The principle of inclusion-exclusion and möbius function as counting techniques in finite fuzzy subsets
- Authors: Talwanga, Matiki
- Date: 2009
- Subjects: Fuzzy logic , Fuzzy sets , Fuzzy systems , Möbius function
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5413 , http://hdl.handle.net/10962/d1005227 , Fuzzy logic , Fuzzy sets , Fuzzy systems , Möbius function
- Description: The broad goal in this thesis is to enumerate elements and fuzzy subsets of a finite set enjoying some useful properties through the well-known counting technique of the principle of inclusion-exclusion. We consider the set of membership values to be finite and uniformly spaced in the real unit interval. Further we define an equivalence relation with regards to the cardinalities of fuzzy subsets providing the Möbius function and Möbius inversion in that context.
- Full Text:
- Date Issued: 2009
- Authors: Talwanga, Matiki
- Date: 2009
- Subjects: Fuzzy logic , Fuzzy sets , Fuzzy systems , Möbius function
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5413 , http://hdl.handle.net/10962/d1005227 , Fuzzy logic , Fuzzy sets , Fuzzy systems , Möbius function
- Description: The broad goal in this thesis is to enumerate elements and fuzzy subsets of a finite set enjoying some useful properties through the well-known counting technique of the principle of inclusion-exclusion. We consider the set of membership values to be finite and uniformly spaced in the real unit interval. Further we define an equivalence relation with regards to the cardinalities of fuzzy subsets providing the Möbius function and Möbius inversion in that context.
- Full Text:
- Date Issued: 2009
A fuzzy logic control system for a friction stir welding process
- Authors: Majara, Khotso Ernest
- Date: 2006
- Subjects: Friction welding , Fuzzy logic , Automatic control , Fuzzy systems
- Language: English
- Type: Thesis , Masters , MTech
- Identifier: vital:9594 , http://hdl.handle.net/10948/405 , Friction welding , Fuzzy logic , Automatic control , Fuzzy systems
- Description: FSW is a welding technique invented and patented by The Welding Institute in 1991. This welding technique utilises the benefits of solid-state welding to materials regarded as difficult to weld by fusion processes. The productivity of the process was not optimised as the real-time dynamics of the material and tool changes were not considered. Furthermore, the process has a plastic weld region where no traditional modelling describing the interaction between the tool and work piece is available. Fuzzy logic technology is one of the artificial intelligent strategies used to improve the control of the dynamics of industrial processes. Fuzzy control was proposed as a viable solution to improve the productivity of the FSW process. The simulations indicated that FLC can use feed rate and welding speed to adaptively regulate the feed force and tool temperature respectively, irrespective of varying tool and material change. The simulations presented fuzzy logic technology to be robust enough to regulate FSW process in the absence of accurate mathematical models.
- Full Text:
- Date Issued: 2006
- Authors: Majara, Khotso Ernest
- Date: 2006
- Subjects: Friction welding , Fuzzy logic , Automatic control , Fuzzy systems
- Language: English
- Type: Thesis , Masters , MTech
- Identifier: vital:9594 , http://hdl.handle.net/10948/405 , Friction welding , Fuzzy logic , Automatic control , Fuzzy systems
- Description: FSW is a welding technique invented and patented by The Welding Institute in 1991. This welding technique utilises the benefits of solid-state welding to materials regarded as difficult to weld by fusion processes. The productivity of the process was not optimised as the real-time dynamics of the material and tool changes were not considered. Furthermore, the process has a plastic weld region where no traditional modelling describing the interaction between the tool and work piece is available. Fuzzy logic technology is one of the artificial intelligent strategies used to improve the control of the dynamics of industrial processes. Fuzzy control was proposed as a viable solution to improve the productivity of the FSW process. The simulations indicated that FLC can use feed rate and welding speed to adaptively regulate the feed force and tool temperature respectively, irrespective of varying tool and material change. The simulations presented fuzzy logic technology to be robust enough to regulate FSW process in the absence of accurate mathematical models.
- Full Text:
- Date Issued: 2006
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