Abstract: An explicit assumption of continuity is used to generate a fuzzy implication operator, which yields an envelope of possibility for the conclusion. A single fuzzy rule A B entails an infinite set of possible hypothese A?B? whose degree of consistency with the original rule is a function of the “distance” between A and A? and the “distance” between B and B?. This distance may be measured geometrically or by set union/intersection. As the distance between A and A? increases, the possibility distribution B* spreads further outside B somewhat like a bell curve, corresponding to common sense reasoning about a continuous process. The manner in which this spreading occurs is controlled by parameters encoding assumptions about (a) the maximum possible rate of change of B? with respect to A? (b) the degree of conservatism or speculativeness desired for the reasoning process (c) the degree to which the process is continuous of chaotic.

Abstract: An explicit assumption of continuity is used to generate a fuzzy implication operator, which yields an envelope of possibility for the conclusion. A single fuzzy rule A B entails an infinite set of possible hypothese A′ B′ whose degree of consistency with the original rule is a function of the “distance” between A and A′ and the “distance” between B and B′. This distance may be measured geometrically or by set union/intersection. As the distance between A and A′ increases, the possibility distribution B* spreads further outside B somewhat like a bell curve, corresponding to common sense reasoning about a continuous process. The manner in which this spreading occurs is controlled by parameters encoding assumptions about (a) the maximum possible rate of change of B′ with respect to A′(b) the degree of conservatism or speculativeness desired for the reasoning process (c) the degree to which the process is continuous of chaotic.