Robert J. Hammell

Interpolation, completion, and learning fuzzy rules

Fuzzy inference systems and neural networks both provide mathematical systems for approximating continuous real-valued functions. Historically, fuzzy rule bases have been constructed by knowledge acquisition from experts while the weights on neural nets have been learned from data. This paper examines algorithms for constructing fuzzy rules from input-output training data. The antecedents of the rules are determined by a fuzzy decomposition of the input domains. The decomposition localizes the learning process, restricting the influence of each training example to a single rule. Fuzzy learning proceeds by determining entries in a fuzzy associative memory using the degree to which the training data matches the rule antecedents. After the training set has been processed, similarity to existing rules and interpolation are used to complete the rule base. Unlike the neural network algorithms, fuzzy learning algorithms require only a single pass through the training set. This produces a computationally efficient method of learning. The effectiveness of the fuzzy learning algorithms is compared with that of a feedforward neural network trained with back-propagation. >

A fuzzy c-means variant for the generation of fuzzy term sets

A fuzzy c-means (FCM) variant is proposed for the generation of fuzzy term sets with ½ overlap. The proposed variant differs from the original mainly in two areas. The first modification ensures that two end terms take the maximum and minimum domain values as their centers. The second modification prevents the generation of non-convex fuzzy terms that often occurs with the original algorithm. The optimal number of terms and the optimal shape of the membership function associated with each term are determined based on the mean squared error criterion. The exponential weight, m, used in the algorithm is found to greatly affect the shape of the membership function. The effect of data size used for the generation of fuzzy terms is also discussed. A generalized π-shaped function with a tunable parameter along with its complement is developed to fit all term sets generated by the FCM variant using various m values.

RULE BASE COMPLETION IN FUZZY MODELS

Approximation theory based on fuzzy sets provides a mathematical tool for modeling complex systems. A fuzzy model is defined by a family of rules whose antecedents consist of fuzzy sets that partition the input domain of the system. An incomplete model is obtained when the information used to construct the model is insufficient to produce rules for each possible input condition. Rule base completion generates new rules by utilizing the similarity of the antecedents of the existing rules to the conditions for which the rule base specifies no action or response. The effectiveness of completion as a tool for building fuzzy models is demonstrated by two applications. The first incorporates completion into an algorithm that learns fuzzy rules from training data and the second uses completion to modify rules in an adaptive fuzzy system.

Granularity and specificity in fuzzy function approximation

This paper describes some preliminary investigations into the relationships between granularity and specificity in fuzzy rule bases. It proposes a strategy for learning fuzzy rules that optimizes granularity based on a desired degree of specificity. In addition, this approach may be used to combine rule bases of various degrees of granularity.

Capturing the value of information in complex military environments: A fuzzy-based approach

Todays military operations require information from an unprecedented number of sources resulting in an overwhelming volume of collected data. A primary challenge for military commanders and their staff is separating the important information from the routine. Currently, the Value of Information (VOI) assigned a piece of information is a multiple step process requiring intelligence collectors and analysts to judge its value within a host of differing operational situations. The cognitive processes behind these conclusions resist codification with exact precision suggesting that new methodologies are required to deal with this significant issue. This paper presents an approach for calculating the VOI in complex military environments using a fuzzy associative memory model as an effective framework for contextually tuning the VOI based on the informations content, source reliability and latency.

A Fuzzy-Based Approach to Support Decision Making in Complex Military Environments

Data for military intelligence operations are increasing at astronomical rates. As a result, significant cognitive and temporal resources are required to determine which information is relevant to a particular situation. Soft computing techniques, such as fuzzy logic, have recently been applied toward decision support systems to support military intelligence analysts in selecting relevant and reliable data within the military decision making process. This article examines the development of one such system and its evaluation using a constructive simulation and human performance model to provided critical understanding of how this conceptual information system might interact with personnel, organizational, and system architectures. In addition, similarities between military intelligence analysts and cyber intelligence analysts are detailed along with a plan for transitioning the current fuzzy-based system to the cyber security domain.

Enhancing Battlefield Situational Awareness through Fuzzy-Based Value of Information

A major tenet of the US Armys data-to-decision initiative and a primary challenge for military commanders and their staff is the ability to shorten the cycle time from data gathering to decisions. Today, military operations require information from an unprecedented number of sources resulting in an unprecedented volume of collected data. Required are decision support technologies to improve the synthesis of data to decisions. Paramount to this process is the ability to better assess the applicability and relevance of information for decisions in complex military environments. Towards this end, this paper presents a soft computing approach and early results for calculating the Value of Information (VoI) in complex military environments using fuzzy associative memory as an effectively framework for contextually tuning its value based on content, reliability and latency.

An adaptive hierarchical fuzzy model

Abstract Fuzzy models have been designed to represent approximate or imprecise relationships in complex systems and have been successfully employed in control systems, database systems and decision analysis. A hierarchical architecture for fuzzy modeling and inference has been developed to allow adaptation based on system performance feedback. A general adaptive algorithm is presented and its performance examined for three types of adaptive behavior: continued learning, gradual change and drastic change. In continued learning, the underlying system does not change and the adaptive algorithm utilizes the real-time data and associated feedback to improve the accuracy of the existing model. Gradual and drastic change represent fundamental alterations to the system being modeled. In each of the three types of behavior, the adaptive algorithm has been shown to be able to reconfigure the rule bases to either improve the original approximation or adapt to the new system.

A Two-Level Architecture for Fuzzy Learning

Fuzzy learning algorithms provide an efficient method for generating approximating functions from training data. The approximations are obtained by constructing a fuzzy associative memory whose entries are determined locally using the information contained in the training set. A two-level fuzzy learning algorithm is introduced that incorporates error analysis into the approximation. The addition of a second fuzzy associative memory provides a significant improvement in the accuracy of the resulting approximations. The construction requires only one additional pass through the training data, maintaining the efficiency of the fuzzy learning algorithms. The improvement in accuracy is obtained without increasing the number of training instances, making this technique particularly suitable for problem domains in which the training information is unavailable or expensive to obtain.

A Theoretical Exploration of the Impact of Packet Loss on Network Intrusion Detection

In this paper we review the problem of packet loss as it pertains to Network Intrusion Detection, seeking to answer two fundamental research questions which are stepping stones towards building a model that can be used to predict the rate of alert loss based upon the rate of packet loss. The first question deals with how the packet loss rate affects the sensor alert rate, and the second considers how the network traffic composition affects the results of the first question. Potential places where packet loss may occur are examined by dividing the problem into network, host, and sensor based packets loss. We posit theories about how packet loss may present itself and develop the Packet Dropper that induces packet loss into a dataset. Drop rates ranging from 0% to 100% are applied to four different data sets and the resulting abridged data sets are analyzed with Snort to collect alert loss rate. Conclusions are drawn about the importance of the distribution of packet loss and the effect of the network traffic composition.