New Methods for Fuzzy Decision Making and Fuzzy Multiple Attributes Group Decision Making Based on Interval Type-2 Fuzzy Sets and Likelihood-Based Comparison Relations

• Main Authors: Li-Wei Lee, 李立偉
• Other Authors: Shyi-Ming Chen
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/32652460477341269634

博士 === 國立臺灣科技大學 === 資訊工程系 === 99 === Fuzzy multiple attributes group decision making is an important research topic. In this dissertation, we present five new methods for fuzzy decision making and fuzzy multiple attributes group decision making based on interval type-2 fuzzy sets and likelihood-based comparison relations. In the first method of this dissertation, we present a new fuzzy decision making method based on likelihood-based comparison relations. First, we introduce the concepts of likelihood-based comparison relations for intervals. Then, we propose the concept of likelihood-based comparison relations for type-1 fuzzy sets and interval type-2 fuzzy sets. Then, we present a new method to rank fuzzy sets by using fuzzy targets based on the proposed likelihood-based comparison relations for fuzzy sets. Finally, we present a new fuzzy decision making method based on the proposed likelihood-based comparison relations for fuzzy sets and the proposed fuzzy ranking method. The proposed fuzzy decision making method has the advantage that the evaluated values can either be represented by crisp values, intervals, type-1 fuzzy sets or interval type-2 fuzzy sets. It can overcome the drawbacks of the existing methods due to the fact that the existing methods can not deal with the ranking of interval type-2 fuzzy sets for fuzzy decision making and can not distinguish the ranking order between the alternatives in some situations. In the second method of this dissertation, we present a new method for fuzzy multiple attributes group decision making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a new fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes. In the third method of this dissertation, we present a new interval type-2 TOPSIS method to handle fuzzy multiple attributes group decision making problems based on interval type-2 fuzzy sets. We present a new fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision making process of the proposed method. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-2 fuzzy sets to represent the evaluating values and the weights of the attributes. In the fourth method of this dissertation, we present a new method for fuzzy multiple criteria hierarchical group decision making based on arithmetic operations and fuzzy preference relations of interval type-2 fuzzy sets. Because the time complexity of the proposed method is O(nk), where n is the number of criteria and k is the number of decision-makers, it is more efficient than the existing methods. Moreover, the proposed method can overcome the drawback of the existing method due to the fact that it can handle evaluating values represented by nonnormal interval type-2 fuzzy sets. The proposed method provides us with a useful way to handle fuzzy multiple criteria hierarchical group decision making problems. In the fifth method of this dissertation, we present a new method for interval linguistic labels aggregation and consensus measure for autocratic decision making using group recommendations based on the likelihood-based comparison relations of interval linguistic labels and the proposed Interval Linguistic Labels Ordered Weighted Average (ILLOWA) operator. First, we propose the concepts of likelihood-based comparison relations of interval linguistic labels. Then, propose the ILLOWA operator to aggregate interval linguistic labels. Based on the likelihood-based comparison relations of interval linguistic labels and the proposed ILLOWA operator, we propose a new method for interval linguistic labels aggregation and consensus measure for autocratic decision making using group recommendations. The proposed method can overcome the drawbacks of existing methods. It provides us with a useful way for interval linguistic labels aggregation and consensus measure for autocratic decision making using group recommendations.