Fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. In this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. We focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. At last, fuzzy completecongruen...

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

Complete lattices and closure operators in ordered sets are considered from the point of view of fuzzy logic. A typical example of a fuzzy order is the graded subsethood of fuzzy sets. Graded subsethood makes the set of all fuzzy sets in a given universe into a completely lattice fuzzy ordered set (i.e. a complete lattice in fuzzy setting). Another example of a completely lattice fuzzy ordered ...

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

The aim of this paper is to introduce two new types of fuzzy integrals, namely, ⊗-fuzzy integral and →-fuzzy integral, where ⊗ and → are the multiplication and residuum of a complete residuated lattice, respectively. The first integral is based on a fuzzy measure of L-fuzzy sets and the second one on a complementary fuzzy measure of L-fuzzy sets, where L is a complete residuated lattice. Some o...