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https://ptsldigital.ukm.my/jspui/handle/123456789/500198| Title: | Complex multi-fuzzy set and its generalizations |
| Authors: | Yousef Ali Abed Al-Qudah (P86049) |
| Supervisor: | Nasruddin Hassan, Assoc. Prof. Dr. |
| Keywords: | Fuzzy sets Fuzzy numbers Approximation theory Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia |
| Issue Date: | Aug-2018 |
| Description: | The notion of complex fuzzy sets is considered the first model in the fuzzy set literature that has the ability to represent and model two-dimensional information, i.e. information pertaining to the attributes and the periodicity of the elements in a single set. Numerous researchers have developed systems with complex fuzzy sets for better designing and modeling real-life applications. However, most of them have dealt only with one value of membership function. Therefore, we propose the concept of complex multi-fuzzy set (CMFS) to consider values of multi-membership functions in more detail than complex fuzzy set theory, which is generalized from the concept of multi-fuzzy sets by adding the phase term to the definition of multi-fuzzy sets. The CMFS novelty lies in its ability to represent two-dimensional multi-fuzzy information. We then present the distance measure between two complex multi-fuzzy sets (CMFSs). This distance measure is used to define d-equalities of CMFSs. A new structure of relation between two CMFSs, named complex multi-fuzzy relation (CMFR), is also attained. Thereafter, a few related concepts such as Cartesian product, inverse and composition of CMFR is discussed along with some related theorems. Based on the notion of CMFS and the sufficient parameterization tool that represents the problem parameters in a more comprehensive and complete manner, we propose the concept of complex multi-fuzzy soft set (CMFSS). We present its operations and properties so as to improve the concept of multi-fuzzy set to deal with uncertainties in parameterized form and information which utilizes time factor, and apply them to decision making mechanisms. Moreover, we present the axiomatic definition of entropy and similarity measure of CMFSSs and study the basic relations among them. Subsequently, the concept of complex multi-fuzzy soft expert set (CMFSES) is established to represent the information which utilizes time factor and to know the opinions of all the experts in a single model. Finally, we propose a novel concept of the fuzzy parameterized complex multi-fuzzy soft expert set (FP-CMFSES), its operations and properties in order to improve the concept of fuzzy parameterized fuzzy soft expert set to include the time frame which is presented by the phase term and the ability to represent multi-dimensional data. Most importantly, we introduce the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making process. The current research explains various applications concerning the problems of decision-making, where the time factor plays a role and is effectively seen in determining the final decision with the use of the abovementioned proposed methods.,Ph.D. |
| Pages: | 177 |
| Call Number: | QA248.5.A457 2018 tesis |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_110596+SOURCE1+SOURCE1.0.PDF Restricted Access | 1.35 MB | Adobe PDF |  View/Open |
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