A hierarchical structure for representing and learning fuzzy rules

Yager provides an example in which the flat representation of fuzzy if-then rules leads to unsatisfactory results. Consider a rule base consisting to two rules: if U is 12 the V is 29; if U is (10-15) the V is (25-30). If U = 12 we would get V is G where G = (25-30). The application of the defuzzification process leads to a selection of V = 27.5. Thus we see that the very specific instruction was not followed. The problem with the technique used is that the most specific information was swamped by the less specific information. In this paper we shall provide for a new structure for the representation of fuzzy if-then rules. The representational form introduced here is called a Hierarchical Prioritized Structure (HPS) representation. Most importantly in addition to overcoming the problem illustrated in the previous example this HPS representation has an inherent capability to emulate the learning of general rules and provides a reasonable accurate cognitive mapping of how human beings store information

Estimations of expectedness and potential surprise in possibility theory

This note investigates how various ideas of 'expectedness' can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying 'I would not be surprised that...' before an event takes place, or by saying 'I knew it' after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined

Friction characteristics of 20 x 4.4, type 7, aircraft tires constructed with different tread rubber compounds

A test program was conducted at the Langley aircraft landing loads and traction facility to evaluate the friction characteristics of 20 x 4.4, type, aircraft tires constructed with experimental cut-resistant, tread rubber compounds. These compounds consisted of different blends of natural rubber (NR) and an alfin catalyzed styrene-butadiene copolymer rubber (SBR). One tire having a blend of 30 SBR and 70 NR and another having a blend of 60 SBR and 40 NR in the tread were tested together with a standard production tire with no SBR content in the tread rubber. The results of this investigation indicated that the test tires constructed with the special cut-resistant tread rubber compositions did not suffer any significant degradation in tire friction capability when compared with the standard tire. In general, tire friction capability decreased with increasing speed and surface wetness condition. As yaw angle increased, tire braking capability decreased while tire cornering capability increased. Tread-wear data based on number of brake cycles, however, suggested that the tires with alfin SBR blends experienced significantly greater wear than the standard production tire

Traction Characteristics of a 30 by 11.5-14.5, Type 8, Aircraft Tire on Dry, Wet and Flooded Surfaces

A limited test program was conducted to extend and supplement the braking and cornering data on a 30 x 11.5-14.5, type VIII, aircraft tire to refine the tire/runway friction model for use in the development of an aircraft ground performance simulation. Tire traction data were obtained on dry, wet and flooded runway surfaces at ground speeds ranging from 5 to 100 knots and at yaw angles extending up to 12 deg. These friction coefficients are presented as a function of slip characteristics, namely, the maximum and skidding drag coefficients and the maximum cornering coefficients are presented as a function of both ground speed and yaw angle to extend existing data on that tire size. Tire braking and cornering capabilities were shown to be affected by vehicle ground speed, wheel yaw attitude and the extent of surface wetness

Adaptive defuzzification for fuzzy systems modeling

We propose a new parameterized method for the defuzzification process based on the simple M-SLIDE transformation. We develop a computationally efficient algorithm for learning the relevant parameter as well as providing a computationally simple scheme for doing the defuzzification step in the fuzzy logic controllers. The M-SLIDE method results in a particularly simple linear form of the algorithm for learning the parameter which can be used both off- and on-line