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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| Format: | Thesis |
| Language: | English English English |
| Published: |
2020
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| Subjects: | |
| Online Access: | 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 http://eprints.uthm.edu.my/1014/ |
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| Summary: | 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. |
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