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23
Hidden Patterns in Combined and Adaptive Knowledge Networks
 International Journal of Approximate Reasoning
, 1988
"... Uncertain causal knowledge is stored in fuzzy cognitive maps (FCMs). FCMs are fuzzy signed digraphs with feedback. The sign (+ or) of FCM edges indicates causal increase or causal decrease. The fuzzy degree of causality is indicated by a number in [ 1, 1]. FCMs learn by modifying their causal conn ..."
Abstract

Cited by 38 (2 self)
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Uncertain causal knowledge is stored in fuzzy cognitive maps (FCMs). FCMs are fuzzy signed digraphs with feedback. The sign (+ or) of FCM edges indicates causal increase or causal decrease. The fuzzy degree of causality is indicated by a number in [ 1, 1]. FCMs learn by modifying their causal connections in sign and magnitude, structurally analogous to the way in which neural networks learn. An appropriate causal learning law for inductively inferring FCMs from timeseries data is the differential Hebbian law, which modifies causal connections by correlating time derivatives of FCM node outputs. The differential Hebbian law contrasts with Hebbian outputcorrelation learning laws of adaptive neural networks. FCM nodes represent variable phenomena or fuzzy sets. An FCM node nonlinearly transforms weighted summed inputs into numerical output, again in analogy to a model neuron. Unlike expert systems, which are feedforward search trees, FCMs are nonlinear dynamical systems. FCM resonant states are limit cycles, or timevarying patterns. An FCM limit cycle or hidden pattern is an FCM inference. Experts construct FCMs by drawing causal pictures or digraphs. The corresponding connection matrices are used for inferencing. By additively combining augmented connection matrices, any number of FCMs can be naturally combined into a single knowledge network. The credibility wi in [0, 1] of the ith expert is included in this learning process by multiplying the ith expert's augmented FCM connection matrix by w i. Combining connection matrices is a simple type of adaptive inference. In general, connection matrices are modified by an unsupervised learning law, such as the
Interaction between Agents in Routine, Familiar and Unfamiliar Situations
"... A framework for designing a multiagent system (MAS) in which agents are capable of coordinating their activities in routine, familiar, and unfamiliar situations is proposed. This framework is based on the skills, rules and knowledge (SRK) taxonomy of Rasmussen. Thus, the proposed framework shou ..."
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Cited by 20 (6 self)
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A framework for designing a multiagent system (MAS) in which agents are capable of coordinating their activities in routine, familiar, and unfamiliar situations is proposed. This framework is based on the skills, rules and knowledge (SRK) taxonomy of Rasmussen. Thus, the proposed framework should allow agents to prefer the lower skillbased and rulebased levels rather than the higher knowledgebased level because it is generally easier to obtain and maintain coordination between agents in routine and familiar situations than in unfamiliar situations. The framework should also support each of the three levels because complex tasks combined with complex interactions require all levels. To permit agents to rely on low levels, a suggestions is developed: agents are provided with social laws so as to guarantee coordination between agents and minimize the need for calling a central coordinator or for engaging in negotiation which requires intense communication. Finally, implemen...
Design of hybrid models for complex systems
 in Industry, University of Chemical Technology and Metallurgy, 1756
"... ABSTRACT: The paper considers an approach to design adequate models for plants with large uncertainties. Hybrid modelling schemes are described combining the First Principles based models, Fuzzy Logic models, Neural Network models and Statistical models. Several methods of aggregation are proposed: ..."
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Cited by 8 (0 self)
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ABSTRACT: The paper considers an approach to design adequate models for plants with large uncertainties. Hybrid modelling schemes are described combining the First Principles based models, Fuzzy Logic models, Neural Network models and Statistical models. Several methods of aggregation are proposed: (i) Fuzzy gain scheduling of particular parameters of the First Principles model by most important input factors; (ii) Weighted sum of output signals from First Principles gain scheduled model and Fuzzy Logic model; (iii) A hybrid architecture for Hammerstein type model. A Fuzzy Cognitive Map (FCM) is used to aggregate Separate Models and to fit more precisely the plant behaviour at different operational conditions. The presented methods are applied to the modelling of Steam Boiler MillFan.
Global Stability of Generalized Additive Fuzzy Systems
 IEEE Trans. Systems, Man, and Cybernetics  C
, 1998
"... This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable ( ..."
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Cited by 5 (0 self)
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This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable (negative definite). So local rule stability leads to global system stability. This relationship between local and global system stability does not hold for the better known discrete versions of feedback fuzzy systems. A corollary shows that it does hold for the discrete versions in the special but practical case of diagonal rule matrices. The paper first reviews additive fuzzy systems and then extends them to the class of generalized additive fuzzy systems. The Appendix derives the basic ratio structure of additive fuzzy systems and shows how supervised learning can tune their parameters.
PerceptionBased Reasoning and Fuzzy Cardinality Provide Direct Measures of Causality Sensitive to Initial Conditions in the Individual Stroke Patient (Invited Paper)
 Initial Conditions in the Individual Patient’, Int
, 2003
"... Background : Clinical trials in medicine use probabilitybased statistics. Statistics separate the patient's physiologic elements (specified as variables when given numeric form) from his or her body and define causal correlation for the group. Diagnostic and clinical decisions at the individual pat ..."
