By L. C. Biedenharn

This 1985 textual content develops the idea of angular momentum from the point of view of a primary symmetry in nature and exhibits how this idea pertains to utilized components of study in smooth quantum physics

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**Sample text**

This makes the initial value a central measure, a location parameter of the distribution. The determination of the other parameters is simpliﬁed by assuming independence between disturbances affecting different alternatives and equal dispersion. 3 Modeling the Probability Distribution 33 source of the random disturbances, it is reasonable to model the distributions as normal distributions. However, simpliﬁcations may be considered. If the attributes that give rise to the preferences are represented by discrete variables, the approach of Fuzzy Sets Theory, of replacing exact values by membership functions, is naturally taken.

Thus, the nearer the value of µA(y) to unity, the higher the degree of membership of y to A. This deﬁnition of a fuzzy set extends the deﬁnition of a set in the ordinary sense of the term. The degrees of membership of 0 and 1 correspond to the two possibilities of truth and false pertinence to an ordinary set, called a crisp set in the Theory of Fuzzy Sets. 1 Fuzzy Numbers Membership functions for fuzzy sets can be deﬁned in any form as long as they follow the rules of the deﬁnition of a fuzzy set.

In the ﬁrst aspect, the decision maker in the progressive side pays attention to maximize the probabilities of preference according to the criteria examined, while for that in the conservative side the odds that matter are of not minimizing such preferences. The progressive decision maker pays attention to the differences between the alternatives near the frontier of excellence; for the conservative one what is important is to differentiate those near the frontier of worst performance. © Springer International Publishing Switzerland 2015 A.