Document Type : Research Paper


1 Department of Statistics, Payame Noor University, Tehran 19395-3697, Iran

2 Department of Mathematical Sciences, University of Birjand, Birjand, 615-97175, Iran


Here are many situations in real applications of decision making where we deal with uncertain conditions.  Due to the different sources of uncertainty,  since its original definition of fuzzy sets in 1965 \cite{zadeh1965},  different generalizations and extensions of fuzzy sets have been introduced: Type-2 fuzzy sets \cite{6,13}, Intuitionistic fuzzy sets \cite{1}, fuzzy multi-sets \cite{37} and etc. However, in such cases, it is suitable for experts to provide their preferences or assessments by using linguistic information rather than quantitative values.