Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Book
Publication Date
2014
Abstract
In this book we introduce several algebraic structures on the special fuzzy interval [0, 1). This study is different from that of the algebraic structures using the interval [0, n) n ≠ 1, as these structures on [0, 1) has no idempotents or zero divisors under ×. Further [0, 1) under product × is only a semigroup. However by defining min(or max) operation in [0, 1); [0, 1) is made into a semigroup. The semigroup under × has no finite subsemigroups but under min or max we have subsemigroups of order one, two and so on. [0, 1) under + modulo 1 is a group and [0, 1) has finite subgroups. We study [0, 1) with two binary operations min and max resulting in semiring of infinite order. This has no subsemirings which is both an ideal and a filter. However pseudo semiring under min and × has subsemirings which is both a filter and an ideal.
Publisher
Educational Publisher Inc., Ohio
ISSN
978-1-59973-259-6
Language (ISO)
English
Keywords
algebraic structures, fuzzy interval [0, 1), neutrosophic logic, semiring
Recommended Citation
W.B. Vasantha Kandasamy & F. Smarandache. Algebraic Structures on the Fuzzy Interval [0, 1) . Ohio: Educational Publisher, 2014.
Creative Commons License
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Included in
Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Logic and Foundations Commons, Number Theory Commons, Other Mathematics Commons, Set Theory Commons
