Keychains and preferential fuzzy sets with applications
- Authors: Mahlasela, Zuko
- Date: 2024-04-05
- Subjects: Fuzzy sets , Partially ordered sets , Lattice theory , Equivalence relations (Set theory) , Voting patterns , Simplexes (Mathematics) , Preference relation , Decision making
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/435933 , vital:73213 , DOI 10.21504/10962/435935
- Description: In this thesis, we study the preferentiality behaviour of choices under uncertainties using keychains, where a keychain is defined as an (n+ 1)-tuple of non-increasing real numbers in the unit interval, I= [0, 1]. We look at the representations of uncertainties or sets defined by vague properties using the idea of keychains, pins and pinned flags. We then apply the ideas of preferential fuzzy sets to voting patterns, economics and decision making. For voting patterns, we simulate mock trials to investigate the behaviours of choices of different individuals, the outcomes of such voting and make specific conclusions about voting strategies. It can be argued that preferentiality in voting can enhance the democratic processes in national elections. This thesis contains various representations of keychains such as binary digits, weight order, lattice and simplex representations. Another useful aspect of keychains and preferential fuzzy sets is to study the outcomes of decision making linking it to the study of keychains and finite fuzzy sets. We envisage that this study will throw light on computational aspects of any countable situations. , Thesis (PhD) -- Faculty of Science, Mathematics, 2024
- Full Text:
- Date Issued: 2024-04-05
- Authors: Mahlasela, Zuko
- Date: 2024-04-05
- Subjects: Fuzzy sets , Partially ordered sets , Lattice theory , Equivalence relations (Set theory) , Voting patterns , Simplexes (Mathematics) , Preference relation , Decision making
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/435933 , vital:73213 , DOI 10.21504/10962/435935
- Description: In this thesis, we study the preferentiality behaviour of choices under uncertainties using keychains, where a keychain is defined as an (n+ 1)-tuple of non-increasing real numbers in the unit interval, I= [0, 1]. We look at the representations of uncertainties or sets defined by vague properties using the idea of keychains, pins and pinned flags. We then apply the ideas of preferential fuzzy sets to voting patterns, economics and decision making. For voting patterns, we simulate mock trials to investigate the behaviours of choices of different individuals, the outcomes of such voting and make specific conclusions about voting strategies. It can be argued that preferentiality in voting can enhance the democratic processes in national elections. This thesis contains various representations of keychains such as binary digits, weight order, lattice and simplex representations. Another useful aspect of keychains and preferential fuzzy sets is to study the outcomes of decision making linking it to the study of keychains and finite fuzzy sets. We envisage that this study will throw light on computational aspects of any countable situations. , Thesis (PhD) -- Faculty of Science, Mathematics, 2024
- Full Text:
- Date Issued: 2024-04-05
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
- 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
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