Foundations of fuzzy sets

Separated Presheaves of Normed Spaces and -valued Norms

“…an V-fuzzy subset of X) can be identified with a subsheaf of the simple sheaf associated with X. It is very surprising that this result (Höhle and Stout, 1990) has not spread in the "fuzzy" community during the last 23 years. In particular, every V-fuzzy subspace of an ordinary vector space V is nothing but a subsheaf of vector spaces of the simple sheaf over V associated with V. Hence, separated presheaves of vector spaces (or more general modules; Godement, 1964) form a natural source for constructing fuzzy vector spaces (or modules).…”

Products of elements in vague semigroups and their implementations in vague arithmetic

“…An ordinary function f : [3,20,19,24,26]. The notion of extensionality of an ordinary function can be informally expressed as the satisfaction of the intuitive expectation "If two points are similar to each other, so are their images".…”

“…Two-valued logic does not provide a suitable logical frame to represent the notion of indistinguishability, mathematically, and the consideration of indistinguishability within the context of bivalent logic leads to Poincare-like paradoxes [19,24,25]. Many-valued logical representation of indistinguishability, known as many-valued equivalence relations (fuzzy equivalence relations, indistinguishability operators, similarity relations, many-valued equalities, etc.…”

On the category Set(JCPos)

“…[2,6,5,9,10], etc.). In particular, some authors considered the category Set(L) of L-subsets of sets (see e.g.…”