1. UKM Learning and Research Repository
2. PHD Thesis / Tesis PHD
3. Faculty of Science and Technology / Fakulti Sains dan Teknologi

Title:	Complex fuzzy and intuitionistic fuzzy algebra with their soft sets theory
Authors:	Mikhled Okleh Alsarahead (P84072)
Supervisor:	Abd. Ghafur Ahmad, Prof. Dr.
Keywords:	Algebra Fuzzy logic
Issue Date:	13-Mar-2018
Description:	Since the beginning of the introduction of the concept of fuzzy set in 1965, many mathematicians turned their attention towards fuzzifying ordinary mathematical concepts. As an important huge part of the fuzzy mathematical field, complex fuzzy sets were introduced in 2002. So it became necessary to carry all the ordinary algebraic concepts to this important portion. This thesis is accomplished as a serious attempt to complete the fuzzy mathematical field in this direction. The thesis is divided into two parts. In the first part, the concept of complex fuzzy algebra is introduced using Rosenfeld's approach. The relationship between complex fuzzy algebra and fuzzy algebra is investigated. Every complex fuzzy subgroup (subring) yields two fuzzy subgroups (subrings). Furthermore, if the complex fuzzy subgroup is normal (solvable), then these two fuzzy subgroups are normal (solvable) and vice versa. In order to define complex fuzzy subgroups by simple way, the concepts of free complex fuzzy subgroups and complex fuzzy subgroup presentations are defined. Similar to complex fuzzy algebra, complex intuitionistic fuzzy algebra is introduced using Rosenfeld's approach. The relationship between complex intuitionistic fuzzy algebra and intuitionistic fuzzy algebra is also investigated. Every complex intuitionistic fuzzy subgroup (subring) yields two intuitionistic fuzzy subgroups (subrings). The homomorphic image of complex intuitionistic fuzzy subgroup (subring) is also found to be a complex intuitionistic fuzzy subgroup (subring). In the second part, the concepts of complex fuzzy soft algebra and complex intuitionistic fuzzy soft algebra are defined and investigated. As in the first part, every complex fuzzy soft group (ring) yields two fuzzy soft groups (rings). Similarly, every complex intuitionistic fuzzy soft group (ring) yields two fuzzy intuitionistic soft groups (rings). Moreover, the homomorphic images of complex fuzzy soft group, complex fuzzy soft ring, complex intuitionistic fuzzy soft group and complex intuitionistic fuzzy soft ring are also studied.,'Certification of Master's/Doctoral Thesis' is not available
Pages:	183
Call Number:	QA9.64.A437 2018 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.