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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Vaguely Defined Objects - Representations, Fuzzy Sets and Nonclassical Cardinality theory (Paperback, Softcover reprint of the original 1st ed. 1996)
Loot Price: R1,406
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Vaguely Defined Objects - Representations, Fuzzy Sets and Nonclassical Cardinality theory (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Theory and Decision Library B, 33
Expected to ship within 18 - 22 working days
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In recent years, an impetuous development of new, unconventional
theories, methods, techniques and technologies in computer and
information sciences, systems analysis, decision-making and
control, expert systems, data modelling, engineering, etc. ,
resulted in a considerable increase of interest in adequate
mathematical description and analysis of objects, phenomena, and
processes which are vague or imprecise by their very nature.
Classical two-valued logic and the related notion of a set,
together with its mathematical consequences, are then often
inadequate or insufficient formal tools, and can even become
useless for applications because of their (too) categorical
character: 'true - false', 'belongs - does not belong', 'is - is
not', 'black - white', '0 - 1', etc. This is why one replaces
classical logic by various types of many-valued logics and, on the
other hand, more general notions are introduced instead of or
beside that of a set. Let us mention, for instance, fuzzy sets and
derivative concepts, flou sets and twofold fuzzy sets, which have
been created for different purposes as well as using distinct
formal and informal motivations. A kind of numerical information
concerning of 'how many' elements those objects are composed seems
to be one of the simplest and more important types of information
about them. To get it, one needs a suitable notion of cardinality
and, moreover, a possibility to calculate with such cardinalities.
Unfortunately, neither fuzzy sets nor the other nonclassical
concepts have been equipped with a satisfactory (nonclassical)
cardinality theory.
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