On aggregation operators for linguistic trapezoidal fuzzy intuitionistic fuzzy sets and their application to multiple attribute group decision making

Linguistic decision-making tools are very useful in determining the solution to real-life decision problems. In order to represent the complex fuzzy qualitative information more accurately, this paper introduces a novel concept called linguistic trapezoidal fuzzy intuitionistic fuzzy set (LTFIFS), where the degrees of membership (MS) and non-membership (NMS) are represented by trapezoidal fuzzy linguistic numbers. Further, work defines some basic operational laws, score and accuracy values, and a comparison method for LTFIFNs with a brief study of related properties. To aggregate different LTFIFNs, we develop several weighted arithmetic and weighted geometric aggregation operators such as the LTFIFWA operator, the LTFIFOWA operator, the LTFIFOWAWA operator, the LTFIFWG operator, the LTFIFOWG operator, and the LTFIFOWGWG operator. Paper also establishes several important properties and particular cases of these operators. Furthermore, by using proposed aggregation operators, we formulate a decision-making approach for solving group decision-making problems under the LTFIF environment with multiple attributes. Finally, the paper presents a real-life decision problem to validate the effectiveness and flexibility of the newly given approach.