On the basis of Zadeh’s fuzzy sets (FSs) theory, Atanassov proposed the intuitionistic fuzzy sets (IFSs) to characterize the uncertainty of objective information according to degrees of membership and non-membership, which made up for the insufficiency that Zadeh’s fuzzy sets can only characterize fuzzy information by degree of membership. IFSs have attracted extensive attention of many scholars and are applied to all kinds of decision-making problems. IFSs require the sum of degrees of membership and non-membership not more than 1, which restricts its application in practical decision-making scenarios. For example, when decision makers independently give the degrees of membership and non-membership of the attribute values of the alternative, the sum of the two may be greater than 1. To solve this problem, Yager proposed the Pythagorean fuzzy sets (PFSs), whose main characteristic is that the quadratic sum of membership degree and non-membership degree is not greater than 1. After that, to obtain the generalized PFS, Yager further proposed the concept of q-rung orthopair fuzzy sets (q-ROFSs) whose characteristics are that the sum of q (q>1) power of membership degree and non-membership degree is bounded to 1.

Although the FSs, IFSs, PFSs, and q-ROFSs have been extensively studied, their expression for fuzzy decision-making information is still limited. Especially in the extremely complex and contradictory decision-making environment, multiple heterogeneous factors (MHFs), such as experts' subjective preference, the dynamic change of the objective environment, physical condition, bias in model calculations, etc., significantly affect people's cognition and decision making. Therefore, how to embed these multiple realities into the existing fuzzy sets structure to increase their ability of information representation and decision making is an important research topic.

The aim of this Special Issue is to solicit original research and review articles on the extensions and applications of MHFs-driven fuzzy decision making. We sincerely hope that this Special Issue provides a platform for researchers in various areas to exchange ideas on how we can further develop and apply the fuzzy decision making based on MHFs.

Potential topics include but are not limited to the following:

• New concepts and expression of MHFs-driven fuzzy sets
• Information measurement between MHFs-driven fuzzy sets
• Fuzzy optimization under MHFs-driven fuzzy sets
• Fuzzy topological relations of MHFs-driven fuzzy sets
• Differential Calculus of MHFs-driven fuzzy functions
• Analysis of MHFs-driven fuzzy cognitive maps
• Decision-making application under MHFs-driven fuzzy sets in various fields