206667534
Discrete (set) derivatives and "algebraic" fuzzy logic operations
We propose a new way to generalize logical operations from the discrete classical logic to a continuous fuzzy logic, namely we propose to define derivatives for the discrete case, and then to use these derivatives to derive the continuous operations. We show that this natural approach leads to "algebraic" fuzzy operations a/spl middot/b and a+b-a/spl middot/b.
11690500
Fast rotation of a 3D image about an arbitrary line
Abstract A graphical computer system must give the user an opportunity to look at an object from different angles. For that, we must be able, given two points P1 and P2 in space and an angle Φ, to rotate an object by the angle Φ about the line P1P2. This is usually done by rotating vertices (or other points that represent an object) and connecting them. Since an image can have lots of vertices, it is important to be able to rotate each of them quickly. Therefore, we are interested in a rotation method that would consist of the smallest possible number of computational steps. The usual method (see, e.g., [1]) includes four nonarithmetic operations (namely, computing sin Φ, cos Φ, and two square roots), and seven multiplications of 4 × 4 matrices. Nonarithmetic operations are necessary because the known expression for a rotated point includes sin Φ, cos Φ, and a square root. However, we can try to reduce the number of arithmetic operations (+, -, ×, :). In this paper, we propose an algorithm that consists of only 30 arithmetic steps: it is less than 1 10 of the number of steps used in the traditional method.
3008218
Hyperbolic approach to fuzzy control is optimal
In a series of papers and a book, Margaliot and Langholz (1999, 2000) proposed a hyperbolic approach to fuzzy control, in which they apply a certain hyperbolic non-linear transformation to the original variables. We consider all possible nonlinear transformations of this type and show that this hyperbolic transformation is indeed optimal.
13290457
Logic-motivated choice of fuzzy logic operators
Many different "and"- and "or"-operations have been proposed for use in fuzzy logic. It is therefore important to select, for each particular application, the operations which are the best for this particular application. Several papers discuss the optimal choice of "and"- and "or"-operations for fuzzy control, when the main criterion is to get the stablest control (or the smoothest or the most robust or the fastest-to-compute). In reasoning applications, however, it is more appropriate to select operations which are the best in reflecting human reasoning, i.e., operations which are "the most logical". In this paper, we explain how we can use logic motivations to select fuzzy logic operations, and show the consequences of this choice. As one of the unexpected consequences, we get a surprising relation with the entropy techniques, well known in probabilistic approach to uncertainty.
15177336
Interval Methods in Non-Destructive Testing of Material Structures
In many practical situations, e.g., in aerospace applications and in mammography, it is important to test the structural integrity of material structures. We show that interval methods can help.
29337433
Fair Division Under Interval Uncertainty
It is often necessary to divide a certain amount of money between n participants, i.e., to assign, to each participant, a certain portionwi≥0 of the whole sum (so that w1+⋯+ wn=1). In some situations, from the fairness requirements, we can uniquely determine these "weights" wi. However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the intervals of possible fair weights. We show that natural fairness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncertainty.
13924814
Why clustering in function approximation? Theoretical explanation
Follow this and additional works at: http://digitalcommons.utep.edu/cs_techrep Part of the Computer Engineering Commons Comments: UTEP-CS-99-3. Preliminary version published by The Chinese University of Hong Kong, Department of Mechanical and Automation Engineering, as Technical Report CUHK-MAE-99-001, January 1999; full version published in International Journal of Intelligent Systems, 2000, Vol. 15, No. 10, pp. 959-966.