This unique monograph explores the cardinal, or quantitative, aspects of objects in the presence of vagueness, called vaguely defined objects.
In the first part of the book such topics as fuzzy sets and derivative ideas, twofold fuzzy sets, and flou sets are concisely reviewed as typical mathematical representations of vaguely defined objects. Also, a unifying, approximative representation is given. The second part uses this representation, together with Lukasiewicz logic as a basis for constructing a complete, general and easily applicable nonclassical cardinality theory for vaguely defined objects. Applications to computer and information science are discussed.
Audience: This volume will be of interest to mathematicians, computer and information scientists, whose work involves mathematical aspects of vagueness, fuzzy sets and their methods, applied many-valued logics, expert systems and data bases.
Vaguely defined objects have spread from horror films and foreign instructions on assembling toys to advanced mathematics, where they are also known as objects in the presence of vagueness. Wygralak explores the cardinal or quantitative aspects of such objects. He begins by reviewing fuzzy sets and the derivative ideas of two-fold fuzzy sets and flou sets, as typical mathematical representations of vaguely defined objects. He then presents a unifying approximative representation, and combines that with Lukasiewicz logic to construct a complete, general, and easily applicable nonclassical cardinality theory for the objects. Finally he discusses some applications in computer and information science. Of interest to mathematicians or to scientists who would like to use the theory in many-valued logics, expert systems, data bases, and other applications. Annotation c. by Book News, Inc., Portland, Or.
