By R. T. Compton
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Extra info for Adaptive antennas : concepts and performance
Our degree of belief in A is equal to a, and belief in B is equal to b. If we have no other information about A and B, what must the reasonable degree of belief in A&B equal to? This reasonable degree of belief will be denoted by f&(a, b). In the same situation, a reasonable degree of believe in will be denoted by , and will be called an -operation. In describing uncertainty of a membership function, we used the interpretation of membership values π(x) as frequencies. Namely, we assumed that as a truth value t(A) of an uncertain statement A, we take the ratio t(A) = N(A)/N, where N(A) is the number of experts who believe in A, and N is the total number of experts that were questioned.
We can more specifically denote the antecedent condition in this basic case as if V is Ai is possible then .... It is noted that as D increases ℑi will not decrease. In particular a decrease in specificity of the input causes an increase in firing level or relevancy of the rules. There exists an alternative, and as we shall show, more stringent requirement we can make on the antecedent condition. In particular we suggest that an alternative antecedent requirement is “if V is Ai is certain then …” We mean to indicate that the ith rule fires if we can certain the value for V lies in Ai.
However, it is clearly most closely related to the information-based complexity [18, 19], and we shall use a neutral term information throughout this article. This usage obviates the need of axiomatic characterization, which is not germaine to this concept. At the same time there are certain ties to Shannon entropy, which we discuss in the closing section . Other ties, perhaps more significant, are to the possibilistic information on continuous domains. This relationship can be made formal as we point out in the closing section.