# Bipolar fuzzy sets in switchboard automata and optimisation problems

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 problem...

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id my-uthm-ep.1014 uketd_dc my-uthm-ep.10142021-09-20T07:40:58Z Bipolar fuzzy sets in switchboard automata and optimisation problems 2020-03 Md Derus, Khamirrudin QA76 Computer software 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. 2020-03 Thesis http://eprints.uthm.edu.my/1014/ http://eprints.uthm.edu.my/1014/1/24p%20KHAMIRRUDIN%20MD%20DERUS.pdf text en public http://eprints.uthm.edu.my/1014/2/KHAMIRRUDIN%20MD%20DERUS%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/1014/3/KHAMIRRUDIN%20MD%20DERUS%20WATERMARK.pdf text en validuser mphil masters Universiti Tun Hussein Onn Malaysia Fakulti Sains Gunaan dan Teknologi Universiti Tun Hussein Onn Malaysia UTHM Institutional Repository English English English QA76 Computer software QA76 Computer software Md Derus, Khamirrudin Bipolar fuzzy sets in switchboard automata and optimisation problems 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. Thesis Master of Philosophy (M.Phil.) Master's degree Md Derus, Khamirrudin Md Derus, Khamirrudin Md Derus, Khamirrudin Bipolar fuzzy sets in switchboard automata and optimisation problems Bipolar fuzzy sets in switchboard automata and optimisation problems Bipolar fuzzy sets in switchboard automata and optimisation problems Bipolar fuzzy sets in switchboard automata and optimisation problems Bipolar fuzzy sets in switchboard automata and optimisation problems bipolar fuzzy sets in switchboard automata and optimisation problems Universiti Tun Hussein Onn Malaysia Fakulti Sains Gunaan dan Teknologi 2020 http://eprints.uthm.edu.my/1014/1/24p%20KHAMIRRUDIN%20MD%20DERUS.pdf http://eprints.uthm.edu.my/1014/2/KHAMIRRUDIN%20MD%20DERUS%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/1014/3/KHAMIRRUDIN%20MD%20DERUS%20WATERMARK.pdf 1747830704973021184