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A Four-Valued Ambiguous Logic: Application in Designing Ambiguous Inference System for Control Systems

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Abstract

Ambiguous set has recently been introduced as a new branch of mathematics and computer science dealing with the nature of ambiguity of uncertain events. There is much scope for the development of new theories based on the principles of the ambiguous set. In this direction, an idea of ambiguous logic is proposed, which can be regarded as a family of four-valued logic. In this study, the limitations of existing theories such as fuzzy logic, intuitionistic fuzzy logic, and neutrosophic logic that are used to deal with uncertainty are first discussed. Then an introduction to the ambiguous set and ambiguous logic is given. In ambiguous logic, there are four membership degrees for each proposition, which can be characterized as true, false, true-ambiguous, and false-ambiguous. We then analyze the membership degrees of propositions using various connectives, including negation, conjunction, and disjunction. In this study, we discuss various laws that support the different algebraic operations for comparing propositions in terms of membership degrees. An approach is presented to define a rule using a proposition consisting of membership degrees, called an ambiguous rule. The modus ponens rule of inference is defined by combining various ambiguous rules, and is called ambiguous inference. Finally, to demonstrate the real-time application of ambiguous logic, an ambiguous inference system is designed that can be used in machine control systems.

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References

  1. Singh, P., Huang, Y.-P., Lee, T.-T.: A novel ambiguous set theory to represent uncertainty and its application to brain MR image segmentation. In: Proc. of IEEE Int. Conf. on Systems, Man and Cybernetics (SMC), Bari, Italy, pp.2460–2465 (2019)

  2. Hájek, P., Godo, L., Esteva, F.: A complete many-valued logic with product-conjunction. Arch. Math. Log. 35(3), 191–208 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bimbó, K., Dunn, J.M.: Four-valued logic. Notre Dame J. Form. Log. 42(3), 171–192 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Singh, P.: Ambiguous set theory: a new approach to deal with unconsciousness and ambiguousness of human perception. J. Neutrosophic Fuzzy Syst. 5(1), 52–58 (2023)

    Article  Google Scholar 

  5. Singh, P., Bose, S.S.: Ambiguous D-means fusion clustering algorithm based on ambiguous set theory: special application in clustering of CT scan images of COVID-19. Knowl.-Based Syst. 231, 107432 (2021)

    Article  Google Scholar 

  6. Singh, P., Huang, Y.-P.: Membership functions, set-theoretic operations, distance measurement methods based on ambiguous set theory: A solution to a decision-making problem in selecting the appropriate colleges. Int. J. Fuzzy Syst. pp.1–16 (2023)

  7. Singh, P.: A general model of ambiguous sets to a single-valued ambiguous numbers with aggregation operators. Decis. Anal. J. 8, 100260 (2023)

    Article  Google Scholar 

  8. Belnap, N.D.: A useful four-valued logic. In: Dunn, J. M., Epstein, G., Reidel, D. (Eds.) Modern Uses of Multiple-Valued Logic (1977)

  9. Belnap, N.D.: A Useful Four-Valued Logic, pp. 5–37. Springer, Dordrecht (1977)

    MATH  Google Scholar 

  10. Arieli, O., Avron, A.: Four-valued paradefinite logics. Studia Log. 105(6), 1087–1122 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. Font, J.M., Hájek, P.: On łukasiewicz’s four-valued modal logic. Studia Log. 70(2), 157–182 (2002)

    Article  MATH  Google Scholar 

  12. Béziau, J.-Y.: A new four-valued approach to modal logic. Log. Anal. 1, 109–121 (2011)

    MathSciNet  MATH  Google Scholar 

  13. Mamdani, E.H., Assilian, S.: An experiment in lingusitic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 7, 1–13 (1975)

    Article  MATH  Google Scholar 

  14. Passino, K.M., Yurkovich, S.: Fuzzy Control, 1st edn. Addison Wesley Longman, Menlo Park, CA (1998)

    MATH  Google Scholar 

  15. White, C.J., Lakany, H.: A fuzzy inference system for fault detection and isolation: application to a fluid system. Expert Syst. Appl. 35(3), 1021–1033 (2008)

    Article  Google Scholar 

  16. Zhang, J., Shi, P., Xia, Y.: Robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties. IEEE Trans. Fuzzy Syst. 18(4), 700–711 (2010)

    Article  Google Scholar 

  17. Armstrong, A.A., Johnson, A.J.W., Alleyne, A.G.: An improved approach to iterative learning control for uncertain systems. IEEE Trans. Control Syst. Technol. 29(2), 546–555 (2021)

