Fuzzy and probability vectors as elements of a vector space

Haim Shvaytser; Shmuel Peleg

doi:10.1016/0020-0255(85)90055-6

Fuzzy and probability vectors as elements of a vector space

Haim Shvaytser^*
, Shmuel Peleg

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The problem of defining vector space operations on fuzzy and probability vectors is discussed. It is shown that such a definition is equivalent to choosing a 1-1 and onto mapping from the unit interval into the real axis. Although such a mapping cannot be continuous, it is suggested that under certain approximations a continuous mapping can be chosen. A characterization of some useful mappings with applications to image processing is also given.

Original language	English
Pages (from-to)	231-247
Number of pages	17
Journal	Information Sciences
Volume	36
Issue number	3
DOIs	https://doi.org/10.1016/0020-0255(85)90055-6
State	Published - Sep 1985

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AB - The problem of defining vector space operations on fuzzy and probability vectors is discussed. It is shown that such a definition is equivalent to choosing a 1-1 and onto mapping from the unit interval into the real axis. Although such a mapping cannot be continuous, it is suggested that under certain approximations a continuous mapping can be chosen. A characterization of some useful mappings with applications to image processing is also given.

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Fuzzy and probability vectors as elements of a vector space

Abstract

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