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Cited by 2 (0 self)
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Background : Clinical trials in medicine use probabilitybased statistics. Statistics separate the patient's physiologic elements (specified as variables when given numeric form) from his or her body and define causal correlation for the group. Diagnostic and clinical decisions at the individual patient level are currently based on these definitions of causation. Because data is grouped and averaged, the relationship to initial conditions and their connection to the individual patient is lost. We develop an alternative method that directly measures "causality" in the individual patient that is sensitive to initial conditions. Methods: We define the measure of causal connection between elements in the individual patient. Necessary and Su# cient Causal Ground, Formal Causal Ground and Clinical Causal E#ect are derived from the fuzzy subsethood theorem defined by Kosko. From these causal measures, we derive the clinical e#ciency measure K from units of fuzzy cardinality. It is how much causal e#ect is present per unit of a specific patient's initial conditions. Practically, as "sets as points" in a unit hypercube, each patient is represented as a fuzzy set of defined elements at di#erent points in time. E#ciency K is defined as the extracubal causality measure for any process not represented in the cube acting on the patient between two points in the unit hypercube. For any process, 1/K gives us the dosage necessary of that agent needed to move that specific patient's initial condition per unit of causal e#ect. Results: The measures of formal causal ground and clinical causal e#ect are in units of fuzzy cardinality. Thus the Received by the editors November 27, 2002 / final version received December 6, 2002. Key words and phrases. Causation, initial conditions, fuzzy hy...
DECISION MAKING FOR NETWORK HEALTH ASSESSMENT IN AN INTELLIGENT INTRUSION DETECTION SYSTEM ARCHITECTURE
"... This paper describes the use of artificial intelligence techniques in the creation of a networkbased decision engine for decision support in an Intelligent Intrusion Detection System (IIDS). In order to assess overall network health, the decision engine fuses outputs from different intrusion detect ..."
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Cited by 1 (0 self)
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This paper describes the use of artificial intelligence techniques in the creation of a networkbased decision engine for decision support in an Intelligent Intrusion Detection System (IIDS). In order to assess overall network health, the decision engine fuses outputs from different intrusion detection sensors serving as “experts ” and then analyzes the integrated information to present an overall security view of the system for the security administrator. This paper reports on the workings of a decision engine that has been successfully embedded into the IIDS architecture being built at the Center for Computer Security Research, Mississippi State University. The decision engine uses Fuzzy Cognitive Maps (FCM)s and fuzzy rulebases for causal knowledge acquisition and to support the causal knowledge reasoning process.
The Measure of Causality in PerceptionBased Dosing of the Individual Stroke Patient and Responsiveness to Therapeutic Intervention
, 2005
"... We have shown that perceptionbased reasoning and fuzzy cardinality can provide a direct measure of causality sensitive to initial conditions in the individual patient. When the physician doses a medication, he or she carefully considers the expected and actual result of his or her action in the sp ..."
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We have shown that perceptionbased reasoning and fuzzy cardinality can provide a direct measure of causality sensitive to initial conditions in the individual patient. When the physician doses a medication, he or she carefully considers the expected and actual result of his or her action in the specific patient context. Until now, expert opinion in this setting has not been quantifiable, which has forced a reliance on "evidencebased medicine" recommendations derived from group based statistics. Methods: Using fuzzy cardinality and the unit hypercube construct, we defined measures of causal connection between elements using the fuzzy subsethood theorem defined by Kosko. The cubal causation measures of necessary and sufficient causation were defined in this manner and allowed an extracubal causality measure, called the clinical efficiency measure K, to be derived. The measure K quantifies the effect of known and unknown elements in the patient's context on any therapeutic manouever that takes the patient from one physiologic state to another. Representation of the individual patient in the unit hypercube as a fuzzy "set as point" of defined elements at initial and final conditions, allows any process which acts on the patient between two points in the unit cube to be visualized and quantified. In order to make a judgment of clinical acumen, the efficiency measure K of the actual effect of the physician's decision can be compared to that of the desired effect by taking the difference using subtraction. To exemplify this, we chose in this study to calculate K for the causal effect on the International Normalized Ratio of warfarin dosing and compare this measure to that of the desired effect of that dose. Results: The clinical efficiency measure K was calculated for the p...
Rule Based Fuzzy Cognitive Maps  Expressing Time in
"... Time is essential in the study of System Dynamics. When we are trying to represent and analyze the dynamics of complex quantitative systems, the problem of expressing the "effect" of time flow is naturally solved since the mathematical equations that describe the relations between the entities of th ..."
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Time is essential in the study of System Dynamics. When we are trying to represent and analyze the dynamics of complex quantitative systems, the problem of expressing the "effect" of time flow is naturally solved since the mathematical equations that describe the relations between the entities of the system are a function of time. However, if we are dealing with real world qualitative systems that are impossible or difficult to model using mathematical equations, then the use of natural language becomes the best tool to represent the system and expressing time influence becomes a real issue that has not been addressed before. This paper introduces a coherent procedure to implicitly represent time in Rule Based Fuzzy Cognitive Maps which are a previously introduced methodology and tool to represent and simulate the dynamics of qualitative systems.
Automatic Implementation and Simulation of Dynamic Qualitative
"... This paper presents the overview of an ongoing project which goal is to obtain and simulate the dynamics of qualitative systems through the combination of the properties of Fuzzy Boolean Networks and Fuzzy Rule Based Cognitive Maps. ..."
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This paper presents the overview of an ongoing project which goal is to obtain and simulate the dynamics of qualitative systems through the combination of the properties of Fuzzy Boolean Networks and Fuzzy Rule Based Cognitive Maps.