Abstract: The year 2020 came with a new generation of fuzzy inference systems (FISs) called fractional fuzzy inference systems (FFISs). FFISs add to the branch of the calculus of fuzzy rules and fuzzy graphs some new concepts of which are namely: fractional membership functions, fractional compositional rule of inference, fracture index, left and right orders, and so forth. This tutorial sheds light on the reasons for a transition from typical fuzzy inference systems (e.g., Mamdani’s FIS) to their corresponding FFISs. The impetus for the transition derives from the fact that both the generality of an FIS and its applicability to real-world problems are substantially enhanced by replacing the concept of the typical inference mechanism with that of a fractional inference mechanism. The conceptual impressions related to this new generation of FISs are elaborated in the tutorial, and the advantages of FFISs over typical FISs are also explained. In addition, potential applications of FFISs are highlighted, focusing on expert and knowledge-based systems and computational intelligence. Moreover, it has been proved that independent of the problem under consideration, typical FISs never lead to more satisfactory results than those obtained by FFISs. Thus, applying FFISs in the place of typical FISs brings us higher performance, more accuracy, less error, more efficiency, higher quality, more accurate prediction, and eventually increases the degree of computational intelligence.
This tutorial briefly introduces the fractional fuzzy inference systems intuitively and conceptually rather than technically. As an initial step towards being familiar with the new generation of fuzzy inference systems, this tutorial helps
Maximum Number of Attendees Participating: No limit.
Hands-On/Practice Content: The attendees don’t need to prepare anything in advance. However, some documents and a Matlab Package with a video file are provided for the distribution between participants.
Tutorial Speaker with Title and Affiliations:
Dr. Mehran Mazandarani, Shenzhen University, firstname.lastname@example.org
Dr. Mehran Mazandarani received a Ph.D. degree in electrical engineering, control field, from the Ferdowsi University of Mashhad. As a researcher, he joined the Computational Mathematics and Engineering Division, Ton Duc Thang University, Ho Chi Minh City, Viet Nam, during 2017-2018. Then, at the Harbin Institute of Technology, Shenzhen, China, he worked as a visiting researcher during 2018-2019.
As a postdoctoral researcher, he was with the Department of Information Sciences and Technology, Tsinghua University, China, during 2019-2022. Subsequently, as a senior researcher, Dr. Mazandarani started his work with the Department of Mechatronics and Control Engineering, Shenzhen University, China. His interests fall within some branches of fuzzy logic. He has elaborated on using fuzzy mathematics in control theory and introduced new frameworks in this regard. In fuzzy mathematics, he has introduced, for the first time, the type-2 fuzzy differential equations and type-2 fractional fuzzy differential equations - type-2 fuzzy calculus. By presenting the concept of granular differentiability of fuzzy number-valued functions, he revolutionized fuzzy differential equations.
In 2019, Dr. Mazandarani made a firm framework for studying a class of differential equations called Z-differential equations and presented the outline of Z-calculus. He has recently introduced a new generation of fuzzy inference systems called fractional fuzzy inference systems, which outperform all the typical fuzzy inference systems. By this achievement, a new branch in fuzzy inference systems has been created. His current research work focuses on the foundation principles of fuzzy logic, fractional fuzzy inference systems, computing with perceptions, and their potential applications in intelligent systems.
Intended Audience and Level: This tutorial is intended for those working or studying mathematics, computer science, and some branches of engineering fields such as mechanical engineering and electrical engineering. A piece of basic knowledge about fuzzy systems might facilitate catching the points given in this tutorial. Those who would like to be familiar with FFISs in advance may refer to the following web pages: