Generalized Interval-valued Hesitant Fuzzy Aggregation Operators And Their Applications To Multi-attribute Group Decision Making

Multiple attribute group decision making is the intersection research field of multiple attribute decision making and group decision making, which also is an important research field of management science. It’s basic theory and decision making method have been widely used in economic management, pattern recognition, medical diagnosis, risk investment and so on. Therefore, there have important theoretical significance and practical values to research multiple attribute group decision making problems. In order to promote the development of human society, the theories of fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets have been widely used and developed. However, when people make a decision, they are usually hesitant for one thing or another, which makes it difficult to determine the membership of an element to a set due to doubts among a few different values. In this case, scholars proposed the hesitant fuzzy set, and then introduced the interval-valued hesitant fuzzy set considered as the generalization of hesitant fuzzy sets, and applied to multiple attribute group decision making problems. Due to it can express the information more comprehensive and accurate, interval-valued hesitant fuzzy set has received more and more attention in recent years, and has achieved some theoretical research results.In this paper, we investigate two types of generalized interval-valued hesitant fuzzy information aggregation operators and their applications to multiple attribute group decision making. The main contents include:1. We first introduce some interval-valued hesitant fuzzy operations based on Archimedean t-conorm and t-norm, including generalized interval-valued hesitant fuzzy sum operation, product operation, scalar multiplication operation and power operation, and then analyze some relations of these operations.2. Based on the new interval-valued hesitant fuzzy operations, we propose two kinds of generalized interval-valued hesitant fuzzy aggregation operators, such as generalized interval-valued hesitant fuzzy Choquet ordered averaging (G-IVHFCOA) operator and generalized interval-valued hesitant fuzzy Choquet ordered geometric (G-IVHFCOG) operator. Furthermore, we discuss some of their desirable properties in detail, including commutativity, idempotency, monotonicity, boundedness and the other excellent properties.3. We discussed in some special circumstances, the generalized interval-valued hesitant fuzzy Choquet integral operators will be convert into some common interval-valued hesitant fuzzy information aggregation operators. When classified on then basis of fuzzy measure, G-IVHFCOA (G-IVHFCOG) operator can convert into maximum (minimum) operator, generalized interval-valued hesitant fuzzy weighted averaging (geometric) operator and generalized interval-valued hesitant fuzzy ordered weighted averaging (geometric) operator, respectively. When classified on then basis of additive operator, G-IVHFCOA (G-IVHFCOG) operator can reduces to interval-valued hesitant fuzzy Choquet ordered averaging (geometric) operator, interval-valued hesitant fuzzy Einstein Choquet ordered averaging (geometric) operator, interval-valued hesitant fuzzy Hamacher Choquet ordered averaging (geometric) operator and interval-valued hesitant fuzzy Frank Choquet ordered averaging (geometric) operator, respectively. An approach to interval-valued hesitant fuzzy multi-attribute group decision making is developed based on the proposed operators, and a numerical example is given to illustrate the behavior of the proposed approach.4. On the basis of interval-valued hesitant fuzzy complement operation, we investigate the relationships between G-IVHFCOA operator and G-IVHFCOG operator, and then compare the size of IVHFCOA operator, IVHFECOA operator, IVHFCOG operator and IVHFECOG operator.