Abstract
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.
Highlights
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]–[6]
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
Linguistic hierarchy can be built on several sets of linguistic terms, which together with 2-tuple fuzzy linguistic representation model can be utilized to construct and manage multi-granular linguistic terms and apply in multi-granular linguistic decision making [37]–[52]. It can be noticed from a linguistic variable (L, H, U, G, M ) that a linguistic value is characterized by a syntactic value and a semantic value, the linguistic term is utilized to describe the fuzzy set, the fuzzy set is used to represent meaning of the linguistic term because it is fuzziness or unsharp boundaries on U
Summary
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]–[6]. Linguistic hierarchy can be built on several sets of linguistic terms, which together with 2-tuple fuzzy linguistic representation model can be utilized to construct and manage multi-granular linguistic terms and apply in multi-granular linguistic decision making [37]–[52] It can be noticed from a linguistic variable (L, H , U , G, M ) that a linguistic value is characterized by a syntactic value (name or linguistic term) and a semantic value (a fuzzy set on the universe U ), the linguistic term is utilized to describe the fuzzy set, the fuzzy set is used to represent meaning of the linguistic term because it is fuzziness or unsharp boundaries on U. Symbolic linguistic terms are man-made language, linguistic results are beyond comprehension because fuzzy sets are not utilized to represent meaning of them It seems that linguistic term and fuzzy set of a linguistic value is entity, only using one of them maybe lead to drawbacks in computing with words or linguistic information process.
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