Ramakrishnan, T V; Dr.Thrivikraman, T(Cochin University of Science And Technology, November , 1995)
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Abstract:
Mathematical models are often used to describe
physical realities. However, the physical realities are
imprecise while the mathematical concepts are required to be
precise and perfect. Even mathematicians like H. Poincare
worried about this. He observed that mathematical models
are over idealizations, for instance, he said that only in
Mathematics, equality is a transitive relation. A first
attempt to save this situation was perhaps given by K.
Menger in 1951 by introducing the concept of statistical
metric space in which the distance between points is a
probability distribution on the set of nonnegative real
numbers rather than a mere nonnegative real number. Other
attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A.
Sklar and others. An aspect in common to all these
approaches is that they model impreciseness in a
probabilistic manner. They are not able to deal with
situations in which impreciseness is not apparently of a
probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.
Description:
Department of mathematics, Cochin University of Science And Technology