Rough sets induced by fuzzy ideals in BCK-Algebras

Rough Pythagorean Fuzzy Sets in UP-Algebras

“…The concept of rough sets (RSs) was first considered by Pawlak [18] in 1982. After the introduction of the concept of RSs, several authors have applied the concept of RSs to the generalizations of the concept of FSs in many algebraic structures such as: Chen and Wang [6] combined RSs and fuzzy subalgebras (fuzzy ideals) fruitfully by defining rough fuzzy subalgebras (rough fuzzy ideals) of BCI-algebras, Moradiana et al [17] presented a definition of the lower and upper approximation of subsets of BCK-algebras concerning a fuzzy ideal. Ahn and Kim [1] introduced the concept of rough fuzzy filters in BE-algebras, Ahn and Ko [2] introduced the concept of rough ideals and rough fuzzy ideals in BCK/BCIalgebras, Hussain et al [10] introduced the concept of rough Pythagorean fuzzy ideals in semigroups, Chinram and Panityakul [7] introduced rough Pythagorean fuzzy ideals in ternary semigroups and gave some remarkable properties.…”

New types of rough Pythagorean fuzzy UP-filters of UP-algebras

“…The concept of rough sets (RSs) was first considered by Pawlak [20] in 1982. After the introduction of the concept of RSs, several authors have applied the concept of RSs to the generalizations of the concept of FSs in many algebraic structures such as: Chen and Wang [6] combined RSs and fuzzy subalgebras (fuzzy ideals) fruitfully by defining rough fuzzy subalgebras (rough fuzzy ideals) of BCI-algebras, Moradiana et al [19] presented a definition of the lower and upper approximation of subsets of BCK-algebras concerning a fuzzy ideal, Ahn and Kim [1] introduced the concept of rough fuzzy filters in BE-algebras, Ahn and Ko [2] introduced the concept of rough ideals and rough fuzzy ideals in BCK/BCI-algebras, Hussain et al [10] introduced the concept of rough Pythagorean fuzzy ideals in semigroups, and Chinram and Panityakul [7] introduced rough Pythagorean fuzzy ideals in ternary semigroups and gave some remarkable properties. In 2022, Satirad et al [22] combined notion of RSs and PFSs by defining rough Pythagorean fuzzy sets (RPFSs) in UP-algebras, studied relation between RPFSs and PFSs, discussed relation between PSFs and special subset of UP-algebras with t-level subset.…”