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
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
A study of fuzzy sets and systems with applications to group theory and decision making
- Authors: Gideon, Frednard
- Date: 2006
- Subjects: Fuzzy sets , Fuzzy systems , Abelian groups , Decision making
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5417 , http://hdl.handle.net/10962/d1005231 , Fuzzy sets , Fuzzy systems , Abelian groups , Decision making
- Description: In this study we apply the knowledge of fuzzy sets to group structures and also to decision-making implications. We study fuzzy subgroups of finite abelian groups. We set G = Z[subscript p[superscript n]] + Z[subscript q[superscript m]]. The classification of fuzzy subgroups of G using equivalence classes is introduced. First, we present equivalence relations on fuzzy subsets of X, and then extend it to the study of equivalence relations of fuzzy subgroups of a group G. This is then followed by the notion of flags and keychains projected as tools for enumerating fuzzy subgroups of G. In addition to this, we use linear ordering of the lattice of subgroups to characterize the maximal chains of G. Then we narrow the gap between group theory and decision-making using relations. Finally, a theory of the decision-making process in a fuzzy environment leads to a fuzzy version of capital budgeting. We define the goal, constraints and decision and show how they conflict with each other using membership function implications. We establish sets of intervals for projecting decision boundaries in general. We use the knowledge of triangular fuzzy numbers which are restricted field of fuzzy logic to evaluate investment projections.
- Full Text:
- Date Issued: 2006
Monitoring and intelligent control for complex curvature friction stir welding
- Authors: Hua, Tao
- Date: 2006
- Subjects: Friction welding , Fuzzy systems
- Language: English
- Type: Thesis , Doctoral , DTech
- Identifier: vital:9612 , http://hdl.handle.net/10948/420 , Friction welding , Fuzzy systems
- Description: A multi-input multi-output system to implement on-line process monitoring and intelligent control of complex curvature friction stir welding was proposed. An extra rotation axis was added to the existing three translation axes to perform friction stir welding of complex curvature other than straight welding line. A clamping system was designed for locating and holding the workpieces to bear the large force involved in the process between the welding tool and workpieces. Process parameters (feed rate, spindle speed, tilt angle and plunge depth), and process conditions (parent material and curvature), were used as factors for the orthogonal array experiments to collect sensor data of force, torque and tool temperature using multiple sensors and telemetry system. Using statistic analysis of the experimental data, sensitive signal features were selected to train the feed-forward neural networks, which were used for mapping the relationships between process parameters, process conditions and sensor data. A fuzzy controller with initial input/output membership functions and fuzzy rules generated on-line from the trained neural network was applied to perceive process condition changes and make adjustment of process parameters to maintain tool/workpiece contact and energy input. Input/output scaling factors of the fuzzy controller were tuned on-line to improve output response to the amount and trend of control variable deviation from the reference value. Simulation results showed that the presented neuro-fuzzy control scheme has adaptability to process conditions such as parent material and curvature changes, and that the control variables were well regulated. The presented neuro-fuzzy control scheme can be also expected to be applied in other multi-input multi-output machining processes.
- Full Text:
- Date Issued: 2006
The control of a multi-variable industrial process, by means of intelligent technology
- Authors: Naidoo, Puramanathan
- Date: 2001
- Subjects: Fuzzy systems , Intelligent control systems
- Language: English
- Type: Thesis , Masters , MTech (Electrical Engineering)
- Identifier: vital:10813 , http://hdl.handle.net/10948/48 , Fuzzy systems , Intelligent control systems
- Description: Conventional control systems express control solutions by means of expressions, usually mathematically based. In order to completely express the control solution, a vast amount of data is required. In contrast, knowledge-based solutions require far less plant data and mathematical expression. This reduces development time proportionally. In addition, because this type of processing does not require involved calculations, processing speed is increased, since rule process is separate and all processes can be performed simultaneously. These results in improved product quality, better plant efficiency, simplified process, etc. Within this project, conventional PID control has already been implemented, with the control parameter adjustment and loop tuning being problematic. This is mainly due to a number of external parameters that affects the stability of the process. In maintaining a consistent temperature, for example, the steam flow rate varies, the hot well temperature varies, the ambient may temperature vary. Another contributing factor, the time delay, also affects the optimization of the system, due to the fact that temperature measurement is based on principle of absorption. The normal practice in industry to avoid an unstable control condition is to have an experienced operator to switch the controller to manual, and make adjustments. After obtaining the desired PV, the controller is switched back to automatic. This research project focuses on eliminating this time loss, by implementing a knowledge-based controller, for intelligent decision-making. A FLC design tool, which allows full interaction, whilst designing the control algorithm, was used to optimize the control system. The design tool executed on a PC is connected to a PLC, which in turn is successfully integrated into the process plant.
- Full Text:
- Date Issued: 2001
Methods for designing and optimizing fuzzy controllers
- Authors: Swartz, Andre Michael
- Date: 2000
- Subjects: Fuzzy sets , Fuzzy systems , Automatic control
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5412 , http://hdl.handle.net/10962/d1005226 , Fuzzy sets , Fuzzy systems , Automatic control
- Description: We start by discussing fuzzy sets and the algebra of fuzzy sets. We consider some properties of fuzzy modeling tools. This is followed by considering the Mamdani and Sugeno models for designing fuzzy controllers. Various methods for using sets of data for desining controllers are discussed. This is followed by a chapter illustrating the use of genetic algorithms in designing and optimizing fuzzy controllers.Finally we look at some previous applications of fuzzy control in telecommunication networks, and illustrate a simple application that was developed as part of the present work.
- Full Text:
- Date Issued: 2000