Smarandache Fuzzy Algebra

In any human field, a Smarandache n-structure on a set S means a weak structure {w0} on S such that there exists a chain of proper subsets Pn–1 included in Pn–2 included in … included in P2 included in P1 included in S whose corresponding structures verify the chain {wn–1} > {wn–2} > … > {w2} > {w1} > {w0}, where ‘>’ signifies ‘strictly stronger’ (i.e. structure satisfying more axioms). This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w0} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w1}.

Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-rings, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems.

Also applications of Smarandache groupoids, near-rings, and semi-rings in automaton theory, in error-correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.

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