Structures of Fuzzy Soft Sets and Fuzzy Derivations on PMS-Algebras

Nibret, Melese Kassahun

dc.contributor.author	Nibret, Melese Kassahun
dc.date.accessioned	2025-06-19T08:53:52Z
dc.date.available	2025-06-19T08:53:52Z
dc.date.issued	2025-04
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/16739
dc.description.abstract	This dissertation establishes structures of fuzzy soft sets and fuzzy deriva- tions on PMS-algebras. This dissertation introduces and studies the proper- ties of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealis- tic soft PMS-algebras. It establishes the restricted and extended intersections, unions, AND operations, and Cartesian products of these structures. In this dissertation, it investigates the homomorphic image and inverse images of soft PMS-algebras, soft PMS-ideals, and idealistic soft PMS-algebras. Recogniz- ing that the above structures are based on classical binary operations, the dis- sertation also describes and characterizes soft PMS-algebras and soft quotient PMS-algebras based on soft binary operations. This dissertation also defines fuzzy soft PMS-algebras and fuzzy soft PMS-ideals, discusses their properties, equivalence with classical soft PMS-algebras, explores further properties, and characterizes soft set operations on fuzzy soft PMS-ideals. The dissertation also explores derivations in PMS-algebras, revealing their various characteristics. It establishes that the set of all derivations associated with the defined binary op- eration on a PMS-algebra forms a semigroup, thus enhancing our understand- ing of derivations within this algebraic structure. It introduces t-derivations on PMS-algebras, exploring related characteristics and demonstrating that the set of all t-derivations also forms a semigroup. The dissertation further defines f- derivations and regular f-derivations of PMS-algebras, investigating their prop- erties and defining f-invariant and df-invariant PMS-ideals, examining their re- lationships. It establishes that the set of all f-derivations forms a semigroup. The study established fuzzy derivations of PMS-subalgebras and PMS-ideals as ex- tensions of derivations of PMS-subalgebras and derivations of PMS-ideals and explored their properties. It characterizes the Cartesian product of fuzzy deriva- tions on PMS-subalgebras and fuzzy left (right) derivations on PMS-ideals. As generalizations, it defines t-fuzzy derivations on PMS-subalgebras and t-fuzzy left (right) derivations on PMS-ideals. Finally, it proves that the intersection of fuzzy derivations on PMS-subalgebras is a fuzzy derivation on the PMS- subalgebra. The research problem handles uncertainty in PMS algebras, ex- tending algebraic structures and investigating derivations in PMS algebras, gen- eralizing the existing theory of PMS algebras by the introduction of soft sets and	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Structures of Fuzzy Soft Sets and Fuzzy Derivations on PMS-Algebras	en_US
dc.type	Dissartation	en_US