Fuzzy set theory, first introduced by Zadeh, is a powerful mathematical tool for dealing with uncertainty connected with the imprecision of states, perceptions, and preferences. With the rise of an intelligent era in human society, fuzzy sets and related applications have become increasingly active research topics in various fields. These are widely scattered over many disciplines, such as algebraic structures, artificial intelligence, computer science, control engineering, data mining, decision analysis, expert systems, management science, non-classical logic, operations research, pattern recognition, and robotics, among others.

The notion of infinite-valued logic was introduced in Zadeh’s seminal work “Fuzzy Sets” where he described the mathematics of fuzzy set theory, and by extension, fuzzy logic. This theory proposed making the membership function (or the values F and T) operate over the range of real numbers [0, 1]. New operations for the calculus of logic were proposed and shown to be in principle at least a generalisation of classical logic. Fuzzy logic provides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associated with human cognitive processes like thinking and reasoning. The role of logic in mathematics and computer science is twofold: as a tool for applications in both areas, and as a technique for laying foundations. Non-classical logic, including many-valued logic and fuzzy logic, takes the advantages of classical logic to handle information with various facets of uncertainty, such as fuzziness or randomness. Non-classical logic has become a formal and useful tool for computer science to deal with fuzzy information and uncertain information. Fuzziness and incomparability are two kinds of uncertainties often associated with intelligent human activities in the real world, and they exist not only in the processed object itself, but also in the course of the object being dealt with.

This Special Issue will be devoted to state-of-the-art research on fuzzy sets and their extensions with applications for the investigation of logical algebras (such as MV-algebra, BL-algebra, MTL-algebra and EQ-algebra, lattice implication algebra, and equality algebra) and the development of various intelligent systems in engineering. The theory of fuzzy sets and their extensions can be easily applied to different fields to overcome their associated challenges: decision-making problems, graph theory, and engineering applications; logic and fuzzy algebraic structures; neutrosophic sets and extensions; and non-classical logic and applications in engineering. We invite current advances concerning new discoveries and challenges in all aspects of logical algebras and non-classical logic, from their mathematical foundations to practical applications in artificial intelligence, data mining, decision support, expert systems, industrial control, and other areas of engineering.

Potential topics include but are not limited to the following:

• Fuzzy decision-making methods
• Fuzzy graph theory and engineering applications
• Fuzzy logic and fuzzy algebraic structures
• Fuzzy optimisation in engineering
• Fuzzy pattern mining in engineering
• Fuzzy rough sets and extensions
• Fuzzy soft rough sets and extensions
• Fuzzy soft sets and extensions
• Generalised orthopair fuzzy sets
• Hesitant fuzzy sets and extensions
• Intuitionistic fuzzy (soft) sets and extensions
• Logical algebras and applications in engineering
• Neutrosophic sets and extensions
• Non-classical logic and applications in engineering