From Classical Logic to Fuzzy Logic and Quantum Logic: A General View

IAENG Internaitonal journal of computer science

article

Sorin Nadaban¹ 

[1] Aurel Vlaicu University of Arad, Department of Mathematics and Computer Science

关键词: fuzzy logic;    quantum logic;    orthomodular lattice;    Hilbert space;    quantum mechanics;    effect algebras.;   

DOI  :  10.15837/ijccc.2021.1.4125

学科分类：计算机科学（综合）

来源: International Association of Engineers

【 摘 要 】

The aim of this article is to offer a concise and unitary vision upon the algebraic connections between classical logic and its generalizations, such as fuzzy logic and quantum logic. The mathematical concept which governs any kind of logic is that of lattice. Therefore, the lattices are the basic tools in this presentation. The Hilbert spaces theory is important in the study of quantum logic and it has also been used in the present paper.During the last decades, the art and science of fuzzy logic have witnessed significant developments and have found applications in many active areas, such as pattern recognition, classification, control systems, etc. A lot of research has demonstrated the ability of fuzzy logic in dealing with vague and uncertain linguistic information. For the purpose of representing human perception, fuzzy logic has been employed as an effective tool in intelligent decision making. Due to the emergence of various studies on fuzzy logic-based decision-making methods, it is necessary to make a comprehensive overview of published papers in this field and their applications. This paper covers a wide range of both theoretical and practical applications of fuzzy logic in decision making. It has been grouped into five parts: to explain the role of fuzzy logic in decision making, we first present some basic ideas underlying different types of fuzzy logic and the structure of the fuzzy logic system. Then, we make a review of evaluation methods, prediction methods, decision support algorithms, group decision-making methods based on fuzzy logic. Applications of these methods are further reviewed. Finally, some challenges and future trends are given from different perspectives. This paper illustrates that the combination of fuzzy logic and decision making method has an extensive research prospect. It can help researchers to identify the frontiers of fuzzy logic in the field of decision making.

【 授权许可】

CC BY