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Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num- bers: the natural numbers. That these complementary aspects of the counting pro- cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created...

This book presents methods of intelligent counting that are human-consistent, are reflections and formalizations of real, human counting procedures. The text is self-contained, systematic and equipped with many examples, figures and tables.

Counting belongs to the most elementary and frequent mental activities of human beings. Its results are a basis for coming to a decision in a lot of situations and dimensions of our life. This book presents a novel approach to the advanced and sophisticated case, called intelligent counting, in which the objects of counting are imprecisely, fuzzily specified. Formally, this collapses to counting in fuzzy sets, interval-valued fuzzy sets or I-fuzzy sets (Atanassov's intuitionistic fuzzy sets). The monograph is the first one showing and emphasizing that the presented methods of intelligent...

Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num- bers: the natural numbers. That these complementary aspects of the counting pro- cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created...