Algebraic structure through interval-valued fuzzy signature based on interval-valued fuzzy sets

This paper delivers three different ways to establish the initial structure of the interval-valued fuzzy signature (IVFSig). In recent years, interval-valued fuzzy set theory has proven more capable of dealing with uncertainty and vagueness than fuzzy set theory due to its increased flexibility. Therefore, the primary goal of this work is to develop an algebraic framework for an IVFSig based on the aspects of an interval-valued fuzzy set (IVFS). First, the IVFSig's are constructed with the aid of IVFSs, which may be considered the truth values of IVFSs. Second, the families of IVFSig's, as well as meet and join operators, are formulated, and then their lattice algebraic structure is verified. Third, the relation of partial ordering is established in an IVFSig family. Precisely, the addressed design is compared with recent well-known framework. Finally, the numerical illustrations provide a higher degree of representation than other existing framework.