Even degree B-spline curves and surfaces: A note on the paper “B-spline Curves and Surfaces Viewed as Digital Filters” by A. Goshtasby,F. Cheng,and B. Barsky

This paper compares two different ways of building B-spline curves and surfaces for even degree polynomial splines. Viewing these problems as digital filters, we find that one way gives better results than the other one. This paper is intended to be a reflection and a continuation of the paper “B-spline Curves and Surfaces Viewed as Digital Filters,” by A. Goshtasby, F. Cheng, and B. Barsky (Comput. Vision Graphics Image Process. 52, 1990, 264–275).     

A review of: “FUZZY SETS,UNCERTAINTY, AND INFORMATION,” by George J. Klir and Tina A. Folger. Prentice Hall,Englewood Cliffs,N.J., 1988, XI+ 355 pp.

Possibility distribution introduced by Zadeh ["Fuzzy sets as a basis for a theory of possibility theory", Fuzzy Sets Syst. 1 (1978) 3-28] in his introductory paper of possibility theory assumes a normal distribution, in the sense that it supposes the existence of at least one element s 0 of the universe of discourse U , for which the distribution ~ is fully compatible with the context of interest: ~ (s 0 )=1. However, when such element does no longer exist, it leads to a subnormal possibility distribution. This situation may arise from incomplete data, inconsistent statements, or contradictory beliefs. To deal with such case, many authors like Yager ["On the relationships of methods of aggregation evidence in expert systems", Cybern. Syst. , 16 (1985) 1-21; "A modification of the certainty measure to handle subnormal distributions", Fuzzy Sets Syst. , 20 (1986) 317-324], Dubois and Prade ["An alternative approach to the handling of subnormal possibility distributions--A critical comment on a proposal of Yager", Fuzzy Sets Syst. , 24 (1987) 123-126] have put forward some proposals in order to keep track of the consistency of the basic axioms attached to possibility and necessity measures. In this paper, the proposals are reviewed in the light of new results regarding some appealing criteria. Particularly, when subnormal distribution and normal distribution are encountered in the same level, intuitively, two approaches are possible: Either the subnormal distributions are risen up to a normal distribution level, or the normal ones are flatted down to agree with the normal ones. In both cases there is a sort of gaining or losing information. We review some of the proposal solutions. The flatting approach is mainly related to fuzzy arithmetic calculus while the rising effect is motivated by Dempster-Shafer theory of evidence and its normalization paradigm. The two approaches will also be investigated with respect to some appealing criteria like preference preservation, distance minimization, entropy, minimum/maximum specificity, and, further, particular interest is focused on information based uncertainty preservation. Later on, the proposals are discussed according to the f -certainty qualification where the greatest value h of the subnormal distribution is understood as a degree of certainty that must be attached to the resulting normal distribution.     

A review of: “Human Judgments and Optimality.” By M. W. SHELLY,II, and G. L. BRYAN (Editors). (John Wiley, 1964.)

Abstract

In order to evaluate the efficiency of various commercial chemical fabric softeners, a technique of obtaining subjective assessment known as ‘magnitude estimation’ was used to estimate the fabric softness. Particular emphasis was given to subjective scaling and limits of human perception. Comparison between softness and compression ( a physical measure) was demonstrated     

A review of: “Actes du Colloque ELABORATION ET JUSTIFICATION DES MODELES”, edited by P. Delattre and M. Thellier. Maloine S.A., Paris, 1979, 2 volumes, 748 pp.

This paper utilizes trapezoidal rule together with Genetic Algorithm (GA) to convert a continuous-time system with input and state delays to an equivalent discrete-time one. A new method has been proposed to construct the hybrid control of sampled-data system with state and input delays via digital redesign which transforms the control law of a continuous-time system with state and input delays into an equivalent one of a sampled-data system so that the states of the digitally controlled sampled-data system closely match those of the originally well-designed continuous-time system for a relatively longer sampling period. An example is given to demonstrate that the proposed digital redesign is superior to the existing ones under a longer sampling period.     

Work capacity and anticipation in A.A. Ukhtomsky’s concept of dominance

This paper presents the results of theoretical and experimental investigations of human activity and anticipation based on A.A. Ukhtomsky’s concept of brain dominance – a non-equilibrium system-forming factor in living systems. Facts on the stages of dominance formation are presented in relation to the creative abilities of the human brain and the role of fatigue as a “lever” for increasing systems’ work capacity on the basis of “trace exaltation”. Individually, specific features of dominantogenesis are compared with variations in behavioural types. On the basis of chronotopic EEG analysis, we delineate cortical dominants that underlie individual specifics of cognitive processes. The relation is shown between anticipation and the “expansion of dominants” – the broadening of “distal perception” in time and space, as framed by A.A. Ukhtomsky.