Md Derus, Khamirrudin (2020) Bipolar fuzzy sets in switchboard automata and optimisation problems. Masters thesis, Universiti Tun Hussein Onn Malaysia.

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Abstract
Bipolar fuzzy sets can be extended to triangular bipolar fuzzy number and are applied in optimisation problems, specifically critical path problem and reliability system of an automobile. Some of the properties of triangular bipolar fuzzy numbers are introduced and used in critical path problems to find a bipolar fuzzy critical path. As a result, acceptance area and rejection area could be recognised successfully. By using a tree diagram, triangular bipolar fuzzy number is then applied to a reliability system of an automobile in order to find the failure rate to start of an automobile that is based on the ideas of circuits which are connected to the system. An illustrative example is presented and the tolerance level of acceptence (positive membership value) and tolerance level of rejection (negative membership value) could be determined successfully in a reliability system of an automobile. In automata theory, the decomposition theorem for bipolar fuzzy finite state automata and its transformations semigroups are initiated and discussed in order to enrich the structure of algebraic properties in bipolar fuzzy finite state automata. Furthermore, the idea of bipolar general fuzzy finite switchboard automata and asynchronous bipolar general fuzzy switchboard automata is initiated. In particular, the algebraic properties of bipolar general fuzzy switchboard automata are discussed in term of switching and commutative by proving the theorems that are related into these concepts. Finally, the notion of the switchboard subsystems and strong switchboard subsystem of bipolar general fuzzy switchboard automata are initiated. As a result, it can be concluded that every switchboard subsystem is a strong switchboard subsystem throughout the proven theorems. As an application, a concept of Lowen fuzzy topology is induced in switchboard subsystem of bipolar general fuzzy switchboard automata by using Kuratowski closure operator.
Item Type:  Thesis (Masters) 

Subjects:  Q Science > QA Mathematics > QA76 Computer software 
Divisions:  Faculty of Applied Science and Technology > Department of Physics and Chemistry 
Depositing User:  Mrs. Sabarina Che Mat 
Date Deposited:  20 Sep 2021 07:40 
Last Modified:  20 Sep 2021 07:40 
URI:  http://eprints.uthm.edu.my/id/eprint/1014 
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