Linguistic Weighted Standard Deviation

In classical statistics, the first- and second-order statistics, i.e., the mean and standard deviation, are the most important ones. This paper extends the definition of the standard deviation and makes it possible to compute the standard deviation when data contains not only numbers, but also words. The generalized standard deviation is called the Linguistic Weighted Standard Deviation (LWSD). The Linguistic Weighted Power Mean (LWPM) operation is also reviewed in this paper, and the LWSD is viewed as a special case of the LWPM when the parameter r in the LWPM is set to be 2. Two numerical examples that utilize the new LWSD are presented: one is synthetic where all the data are generated randomly, and the other is a practical decision making problem. These examples demonstrate that the LWSD can provide extra information to a decision maker when only uncertain input data (words) are available. We believe that the concept of the LWSD will certainly play an important role in many future applications.