. We discuss briefly the problems associated with using these in Section 11. In Section 111 wc propose a new approach that aims to improve the interpretation of the much simpler fuzzy rules and reduce the complexity of the problem domain, using some examples to illustrate our approach. The paper concludes in Section IV. 0-where x,, i=I ,..., k is the ith input to the fuzzy system, which is dcfined on the universe of discourse U,; A, is a fizzy sct on U,; y is the system output defined on a universe of discourse V, and B is a fuzzy set on V. For simpIicity we are assuming B in this case to be on a one-dimensional output space. We discuss a multi-dimensional output space in the next section.To derive the fuzzy if-then rules, several approaches have been proposed. Some of the common approaches are outlined in the following subscctions: A . Grid PartitioningThe most common method to construct fuzzy rules is to partition the input sp...
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