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	 Fuzzy Flip-Flops and their Applications to Fuzzy Memory Element and Circuit Design using FPGA
    Shin-ichi Yoshida, Yasufumi Takama and Kaoru Hirota
 Deptartment of Computational Intelligence and Systems Science
Interdisciplinary Graduate School of Science and Engineering Tokyo Institute of Technology 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
    
    
Received:September 29, 2023Accepted:October 16, 2000Published:September 20, 2000    
	
    
    
Keywords:Fuzzy flip-flop, Memory element, Fuzzy logic, FPGA, Logic circuit	
	Abstract	
    D, T, and SR fuzzy flip-flops are proposed and their characteristics are shown in four - max-min, algebraic, bounded, drastic - logical operation systems. The circuits of the proposed flip-flops are designed and simulated on a Synopsys circuit simulator. The result of synthesis show the areas of D, T, SR fuzzy flip-flops are nearly 0, 2/3 1/2 of that of conventional JK fuzzy flip-flops and the delay times of D, T, SR fuzzy flip-flops are nearly 0, 2/3, 2/3 of that of the JK type. Moreover, max-min fuzzy memory element based on functions required for memory is proposed independently of fuzzy flip-flops. As it uses 1/2 circuit area of the SR fuzzy flip-flops, it is more suitable for fuzzy memory element than other fuzzy flipflops.		
	
	
    
    Cite this article as:S.  Yoshida, Y.  Takama, and K.  Hirota, “Fuzzy Flip-Flops and their Applications to Fuzzy Memory Element and Circuit Design using FPGA,” J. Adv. Comput. Intell. Intell. Inform., Vol.4 No.5, pp. 380-386, 2000.Data files: