Using the notion of a vaguely defined object, we systematize and unify different existing approaches to vagueness and its mathematical representations, including fuzzy sets and derived concepts. Moreover, a new, approximative approach to vaguely defined objects will be introduced and investigated.
Sensor placement is an optimisation problem that has recently gained great relevance. In order to achieve accurate online updates of a predictive model, sensors are used to provide observations. When sensor location is optimally selected, the predictive model can greatly reduce its internal errors. A greedy-selection algorithm is used for locating these optimal spatial locations from a numerical embedded space. A novel architecture for solving this big data problem is proposed, relying on a variational...
We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that...
The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ωε = ε). It is a collection φα of the Veblen Functions where φ0(β) = ωβ and φ1(β) = εβ. The sequence of fixpoints of φ1 function form φ2, etc. For a limit non empty ordinal λ the function φλ is the sequence of common fixpoints of all functions φα where α < λ.The Mizar formalization of the concept cannot be done directly as the Veblen functions are classes (not (small) sets). It is done...
This paper is concerned with a formal verification of the Formal Concept Analysis framework. We use the PVS system to represent and formally verify some algorithms of this theory. We also develop a method to transform specifications of algorithms based on finite sets into other executable ones, preserving its correctness. We illustrate this method by constructing an executable algorithm to compute an implicational base of the system of implications between attributes of a finite formal context.
A visual system prototype that detects anomalies or defects in real time under normal lighting operating conditions was built for NASA at the Kennedy Space Center (KSC). The system prototype is basically a learning machine that integrates the three elements of soft computing, Fuzzy Logic (FL), Artificial Neural Network (ANN), and Genetic Algorithm (GA) schemes to process the image, run the learning process, and finally detect the anomalies or defects. The system acquires the image, performs segmentation...