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Rickard J.T.,Distributed Infinity Inc | Aisbett J.,University of Newcastle | Yager R.R.,The College of New Rochelle
IEEE Transactions on Fuzzy Systems | Year: 2015

We introduce a new structure for fuzzy cognitive maps (FCM) where the traditional fan-in structure involving an inner product followed by a squashing function to describe the causal influences of antecedent nodes to a particular consequent node is replaced with a weighted mean type operator. In this paper, we employ the weighted power mean (WPM). Through appropriate selection of the weights and exponents in the WPM operators, we can both account for the relative importance of different antecedent nodes in the dynamics of a particular node, as well as take a perspective ranging continuously from the most pessimistic (minimum) to the most optimistic (maximum) on the normalized aggregation of antecedents for each node. We consider this FCM structure to be more intuitive than the traditional one, as the nonlinearity involved in the WPM is more scrutable with regard to the aggregation of its inputs. We provide examples of this new FCM structure to illustrate its behavior, including its convergence, and compare it with a traditional FCM architecture on a scenario presented in previous works. © 2015 IEEE.


Rickard J.T.,Distributed Infinity Inc | Aisbett J.,University of Newcastle | Yager R.R.,The College of New Rochelle | Gibbon G.,University of Newcastle
IEEE International Conference on Fuzzy Systems | Year: 2011

We have introduced the linguistic weighted power mean and its computation via a generalization of the Karnick-Mendel algorithm. This new family of aggregation operators admits interval type-2 fuzzy membership functions for both its inputs and its weights to account for imprecise knowledge of these quantities. The simplest member of this family, the linguistic weighted average, is the primary instantiation of a "perceptual computing" engine in Mendel and Wu's recent book by this title. This paper presents a comparison of the linguistic weighted power mean and the linguistic weighted average on one of the examples they describe in detail the "investment judgment advisor". Our results illustrate the flexibility and range of logical inference provided by this very versatile aggregation operator for computing with words applications. © 2011 IEEE.


Aisbett J.,University of Newcastle | Rickard J.T.,Distributed Infinity Inc | Morgenthaler D.,Lockheed Martin
Fuzzy Sets and Systems | Year: 2011

This paper explores the link between type-2 fuzzy sets and multivariate modeling. Elements of a space X are treated as observations fuzzily associated with values in a multivariate feature space. A category or class is likewise treated as a fuzzy allocation of feature values (possibly dependent on values in X). We observe that a type-2 fuzzy set on X generated by these two fuzzy allocations captures imprecision in the class definition and imprecision in the observations. In practice many type-2 fuzzy sets are in fact generated in this way and can therefore be interpreted as the output of a classification task. We then show that an arbitrary type-2 fuzzy set can be so constructed, by taking as a feature space a set of membership functions on X. This construction presents a new perspective on the Representation Theorem of Mendel and John. The multivariate modeling underpinning the type-2 fuzzy sets can also constrain realizable forms of membership functions. Because averaging operators such as centroid and subsethood on type-2 fuzzy sets involve a search for optima over membership functions, constraining this search can make computation easier and tighten the results. We demonstrate how the construction can be used to combine representations of concepts and how it therefore provides an additional tool, alongside standard operations such as intersection and subsethood, for concept fusion and computing with words. © 2010 Elsevier B.V. All rights reserved.


Aisbett J.,University of Newcastle | Rickard J.T.,Distributed Infinity Inc
Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, IFSA/NAFIPS 2013 | Year: 2013

Centroids are a common defuzzification method for fuzzy sets defined on the real line, and thus are practically important in type-1 and type-2 fuzzy logic systems. We propose a modified definition of the centroid that takes account of singleton spikes in membership. Such spikes are encountered in aggregates that combine fuzzy sets whose support is discrete with fuzzy sets whose support is defined on an interval. Our modified definition avoids a computational problem with the choice of discretization in the standard definition when spikes are present, and reduces to the usual one in the absence of spikes. © 2013 IEEE.


Aisbett J.,University of Newcastle | Rickard J.T.,Distributed Infinity Inc | Morgenthaler D.G.,Lockheed Martin
IEEE Transactions on Fuzzy Systems | Year: 2010

For many readers and potential authors, type-2 (T2) fuzzy sets might be more readily understood if expressed by the use of standard mathematical notation and terminology. This paper, therefore, translates constructs associated with T2 fuzzy sets to the language of functions on spaces. Such translations may encourage researchers in different disciplines to investigate T2 fuzzy sets, thereby potentially broadening their application and strengthening the underlying theory. © 2006 IEEE.


Aisbett J.,University of Newcastle | Rickard J.T.,Distributed Infinity Inc
IEEE Transactions on Fuzzy Systems | Year: 2014

Centroids are practically important in type-1 and type-2 fuzzy logic systems as a method of defuzzification and type reduction. However, computational problems arise when membership functions (MF) have singleton spikes. The novel thresholding aggregation operators that were described in our companion paper ' New Classes of Threshold Aggregation Functions Based Upon the Tsallis q-Exponential with Applications to Perceptual Computing' produce such MFs with spikes. Such spikes may occur when modeling concepts defined on a real-valued domain, and they are also formed in unions of fuzzy sets in which some have MFs with discrete support and others have support defined on an interval. This paper presents a modified definition of the centroid of a fuzzy set that avoids the computational problems associated with the usual definition and reduces to this definition when MFs are continuous and normal (i.e., of unit height) on some interval. We also present an enhanced Karnik-Mendel-type algorithm to compute the modified centroid of interval type-2 fuzzy sets whose MFs have spikes. © 2014 IEEE.


