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.
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- 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.
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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.
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- 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.
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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.
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- 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.
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