Ranking type-2 fuzzy values and its application to type-2 fuzzy shortest path problem

Abstract

Most systems in the real world have an ambiguity that is inherent in their nature, which often leads to the ambiguity in the decision procedure. Fuzzy sets are developed to express and handle this ambiguity in the systems. Although there have been numerous researches in the area of fuzzy systems, the majority of them are focused on the simplest level of ambiguity: type-1 fuzzy system. However, there are many situations where the ambiguity in the system cannot be explained well enough using type-1 fuzzy system. For this reason, we need to develop a method to handle more complex level of ambiguity using type-2 fuzzy systems. This makes it necessary to extend the operations defined on type-1 fuzzy sets to the domain of type-2 fuzzy sets. In this thesis, a method is proposed for comparing and ranking type-2 fuzzy values. The proposed method is based on the preference degree that indicates the relative preference of the given solution over the other alternatives. Two kinds of preference degrees are proposed: the preference degree of comparison (PDC) and the preference degree of sequence (PDS). PDC provides a relative degree between two fuzzy values that means how much a fuzzy value is considered to be preferred than the other, and PDS gives an information on which ranked sequence is the most preferred sequence or the next-best alternative. These preference degrees can be used to determine the most-preferred solution and its alternatives from a given set of possible solutions. To show an example of the decision making in a type-2 fuzzy environment, we formulate the shortest path problem in type-2 fuzzy weighted graphs. An algorithm for the type-2 fuzzy shortest path is also developed using the proposed method. In the proposed algorithm, the possibility degree of each edge is calculated based on the preference degree. These possibility degrees are used to reconstruct the shortest path at different confidence levels. Using the proposed algorithm, we can make a decision...