Rickard J.T.,Distributed Infinity Inc | Aisbett J.,University of Newcastle
IEEE Transactions on Fuzzy Systems | Year: 2014

We introduce two new classes of single-parameter aggregation functions based upon the Tsallis $q$-exponential (QE) function of nonextensive statistical mechanics. These aggregation functions (denoted QE aggregation) facilitate simple modeling of the common human reasoning trait of 'threshold' inference, where either 1) at least one input must exceed a threshold in order to achieve a nonzero aggregation output; or 2) if any one of the inputs exceeds a different threshold, the aggregation output takes its maximum value. We illustrate the thresholding behavior of these functions on interval type-2 fuzzy inputs using an example known in the literature as the Investment Judgment Advisor. We believe that the new QE class of aggregation operators will prove useful in extending the range of options available for the design of perceptual computing systems. © 2014 IEEE.


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase II | Award Amount: 743.07K | Year: 2011

ABSTRACT: We have shown in Phase I the technology provides unique benefits in scenario metrics, what-if analysis, and action/response assessment. We have also demonstrated a Phase I prototype that validates application in the relevant domain and the remaining work required to develop a transitionable adversarial threat assessment tool in Phase II. We propose to design, develop, and deliver a ground breaking tool that will significantly aide analyst work in predicting and combating such threats. The Space Assessment Simulator (SAS) will include complex models of relevant naturally occurring events, as well as models of potential adversary resources including both kinetic and cyber capabilities. SAS will apply powerful game-theoretic algorithms to deduce a wide range of possible threats, ranging from most likely to most dangerous. It will include a sophisticated timing model to capture possibilities of adversaries launching attacks coordinated with natural events to disguise or confuse interpretation of their actions. These threat trees will be passed to the analysts for use in developing appropriate countermeasures. BENEFIT: The Space Assessment Simulator contains a library of possible actions, goals, and domains that are potentially applicable to either the defender of the space assets, or an adversary. Player models are then developed that contain a subset of these moves available to each player. Potential interactive natural events are also stored. The Space Assessment Engine can then examine millions of possibilities, and output rank ordered threats.


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase I | Award Amount: 98.37K | Year: 2011

ABSTRACT: Virtualization technologies have the capability to provide significant improvements in horizontal network scalability. There are significant challenges, however, when adapting these technologies to tactical networks, where bandwidth, latency, and connection reliability issues combine to foil network characteristics that many network protocols within a virtualized network rely on. In particular, providing secure communication with minimum reliance on bandwidth and latency is absolutely critical. We propose to develop a new protocol applicable to this problem, which can enable secure communication between virtual network nodes with minimal bandwidth and latency constraints. It will do so with an emphasis on security, maintaining the ability to provide access control to virtual nodes as desired without burdening the system with the need to pass large access control restriction lists around the system, a requirement already presenting a significant burden on our tactical networks even without the expanded issues presented by network virtualization. BENEFIT: The need for a small bandwidth footprint and low latency impact are self-evident. In addition to these requirements, tactical networks require the ability to execute in a secure, and in some cases anonymous manner. If unprivileged network observers were able to deduce elements of the data addressed there could be catastrophic repercussions in the field of operation. In some cases, even deducing the participants in a data exchange operation can be vital information to an enemy. A virtualized network, with the potential for non-static location identifiers has an above average ability to provide such anonymity, but only if the protocol providing secure communication does not compromise this by requiring static key exchanges or other stable patterns allowing for information extraction by a participant in the networking environment.


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase I | Award Amount: 99.80K | Year: 2010

The United States has expended tremendous amounts of time and effort in maintaining the capability of our most critical space assets with a high degree of fidelity despite a wide range of possible occurrences. For the most part, however, the current threat model is largely natural. It has become increasingly important to improve our asset protection methodologies against malicious, intentional acts. These acts may be kinetic, cyber, or a combination, and may be timed to coincide with naturally occurring events that reduce our asset resiliency temporarily. We propose to design, develop, and deliver a ground breaking tool that will significantly aide analyst work in predicting and combating such threats. The Space Assessment Simulator (SAS) will include complex models of relevant naturally occurring events, as well as models of potential adversary resources including both kinetic and cyber capabilities. SAS will apply powerful game-theoretic algorithms to deduce a wide range of possible threats, ranging from most likely to most dangerous. It will include a sophisticated timing model to capture possibilities of adversaries launching attacks coordinated with natural events to disguise or confuse interpretation of their actions. These threat trees will be passed to the analysts for use in developing appropriate countermeasures. BENEFIT: The Space Assessment Simulator contains a library of possible actions, goals, and domains that are potentially applicable to either the defender of the space assets, or an adversary. Player models are then developed that contain a subset of these moves available to each player. Potential interactive natural events are also stored. The Space Assessment Engine can then examine millions of possibilities, and output rank ordered threats.

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