For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as o...

Logicians have, by and large, engaged in the convenient fiction that sentences of natural languages (at least declarative sentences) are either true or false or, at worst, lack a truth value, or have a third value often interpreted as 'nonsense'. And most contemporary linguists who have thought seriously about semantics, especially formal semantics, have largely shared this fiction, primarily f...

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as o...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

Conventionally, we use a chi-square test of homogeneity to determine whether the cell probabilities of a multinomial are equal. However, this process of testing hypotheses is based on the assumption of two-valued logic. If we collect questionnaire data using fuzzy logic, i.e., we record the category data with memberships instead of with a 0-1 type, then the conventional test of goodness-of-fit ...

Then SetF(Ω) is a category with Ω-sets as objects and maps f : A → B such that γ(f(x), f(y)) ≥ δ(x, y) for all x, y ∈ A as morphisms f : (A, δ) → (B, γ). Moreover, by SetR(Ω) we understand a category which is an analogy of a category of sets with relations between sets as morphisms. Objects of this category SetR(Ω) are the same as in the category SetF(Ω) and morphism f : (A, δ) → (B, γ) are map...

Web usage mining is a research field for searching potentially useful and valuable information from web log file. Web log file is a simple list of pages that users refer. Therefore, it is not easy to analyze user’s current interest field from web log file. This paper presents web usage mining method for finding users’ current interest based on Fuzzy category. We consider not only how many times...

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.