Basic substructural core fuzzy logics and their extensions: Mianorm-based logics ?
This paper addresses standard completeness for non-associative, non-commutative, substructural fuzzy logics and their axiomatic extensions. First, fuzzy systems, which are based on mianorms  (binary monotonic identity aggregation operations on the real unit interval [0,1] [ 0 , 1 ] ), their corresponding algebraic structures, and algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0,1] [ 0 , 1 ] , so-called standard completeness, is established for these systems using construction in the style of JeneiMontagna. Finally, some axiomatic extensions of the non-associative, non-commutative core fuzzy logics having axioms corresponding to the structural rule(s) of exchange and/or associativity are considered.
mianorms substructural logics mia operators non-associative non-commutative fuzzy logics