Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision making

•A new raking method of TIFNs is given based on weighted possibility attitudinal expected values.•The sensitivity analyses on attitudinal character parameter are made.•TIFOWA, TIFOWG, IFHWA, TIFGOWA, and TIFGHWA operators are developed.•DMs’ weights are determined by TOPSIS and attribute weights are derived through constructing the multi-objective programming.•A new method for MAGDM with TIFNs is proposed.

The aim of this paper is to develop some new generalized aggregation operators for triangular intuitionistic fuzzy numbers (TIFNs) and apply to multi-attribute group decision making (MAGDM) problems. First, the weighted possibility attitudinal expected values of TIFNs are defined and a new method is presented to rank TIFNs considering risk attitude of decision maker (DM). The sensitivity analyses on attitudinal character parameter are given. Then, the triangular intuitionistic fuzzy weighted averaging (TIFWA) operator, ordered weighted averaging (TIFOWA) operator, ordered weighted geometric (TIFOWG) operator and hybrid weighted averaging (TIFHWA) operator are defined. We further develop some new generalized aggregation operators for TIFNs, involving the triangular intuitionistic fuzzy generalized ordered weighted averaging (TIFGOWA) operator and generalized hybrid weighted averaging (TIFGHWA) operator. Some desirable properties for these operators are discussed in detail. Utilizing the TIFGHWA and TIFWA operators, we propose a new method for MAGDM with TIFNs and incomplete weight information. In this method, DMs’ weights are determined by Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and the weights of attributes are objectively derived through constructing a multi-objective programming model which is transformed into a linear goal program to solve. Finally, the example analysis of an investment selection example verifies the effectiveness and practicability of the proposed method in this paper.