The concept of fuzzy set was developed in 1965. Since then, researchers have used this key set in many disciplines. As a brand-new conceptual system to support human-centric framework, fuzzy set has proved quite promising and effective in modeling human involvement in human-based intelligence to attain modernity in many departments like data analyzing, data mining, image coding and explaining, as well as in intelligence systems. Fuzzy set has also become an acknowledged research subject in both pure as well as in applied mathematics and statistics, showing how this theory is highly applicable and productive in many applications. Despite being a core subject for many years, fuzzy set still attracts researchers for putting forth solutions for prime issues with certain features questioned by these notions. Fuzzy set can effectively deal with a wide spectrum of problems of the physical world via cooperation, which may be beyond the capability of classical techniques. This means the fuzzy set could have the ability to handle a wide range of problems, for instance, decision making, intelligent data analysis, processing information, pattern recognition, and optimization.
The goal of this Special Issue is to dive deeper into the new trends of fuzzy set theory and the extension of fuzzy set theory with applications in group theory, ring theory, statistics, topological spaces, graph theory, decision making and other engineering applications.
Potential topics include but are not limited to the following:
- Fuzzy sets and their extensions
- Fuzzy subgroups and their extended forms
- Applications of fuzzy sets in ring theory
- Fuzzy sets and their extensions in graph theory
- Statistics on the application of fuzzy informatics
- Fuzzy sets and their extensions in topological spaces
- Decision making application with fuzzy logic
fuzzy logic, in mathematics, a form of logic based on the concept of a fuzzy set. Membership in fuzzy sets is expressed in degrees of truth—i.e., as a continuum of values ranging from 0 to 1. In a narrow sense, the term fuzzy logic refers to a system of approximate reasoning, but its widest meaning is usually identified with a mathematical theory of classes with unclear, or “fuzzy,” boundaries. Control systems based on fuzzy logic are used in many consumer electronic devices in order to make fine adjustments to changes . Fuzzy logic concepts and techniques have also been profitably used in linguistics, the behavioral sciences, the diagnosis of certain diseases, and even analysis.
Fuzzy sets
Most concepts used in everyday language, such as “high temperature,” “round face,” or “aquatic animal,” are not clearly defined. In 1965 Lotfi Zadeh, an engineering professor at the University of California at Berkeley, proposed a mathematical definition of those classes that lack precisely defined criteria of membership. Zadeh called them fuzzy sets. Membership in a fuzzy set may be indicated by any number from 0 to 1, representing a range from “definitely not in the set” through “partially in the set” to “completely in the set.” For example, at age 45 a man is neither very young nor very old. This makes it difficult in traditional logic to say whether or not he belongs to the set of “old persons.” Clearly he is “sort of” old, a qualitative assessment that can be quantified by assigning a value, or degree of membership, between 0 and 1—say 0.30—for his inclusion in a fuzzy set of old persons.
