BASES OF FUZZY ALGEBRAIC SUBSTRUCTURES

An axiomatic approach is developed concerning the existence of a basis for certain fuzzy algebraic substructures. Let the set of truth value s be a complete Brouwerian lattice L. Let G be an Abelian group. We sh ow that there exists an L-subgroup of G which does not have a p-basis even if G is finite. Let F be a field of characteristic p > 0 and let A, B be L-subfields of F such that A superset-or-equal-to B. We show t here exists an intermediate L-subfield of A/B which does not have a re lative p-basis over B even if F has finite relative imperfection degre e over the support of B. When L = [0, 1], we show that every fuzzy sub group of G with the sup property has a p-basis and that every intermed iate fuzzy subfield of A/B with the sup property has a relative p-basi s if certain compatibility conditions hold.