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...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

This paper uses a formal approach to incorporating uncertainty of input information into the fusion process and decision making. Fuzzy set theory (fuzzy numbers, and fuzzy operators) is used to characterize and then manipulate (reason about) uncertainty. A library of speci cations of fuzzy set theory is developed using category theory and Specware, a tool that supports category theory based alg...

one category of sokuks is “sokuk estesna’”. they are issued, offered and transferred, based upon a contract of estesna’ in construction of a specified property and/or its completion or in civil construction projects. “sokuk estesna” are divided and analyzed into two categories: the plain ones (direct and indirect) based upon a credit instrument; and complex (pursuant to a directive). the legal ...

For a small quantaloid Q, a Q-closure space is a small category enriched in Q equipped with a closure operator on its presheaf category. We investigate Q-closure spaces systematically with specific attention paid to their morphisms and, as preordered fuzzy sets are a special kind of quantaloid-enriched categories, in particular fuzzy closure spaces on fuzzy sets are introduced as an example. By...