Goguen categories were introduced as a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study the algebraic structures derived from Goguen categories by replacing its second-order axiom by some weaker versions.

The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincaré or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita and Takesaki) of the algebraic formulation of QFT has an interesting nontrivial chiral generalization to the diffeomorphisms of the circle. Combined with re...

In this paper, fuzzy quantitative models of language statistics are constructed. All suggested models are based on the assumption about a superposition of two kinds of uncertainties: probabilistic and possibilistic. The realization of this superposition in statistical distributions is achieved by the probability measure splitting procedure. In this way, the fuzzy versions of generalized binomia...

The concept of representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets is widely used in the literature for the classi…cation and study of fuzzy algebraic structures on the same underlying set. The problem of existence of such fuzzy sets was investigated by various authors. As far as we know, the problem of uniquene...

The goal of this work is the further development of neoclassical analysis, which extends the scope and results of the classical mathematical analysis by applying fuzzy logic to conventional mathematical objects, such as functions, sequences, and series. This allows us to reflect and model vagueness and uncertainty of our knowledge, which results from imprecision of measurement and inaccuracy of...

Our aim in this paper is to introduce the notion of fuzzy soft near-subtraction semigroups and fuzzy soft ideals of near-subtraction semigroups. We discuss some important properties of these new fuzzy algebraic structure and investigate some examples and counter examples.

The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc) on an ordinary set X, while for the second one the starting point are L-valued sets, that is a set equipped with some L-valued equality E : X × X → L (L being a lattice usuall...