Annals of Communications in Mathematics

AbstractThis paper aim is to apply the notions of the intersection and the union of any fuzzy set to UP-algebras. We investigate properties of the intersection and the union of T-fuzzy UP-subalgebras, T-fuzzy near UP-filters, T-fuzzy UP-filters, T-fuzzy UPideals, T-fuzzy strongly UP-ideals, anti-T-fuzzy UP-subalgebras, and anti-T-fuzzy near UP-filters of UP-algebras.

AbstractIn this paper, we introduce a new kind of an m-polar fuzzy ideal of a BCK/ BCI-algebra called, an m-polar (∈, ∈ ∨q) fuzzy ideal and investigate some of its properties. Ordinary ideals and m-polar (∈, ∈ ∨ q) fuzzy ideals are connected by means of level cut subset.

AbstractThis paper consists of two sections A and B. Section A exhibits rectangles, where, in each rectangle, the area added with its semi-perimeter is a Trimorphic number. Section B presents rectangles, where, in each rectangle, the area minus its semi-perimeter is a Trimorphic number.

AbstractThis paper continues the study of fuzzy group theory which has been explored over times. We propose maximal fuzzy subgroups and Frattini fuzzy subgroups of fuzzy groups as extensions of maximal subgroups and Frattini subgroups of classical groups. It is shown that every Frattini fuzzy subgroup is both characteristic and normal, respectively. Finally, some results are established in connection to level subgroups and alpha cuts of fuzzy groups.

AbstractThis paper deals with some existence and uniqueness of random solutions for a coupled system of Caputo–Hadamard fractional differential equations with four-point boundary conditions and random effects in generalized Banach spaces. Some applications are made of generalizations of classical random fixed point theorems on generalized Banach spaces. An illustrative example is presented in the last section.

AbstractIn BCK/BCI-algebras, the notion of Sup-hesitant fuzzy subalgebra is introduced, and related properties are investigated. Characterizations of a Sup-hesitant fuzzy subalgebra are discussed. Sup-hesitant fuzzy translation and Sup-hesitant fuzzy extension of Sup-hesitant fuzzy subalgebras are introduced, and their relations are investigated.