Data can be in the form of a binary set such as + 1 and - 1, 0 and 1, and so on. Sometimes, it can be in the form of a real number. It can also be represented by vector of real numbers corresponding to an appropriate linear space. However, there are numerous times that we encounter uncertainty in the data. This type of data can be produced by the imprecision of an agent who collected the data, or produced by a natural language, and can be modeled by a fuzzy subset. It is called a linguistic variable, and a vector of fuzzy subsets in Euclidean space is called a linguistic vector.
Several linguistic algorithms are developed to analyze the data that contains linguistic vectors. For example:
These linguistic algorithms are developed based on the extension principle and the decomposition theorem.