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. The 1st chapter give a brief summary of the
arithmetic of fuzzy real numbers and the fuzzy normed
algebra M(I). Also we explain a few preliminary definitions
and results required in the later chapters. Fuzzy real
numbers are introduced by Hutton,B [HU] and Rodabaugh,
S.E[ROD]. Our definition slightly differs from this with an
additional minor restriction. The definition of Clementina
Felbin [CL1] is entirely different. The notations of
[HU]and [M;Y] are retained inspite of the slight difference
in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I)
we give a fuzzy extension of real Hahn-Banch theorem. Some
consequences of this extension are obtained. The idea of
real fuzzy linear functional on fuzzy normed linear space is
introduced. Some of its properties are studied. In the
complex case we get only a slightly weaker analogue for the
Hahn-Banch theorem, than the one [B;N] in the crisp case
Description:
School of Mathematical Sciences , Cochin University of Science
and Technology