在真實世界中，多屬性決策問題愈來愈具有不確定性與複雜性。近幾年來，根據區間Type-2模糊集合及區間直覺模糊集合以作多屬性決策是非常重要的研究課題。在本論文中，我們根據區間Type-2模糊集合及區間直覺模糊集合分別提出三個多屬性決策之新方法，其中(1)我們根據區間Type-2模糊集合的排序及區間Type-2模糊集合的-切割提出一個新的多屬性決策方法，(2)我們根據區間直覺模糊集合、線性規劃法及TOPSIS法提出一個新的多屬性決策方法，其中各方案之屬性的評估值及各屬性的權重值均以區間直覺模糊值表示，且線性規劃法被用來求得各屬性之最佳權重值，及(3)我們根據所提之區間直覺模糊集合的得分函數及線性規劃法提出一個改進的多屬性決策方法。實驗結果顯示我們所提之多屬性決策方法均能克服目前已存在之方法的缺點，其中目前已存在之方法的缺點為它們在某些情形下得到不合理的方案之優先順序的排序及它們在某些情形下未能得到方案的優先順序的排序。我們所提之多屬性決策方法分別提供我們在區間Type-2模糊環境及區間直覺模糊環境下非常有用的方法以作多屬性決策。

Many multiple attribute decision making problems in the real-world become more uncertain and more complex. In recent years, multiple attribute decision making based on interval type-2 fuzzy sets and interval-valued intuitionistic fuzzy sets become important research topics. In this dissertation, we propose three new multiple attribute decision making methods based on interval type-2 fuzzy sets and interval-valued intuitionistic fuzzy sets, respectively, where (1) we propose a new multiple attribute decision making method based on ranking interval type-2 fuzzy sets and the -cuts of interval type-2 fuzzy sets, (2) we propose a new multiple attribute decision making method based on interval-valued intuitionistic fuzzy sets, the linear programming methodology and the extended technique for order preference by similarity to ideal solution (TOPSIS) method, where the ratings of the attributes of alternatives and the weights of attributes are represented by interval-valued intuitionistic fuzzy values and the linear programming methodology is used to obtain optimal weights of attributes, and (3) we propose an improved multiple attribute decision making method based on the proposed new score function of interval-valued intuitionistic fuzzy sets and the linear programming methodology. The experimental results show that the proposed multiple attribute decision making methods can overcome the drawbacks of the existing methods, where the existing methods have the drawbacks that they get unreasonable preference orders of the alternatives in some situations and they cannot get the preference order of the alternatives in some situations. The proposed methods provide us with a very useful way for multiple attribute decision making in interval type-2 fuzzy environments and interval-valued intuitionistic fuzzy environments, respectively.

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