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https://ptsldigital.ukm.my/jspui/handle/123456789/499700| Title: | Some generalised properties in double fuzzy topological spaces |
| Authors: | Mahmood Mohammed Fatimah (P59462) |
| Supervisor: | Mohd. Salmi Md. Noorani, Professor Dr. |
| Keywords: | Fuzzy sets Fuzzy topological Mathematical tool Fuzzy topology. |
| Issue Date: | 24-Jul-2015 |
| Description: | The thesis explores some aspects of the generalisation of some sets and functions indouble fuzzy topology. The study of fuzzy sets and its properties was initiated byZadeh in 1965 when he introduced the concept of a fuzzy set as a general mathematical tool for sets. Then, the term double fuzzy topological spaces came into being in 2005 by Gutierrez Garcia and Rodabaugh. We start this research by recalling the history and the developments of this subject in the background and terminology section which contains basic concepts of fuzzy sets, double fuzzy topological spaces and functions related to double fuzzy topological spaces. Later, as generalisation of fuzzy sets we used the notion of ψ-operations in double fuzzy topological spaces to study the concept of (r, s)-fuzzy generalised ψρ-closed sets and (r, s)-fuzzy generalized ψρ-open sets, some characterisations and properties of these concepts are given. Consequently, we discuss the relationship between these sets in double fuzzy topological spaces. Firstly, we take (r, s)-generalised fuzzy b-closed sets and (r, s)-generalised fuzzy b-closed sets as an application of the notion of ψρ-operations in double fuzzy topological spaces. Secondly, we define new notions from (r, s)-generalised double fuzzy preopen sets such as (r, s)-generalised fuzzy pre-border, (r, s)-generalised fuzzy pre-exterior and (r, s)-generalised fuzzy pre-frontier in double fuzzy topological spaces, also some characterisations of generalised double fuzzy preopen, generalized double fuzzy preclosed, generalised double fuzzy pre-continuous and generalized double fuzzy preclosure-irresolute functions are studied and investigated. Furthermore, the relationships among the new concepts are discussed with some of necessary examples. Additionally, in the beginning several results about continuity of functions are obtained such as slightly double fuzzy continuous functions, slightly generalized double fuzzy semicontinuous functions, somewhat slightly generalised double fuzzy semicontinuous functions and somewhat slightly generalised double fuzzy semiopen functions. Several interesting properties and characterisations are introduced and discussed. Furthermore, the relationships among the concepts are introduced and established with some interesting counter examples. After that, totally continuous, totally semi-continuous functions and the concept of semi totally continuous function which is stronger than totally continuous function in double fuzzy topological spaces are investigated with characteristic properties. Also, we studied connectedness in double fuzzy topological spaces and some results on the concept of generalised double fuzzy semi-basically disconnected space and related notions such as (r, s)-generalised fuzzy semiopen-Fσ sets, (r, s)-generalised fuzzy semiclosed-Gδ sets and generalized double fuzzy semi -irresolute function. Then, the concept generalised double fuzzy semi-basically disconnected and generalised double fuzzy semi -irresolute spaces are introduced. On the other hand, some properties and characterisations of generalized double fuzzy semi-extremally disconnected spaces are investigated. Also, we study several notions of compactness in double fuzzy topological spaces known as generalized double fuzzy semi-compactness, generalised double fuzzy nearly semi-compactness and generalised double fuzzy weakly semi-compactness with some interesting propertiesm and characterisations. Finally, we end this thesis by conclusions and suggestion for further works.,Ph.D |
| Pages: | 154 |
| Call Number: | QA611.2 .M337 2015 |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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