Keychains and preferential fuzzy sets with applications - Mahlasela, Zuko (Rhodes University, Faculty of Science, Department of Mathematics)
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.
Keywords: Fuzzy sets; Partially ordered sets; Lattice theory; Equivalence relations (Set theory); Voting patterns; Simplexes (Mathematics); Preference relation; Decision making