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Title:	Complex neutrosophic soft expert sets and some models of single-valued neutrosophic soft expert set
Authors:	Ashraf Naser Faris Al-Quran (P80571)
Supervisor:	Nasruddin Hassan, Assoc. Prof. Dr.
Keywords:	Fuzzy sets Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	Jan-2018
Description:	As an extension of fuzzy sets and intuitionistic fuzzy sets, single-valued neutrosophic sets (SVNSs) have been developed to represent uncertain, indeterminate and incomplete information that exists in the real world. SVNS is a set where each element of the universe has a degree of truth, indeterminacy and falsity and it lies within the real interval [0;1]. The single-valued neutrosophic soft expert set (SVNSES) is an influential mathematical framework that deals with different types of uncertainties including indeterminacy and has a mechanism to incorporate the parameters set and the opinions of all experts in one model. Discussion will begin on the real space before moving on to the complex space, which forms the main text of the thesis. We begin by first proposing some models of the SVNSES to illustrate several applications in decision-making. By setting the vague values as the SVNSES's memberships values and as a combination of neutrosophic vague set and soft expert set, we define neutrosophic vague soft expert set (NVSES).We then develop the NVSES to possibility neutrosophic vague soft expert set (PNVSES) where a possibility of each element in the universe is attached to the parameterization of neutrosophic vague sets while defining a NVSES. In the definition of the SVNSES, parameters set is a classical set, and the parameters have the same degree of importance which is considered as 1. This poses a limitation in modeling of some problems. Therefore, we introduce the concept of fuzzy parameterised single-valued neutrosophic soft expert set (FP-SVNSES) based on idea that each of elements of parameters set has got an importance degree. The basic theoretical operations and properties are defined and verified on NVSES, PNVSES and FP-SVNSES. Then we enlarge the discussion to the complex space by establishing the concept of complex neutrosophic soft expert set (CNSES) by extending the ranges of the truth membership function, indeterminacy membership function and falsity membership function of the SVNSES from [0;1] to unit circle in the complex plane i.e. the ranges of these membership functions are represented in terms of complex numbers. CNSES is a hybrid structure of complex neutrosophic set and soft expert set, thus making it highly suitable for use in decisionmaking problems that involve indeterminate data where the extra information provided by the phase terms of the complex numbers play a key role in determining the final decision. Based on this new concept we define the basic theoretical operations. The basic properties are also verified. A new structure of relation between two CNSESs, called complex neutrosophic soft expert relation (CNSER) is obtained. The CNSER is derived to evaluate the degree of interaction between two CNSESs, where the time of interaction represented by the phase terms plays a key role in the final decision. Then, the related concepts such as the Cartesian product, equivalent CNSER, partition, composition and function along with some operations, theorems and propositions are defined and verified. Finally, the fuzzy parameterised complex neutrosophic soft expert set (FP-CNSES) is formally generalised from the concept of FP-SVNSES to deal with two dimensional data. We then study its operations and properties. We also define the weighted fuzzy parameterized complex neutrosophic soft expert set and apply it to a decision-making problem. For both CNSES and FP-CNSES, we introduce the relevant mapping and study its properties. This research is used to illustrate several applications in decision-making problems using the aforementioned proposed methods, where each study is supported by the comparison with other existing methods.,'Certification of Master's/Doctoral Thesis' is not available,Ph.D.
Pages:	173
Call Number:	QA248.5.Q837 2018 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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