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
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- Date Issued: 2024-04-05
Finite fuzzy sets, keychains and their applications
- Authors: Mahlasela, Zuko
- Date: 2009
- Subjects: Fuzzy sets , Finite groups , Lattice theory , Economics -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5406 , http://hdl.handle.net/10962/d1005220 , Fuzzy sets , Finite groups , Lattice theory , Economics -- Mathematical models
- Description: The idea of keychains, an (n+1)-tuple of non-increasing real numbers in the unit interval always including 1, naturally arises in study of finite fuzzy set theory. They are a useful concept in modeling ideas of uncertainty especially those that arise in Economics, Social Sciences, Statistics and other subjects. In this thesis we define and study some basic properties of keychains with reference to Partially Ordered Sets, Lattices, Chains and Finite Fuzzy Sets. We then examine the role of keychains and their lattice diagrams in representing uncertainties that arise in such problems as in preferential voting patterns, outcomes of competitions and in Economics - Preference Relations.
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- Date Issued: 2009
- Authors: Mahlasela, Zuko
- Date: 2009
- Subjects: Fuzzy sets , Finite groups , Lattice theory , Economics -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5406 , http://hdl.handle.net/10962/d1005220 , Fuzzy sets , Finite groups , Lattice theory , Economics -- Mathematical models
- Description: The idea of keychains, an (n+1)-tuple of non-increasing real numbers in the unit interval always including 1, naturally arises in study of finite fuzzy set theory. They are a useful concept in modeling ideas of uncertainty especially those that arise in Economics, Social Sciences, Statistics and other subjects. In this thesis we define and study some basic properties of keychains with reference to Partially Ordered Sets, Lattices, Chains and Finite Fuzzy Sets. We then examine the role of keychains and their lattice diagrams in representing uncertainties that arise in such problems as in preferential voting patterns, outcomes of competitions and in Economics - Preference Relations.
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- Date Issued: 2009
A study of the existence of equilibrium in mathematical economics
- Authors: Xotyeni, Zukisa Gqabi
- Date: 2008
- Subjects: Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5418 , http://hdl.handle.net/10962/d1005232 , Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Description: In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.
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- Date Issued: 2008
- Authors: Xotyeni, Zukisa Gqabi
- Date: 2008
- Subjects: Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5418 , http://hdl.handle.net/10962/d1005232 , Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Description: In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.
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- Date Issued: 2008
Lattice-valued uniform convergence spaces the case of enriched lattices
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
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- Date Issued: 2008
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
- Full Text:
- Date Issued: 2008
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