Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a number of lexicographic orders by means of several measures such as the membership, non-membership, score, accuracy and expectation score functions. Some equivalent characterizations and illustrative examples are provided, from which the relationships among these lexicographic orders are ascertained. We also propose three different compatible properties of preorders with respect to the algebraic sum and scalar product operations of intuitionistic fuzzy values, and apply them to the investigation of compatible properties of various lexicographic orders. In addition, a benchmark problem regarding risk investment is further explored to give a comparative analysis of different lexicographic orders and highlight the practical value of the obtained results for solving real-world decision-making problems.