Granulation of a fuzzy set: Nonspecificity

Granulation (decomposition) of a fuzzy set A defined on a finite set of objects X is studied. Two types of decomposition are considered: external granulation determined by a given equivalence relation on X and internal granulation created by clusters of elements from X with similar membership grades in A. Axiomatic definitions of measures of granular nonspecificity and granular specificity are proposed. Some general approaches to the construction of measures of granular nonspecificity (specificity) are suggested. Relationship between granular nonspecificity, roughness and nonspecificity of a fuzzy set is discussed.