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Interval-Valued Intuitionistic Multiplicative Sets

A generalization of the notion of intuitionistic multiplicative set (IMS) is given in this paper, which is called interval-valued intuitionistic multiplicative set (IVIMS). The IVIMS uses an unsymmetrical scale (Saaty's 1-9 scale) instead of the ordinary symmetrical scale in an intuitionistic fuzzy set or an interval-valued intuitionistic fuzzy set. IVIMSs can reflect our intuition more objectively in some special situations. The basic component of an IVIMS is interval-valued intuitionistic multiplicative number (IVIMN). To rank IVIMNs, the comparison laws are developed. Based on the pseudo-multiplication, we explore some interval-valued intuitionistic multiplicative operations and obtain several specific results when some specific forms are assigned. In addition, some distance measures and weighted distance measures between IVIMSs are developed to describe the difference of any two IVIMSs. By analyzing the range of the uncertain degree, a generalized interval-valued intuitionistic multiplicative set is presented, which is a generalization of the notions of IMS and IVIMS. Finally, a numerical example is given to illustrate our results.