Constructing and managing multi-granular linguistic values are more and more important for linguistic decision making in big data or social computing environments, linguistic variable is the fundamental of constructing and managing multi-granular linguistic values. Based on analysis of linguistic values and drawbacks of symbolic or fuzzy set methods in processing linguistic information, a linguistic value is expressed by a formal linguistic concept, which is constructed by a linguistic term and it’s fuzzy sets, i.e., intension (name) and extension (meaning) of the concept are a linguistic term and it’s fuzzy sets. A new symbolic translation based on fuzzy sets is provided to obtain formal 2-tuple linguistic concepts, which are continuous formal linguistic concepts. By using linguistic hedges, the hierarchy of multi-granular formal linguistic concepts is constructed, and managing multi-granular linguistic values is carried out by a new transformation function between formal linguistic concepts of the hierarchy. Cases study shows that the proposed method combines advantages of symbolic approaches and fuzzy set methods in linguistic information processing and overcomes their drawbacks due to fuzzy sets and linguistic term as entity in linguistic information processing based on formal linguistic concepts, intensions are utilized to deal with linguistic information and extensions are used to represent meanings and obtain natural or artificial language concepts. It seems that constructing and managing multi-granular linguistic values via formal linguistic concepts is an useful and alternative method in linguistic information processing.

Introduction

The concept of linguistic variable plays a pivotal role in all applications of fuzzy logic, especially in computing with words or linguistic information processing [3]–[۶]. Formally, linguistic variable is defined as [7]: A linguistic variable is characterized by a quintuple (L, H, U, G, M), in which L is the name of the variable; H denotes the term set of L, i.e., the set of names of linguistic values of L, with each value being a fuzzy variable denoted generically by X and ranging across a universe of discourse U which is associated with the base variable u; G is a syntactic rule (which usually takes the form of a grammar) for generating the names of values of L; and M is a semantic rule for associating its meaning with each L, M(X), which is a fuzzy subset of U. For example, height is a linguistic variable defined on the universe (0, 2.5m] and high is a linguistic value of height, the trapezoidal fuzzy set µhigh(u) = (1.7, 1.9, 2.5, 2.5) on (0, 2.5m] can be a semantic value or meaning of high. In practical applications, high can be utilized to express qualitative knowledge ‘‘Europeans are high’’ and meaning of high can be represented by µhigh(u), due to calculable character of fuzzy sets, linguistic knowledge ‘‘Europeans are high’’ can be further processed by using µhigh(u) in a knowledge system.