JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2011, Vol. 46 ›› Issue (10): 32-44.

• Articles • Previous Articles     Next Articles

Mix-valued logic and its applications

CHENG Daizhan, ZHAO Yin, XU Xiangru   

  1. Key Laboratory of Systems and Control, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2011-06-24 Online:2011-10-20 Published:2011-10-18

PDF (PC)

2211

Abstract:

Mix-valued logic is a natural generalization of Boolean Logic and k-valued logic. It is a new concept proposed by the authors and their research group. It plays an important role in systems control and related fields, and shows it vivid life. The purpose of the paper is to give a systematic survey on the definition, calculation, and main properties of mix-valued logic, and also to normalize the concepts and notations. Using the semi-tensor product of matrices, this paper introducesthe definition of mix-valued logical operators, its calculations, and its basic properties. Then three applications of mix-valued logic are introduced: (1) dynamic game with finite memory of strategies; (2) solving fuzzy relation equations; (3) dynamic-algebraic Boolean networks.

Key words: semi-tensor product of matrices, mix-valued logic, dynamic game, fuzzy relational equation, dynamic-algebraic Boolean network,  

[1] WANG Shou-feng. A generalization of infix codes [J]. J4, 2013, 48(8): 34-35.
[2] LIN Ping-feng, ZENG Wei, ZENG Chun-yi. Idempotents of semigroup PΓ(Λ×Λ) of binary relations determined by the semilattice Γ on the set Λ [J]. J4, 2013, 48(8): 36-40.
[3] CUI Yu-quan, LI Pei-pei, LI Lin-lin. The analysis of stock index sequence based on timing series model [J]. J4, 2013, 48(8): 68-77.
[4] TANG Ji-hua1, CHEN Bao-hui1*, ZHANG Ling1, BAI Xing-rui2. Function inverse P-sets and the dynamic separationof  inverse P-sets information laws [J]. J4, 2013, 48(8): 104-110.
[5] QIU Xiu-feng1,2, LIU Jian-wei1, WU Qian-hong1, LIU Jian-hua1. Multipath interdomain routing decision verification protocol [J]. J4, 2013, 48(7): 39-45.
[6] XU Xiao-ming. Reflected solutions of anticipated BSDEs and related  optimal stopping time problem [J]. J4, 2013, 48(6): 14-17.
[7] CHEN Xiang-en1, WANG Zhi-wen2, ZHAO Fei-hu1, WEI Jia-jing1, YAO Bing1. General neighbor-distinguishing edge coloring of  strong products and compositions of graphs [J]. J4, 2013, 48(6): 18-22.
[8] WANG Xiu-jian1,2, CHENG Zhi1, DU Xian-neng1*. Morita context rings with a pair of zero homomorphism [J]. J4, 2013, 48(6): 42-45.
[9] SUN Yan-mei1, ZHAO Zeng-qin2. Existence of solutions for a class of second order  singular impulsive differential equations [J]. J4, 2013, 48(6): 91-95.
[10] XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1. Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method [J]. J4, 2013, 48(4): 65-71.
[11] WU Dai-yong. Global attractivity of a nonlinear discrete Logistic model  with feedback control [J]. J4, 2013, 48(4): 114-110.
[12] WU Fang-lan1, ZUO Lian-cui2*. Equitable colorings of a special class of Cartesian products of graphs [J]. J4, 2013, 48(4): 20-24.
[13] JI Pei-sheng1, QI Wei-qing2, LIU Rong-rong1. On the Hyers-Ulam Stability of n-cocycles [J]. J4, 2013, 48(4): 1-4.
[14] HU Li-xia, ZHANG Jian-hua. Lie higher derivable mappings of triangular algebras at zero points [J]. J4, 2013, 48(4): 5-9.
[15] YU Wei, CAO Xiao-hong*. Topological uniform descent and the single valued extension property [J]. J4, 2013, 48(4): 10-14.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd