A note on “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets”

Zhang and Zhang (2013) proposed an extended soft set model called trapezoidal interval type-2 fuzzy soft sets by combining trapezoidal interval type-2 fuzzy sets and soft sets and showed some examples of its operations, along with an application in decision making. However, we found that some results are incorrect. Thus, the purpose of this note is to point out that assertions (3) and (4) of Theorem 3.2 in Zhang and Zhang (2013) are not true, as well, assertion (3) of Theorem 3.5 is generally not true, while assertions (4)-(6) of Theorem 3.5 can be similarly proven to be incorrect. We also introduce the notion of a generalized trapezoidal interval type-2 fuzzy soft subset and fuzzy soft equal, and use these notions to correct the flaw in assertions (3) and (4) of Theorem 3.2 of Zhang and Zhang (2013). Finally we introduce two new definitions and a theorem to improve the work of Zhang and Zhang (2013), along with two examples.