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| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Nasruddin Hassan , Associate Professor Dr. | |
| dc.contributor.author | AlHazaymeh Khaleed Ahmad Aowed (P60769) | |
| dc.date.accessioned | 2023-10-13T09:34:06Z | - |
| dc.date.available | 2023-10-13T09:34:06Z | - |
| dc.date.issued | 2015-02-03 | |
| dc.identifier.other | ukmvital:82085 | |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/499725 | - |
| dc.description | Vague soft set is generalised from the innovative concept of a vague set and soft set by adding a parameterized family of subsets of the universal set to the definition of vague set. The novelty of studying vague soft set lies in the ability of its truth-membership and false-membership functions to achieve a greater range of values. This range of values is extended to the power set of a universe set of both truth-membership and false-membership functions instead of [0, 1] 2 as in the vague set functions. In this research we study, generalise and incorporate the two concepts: vague soft set and soft expert set with the more useful mathematical tools such as interval-valued fuzzy set, generalised fuzzy soft set and possibility fuzzy soft set in helping to transform human knowledge to mathematical formula and vice versa. This research is used to illustrate several applications of vague soft expert set, generalised vague soft expert set, interval-valued vague soft set, generalised vague soft set and possibility vague soft set in solving two of the core application areas of vague soft set theory, which are decision making and medical diagnosis. We divide this research to two main parts. The first part presents several effective mathematical tools by combining vague soft set properties with interval-valued fuzzy set, generalised fuzzy soft set and possibility fuzzy soft set properties. Formal definitions of interval-valued vague soft set, generalised vague soft set and possibility vague soft set are introduced. Also, the basic theoretical operations namely, complement, union, intersection, AND and OR operations are studied on interval-valued vague soft set, generalised vague soft set and possibility vague soft set. Several applications in decision making problems are given using the interval-valued vague soft set, generalised vague soft set and possibility vague soft set. Moreover, an application in medical diagnosis is illustrated by using similarity measurement between possibility vague soft sets. For each concept above we introduce the relevant mapping and study its properties. Therefore, we introduce the concept of vague soft set relations as a vague soft subset of the Cartesian product between the vague soft sets and the related concepts such as the equivalent vague soft set relation, partition, composition and function along with proving some properties. Then, we introduce the symmetric closure, reflexive closure and transitive closure relations on vague soft set followed by examples to illustrate these relations. Introducing the concepts of relation and function on vague soft set inspires future research to seek their more fundamental definitions which allow us to present them on interval-valued fuzzy set, generalised fuzzy soft set and possibility fuzzy soft set. The second part studies vague set theory and soft expert set theory to introduce vague soft expert set theory and generalised vague soft expert set theory by incorporating properties of vague set, soft expert set and parameterisation of fuzzy membership function. Two interesting applications involving vague soft expert set and generalised vague soft expert set are investigated. The basic theoretical operations namely, complement, union, intersection, AND and OR operations are studied on both vague soft expert set and generalised vague soft expert set.,Ph.D | |
| dc.language.iso | eng | |
| dc.publisher | UKM, Bangi | |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
| dc.rights | UKM | |
| dc.subject | Dissertations, Academic -- Malaysia | |
| dc.title | Generalisations of vague soft set and vague soft expert set | |
| dc.type | Theses | |
| dc.format.pages | 185 | |
| dc.identifier.callno | QA248.5 .A439 2015 | |
| dc.identifier.barcode | 001738 | |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_82085+SOURCE1+SOURCE1.0.PDF Restricted Access | 553.09 kB | Adobe PDF |  View/Open |
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