Linguistic Z-number fuzzy soft sets and its application on multiple attribute group decision making problems

In this study, the concept of linguistic Z-number fuzzy soft set (LZnFSS) is proposed to describe multiple uncertainties in practical decision making problems. LZnFSS combines the concepts of fuzzy soft set, linguistic Z-number, and soft set, which could reflect both of the uncertainty in structure and the uncertainty in detailed evaluations. As an initial idea, the set operations on LZnFSSs are put forward, the properties of such operations are also discussed. With traditional soft set based decision procedure and fuzzy soft set based decision procedure, a novel linguistic Z-number fuzzy soft set based group decision procedure is developed to solve multiattribute group decision making with linguistic Z-numbers. Wherein an extended technique for order preference by similarity to ideal solution is also developed. Finally, a numerical example is shown to illustrate the practicality and effectiveness of the given method.