Carl Looney

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Ricardo Jaña

Instituto Antártico Chileno

Imam Machali, S.Pd.I., M.Pd. Imam Machali, S.Pd.I., M.Pd.

UIN Sunan Kalijaga

ahmed adel

Minia University

Georgina Garza-Ramos

Universidad Nacional Autónoma de México

Someswar Rao Sagurthi

Osmania University

Maja Abram

University of Rijeka, Faculty of Medicine

Thomas Farmer

University of York

Jelena Roganović

University of Rijeka

Jack Rutledge

University of Wisconsin-Madison

Khushboo Sharma

IGKV, RAIPUR

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Papers by Carl Looney

Pattern Recognition

Handbook Series for Mechanical Engineering, 2002

Clustering via a kernel fuzzy connectivity matrix

Robust Successive Clustering via Feature Similarity

Fuzzy Analysis and Classification of Mislabeled and Noisy Data

Comparative Experiments on Clustering Validities

A Better Clustering Validity Measure

Logical controls via Boolean rule matrix transformations

IEEE Transactions on Systems, Man, and Cybernetics, 1987

ABSTRACT A model is described that uses Boolean rule matrices that are equivalent to implication ... more ABSTRACT A model is described that uses Boolean rule matrices that are equivalent to implication digraphs to transform truth states associated with rule conditions into deduced or abduced truth states. Such transformations realize propositional logic to deduce controls for complex real-time noninteractive systems. The algorithm runs in deterministically polynomial time and is easy to implement. The rule matrix is decomposable into subsystems with rule submatrices for distributed processing in multiple microprocessors. A single transformation of a truth state fires every entire implication path for which the initial, i.e. root, condition is true, whereas a user-interactive production system fires a single rule at a time and uses the output in the firing of other rules. The method can be used to perform stimulus-response-type control such as humans use to perform such feats as flying airplanes, riding bicycles, or controlling nuclear reactors.

A Krein-Milman type theorem for certain unbounded convex sets

Journal of Mathematical Analysis and Applications, 1974

demonstrated in 1966 that every closed bounded convex set in a dual separable Banach space is the... more demonstrated in 1966 that every closed bounded convex set in a dual separable Banach space is the closed convex hull of its extremal points. Asimow [l] has extended Choquet's notion of well-capped cones to closed convex sets, and has proved that any well-capped closed convex set is equal to the closed convex hull of its extremal points and extre-ma1 rays. In this investigation we consider the case of a closed (unbounded) convex set in a dual separable Banach space and establish a sufficient condition for such a set to be the closed convex hull of its extremal points and extremal rays. The main result is a more general statement (see Proposition 3.1 and corollaries). The criterion alluded to is the property that the closed convex set be well pseudocapped, a more general property than that of being well capped as in Asimow [I] and Choquet . The concepts of dentable sets and denting points [17] are used to obtain well pseudocapped sets. An example shows that the class of sets for which the main result holds, but for which the theory of Asimow does not, is not vacuous. Another example demonstrates that if the denting condition is omitted, then the result doesn't hold. E denotes a LCHTVS (locally convex Hausdorff topological vector space) over IR unless otherwise stated. E' will designate the topological dual, while E* will symbolize the algebraic dual. If XC E, then cl(X), eu-cl(X) and zu*-cl(X), respectively, will designate the closure of X in the original, weak, and weak* topologies, respectively. The sets of extremal points, extremal rays, and exposed points of X will be denoted, respectively, by ext X, extr X, and exp X. The closed line segment between the points x and y in E will be denoted [x, y], from which the meanings of [x, y[, lx, y], and lx, y[

Carl Looney

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