Soft Computing Evaluation Logic

PART TWOGRADED LOGIC AND AGGREGATION

How do human beings aggregate subjective categories, and which mathematical models describe this procedure adequately?

—H.‐J. Zimmermann (question from the last chapter of his book Fuzzy Set Theory— and Its Applications)

In Part Two of the book, we study graded evaluation logic and develop logic aggregators using a strictly anthropocentric approach. We try to answer the fundamental question, “How do human beings aggregate subjective categories, and which mathematical models describe this procedure adequately?” [ZIM96]. We investigate this problem in the context of evaluation reasoning. We also believe that all books about logic and/or decision making should ask this fundamental question explicitly and as early as possible (well, not in the last chapter). In our case, the appropriate place for this question is right here. Then, in Section 2.1.8, we offer an explicit answer to this question.

In the area of aggregation, as the point of departure, it is necessary to differentiate two categories of aggregation problems:

1. Mathematical problems of aggregation of anonymous real numbers.
2. Decision engineering problems of aggregation of arguments that have specific semantic identity.

In the case of aggregation of anonymous real numbers, the goal is to study the widest possible class of aggregation functions. In the case of aggregation of arguments that have semantic identity (i.e. the role, meaning, units of measurement, and impact on attaining specific ...