    Article  Google Scholar 

  18. Jin, X., Tang, Y., Shi, Y., Zhang, W., Du, W.: Event-triggered formation control for a class of uncertain Euler-Lagrange systems: theory and experiment. IEEE Trans. Control Syst. Technol. 30(1), 336–343 (2022)

    Article  Google Scholar 

  19. Tran, V.P., Mabrok, M.A., Garratt, M.A., Petersen, I.R.: Hybrid adaptive negative imaginary-neural-fuzzy control with model identification for a quadrotor. IFAC J. Syst. Control 16, 100156 (2021)

    Article  MathSciNet  Google Scholar 

  20. Ruan, D., Yang, S., Zhang, W.: Fixed/predefined-time synchronization on complex networks in the light of T-S fuzzy system. IFAC J. Syst. Control 24, 100216 (2023)

    Article  MathSciNet  Google Scholar 

  21. Smarandache, F.: A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1999)

    MATH  Google Scholar 

  22. Shangguan, X.-C., He, Y., Zhang, C.-K., Jiang, L., Wu, M.: Adjustable event-triggered load frequency control of power systems using control-performance-standard-based fuzzy logic. IEEE Trans. Fuzzy Syst. 30(8), 3297–3311 (2022)

    Article  Google Scholar 

  23. An, J., Yang, J., Wu, M., She, J., Terano, T.: Decoupling control method with fuzzy theory for top pressure of blast furnace. IEEE Trans. Control Syst. Technol. 27(6), 2735–2742 (2019)

    Article  Google Scholar 

  24. Hong, S.-K., Langari, R.: Robust fuzzy control of a magnetic bearing system subject to harmonic disturbances. IEEE Trans. Control Syst. Technol. 8(2), 366–371 (2000)

    Article  Google Scholar 

  25. Lin, J., Lian, R.-J.: Self-organizing fuzzy controller for gas-assisted injection molding combination systems. IEEE Trans. Control Syst. Technol. 18(6), 1413–1421 (2010)

    Google Scholar 

  26. Liu, Z.-G., Shi, Y.-Y., Liu, L.-X.: Fuzzy adaptive control of nonlinear systems with odd system powers, complex dynamics, and uncertain control coefficients. Int. J. Fuzzy Syst. 23, 1257–1266 (2021)

    Article  MathSciNet  Google Scholar 

  27. Phu, N.D., Hung, N.N., Ahmadian, A., Senu, N.: A new fuzzy PID control system based on fuzzy PID controller and fuzzy control process. Int. J. Fuzzy Syst. 22(7), 2163–2187 (2020)

    Article  Google Scholar 

  28. Li, H., Song, B., Tang, X., Xie, Y., Zhou, X.: Adaptive pareto optimal control of T-S fuzzy system with input constraints and its application. Int. J. Fuzzy Syst. 24, 967–988 (2022)

    Article  Google Scholar 

  29. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MATH  Google Scholar 

  30. Rivieccio, U.: Neutrosophic logics: prospects and problems. Fuzzy Sets Syst. 159(14), 1860–1868 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ross, T.J.: Fuzzy Logic with Engineering Applications, 4th edn. Wiley, New York (2017)

    Google Scholar 

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Funding

This study was funded in part by the National Science and Technology Council, Taiwan, under Grants MOST108-2221-E-346-006-MY3 and MOST111-2221-E-346-002-MY3.

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Authors and Affiliations

  1. Quantum Optimization Research Lab, Department of Data Science and Analytics, Central University of Rajasthan, Ajmer, 305817, Rajasthan, India

    Pritpal Singh

  2. Department of Electrical Engineering, National Penghu University of Science and Technology, Penghu, 88046, Taiwan

    Yo-Ping Huang

  3. Department of Electrical Engineering, National Taipei University of Technology, Taipei, 10608, Taiwan

    Yo-Ping Huang

  4. Department of Information and Communication Engineering, Chaoyang University of Technology, Taichung, 41349, Taiwan

    Yo-Ping Huang

Authors
  1. Pritpal Singh
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  2. Yo-Ping Huang
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Correspondence to Yo-Ping Huang.

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Singh, P., Huang, YP. A Four-Valued Ambiguous Logic: Application in Designing Ambiguous Inference System for Control Systems. Int. J. Fuzzy Syst. 25, 2921–2938 (2023). https://doi.org/10.1007/s40815-023-01582-2

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  • DOI: https://doi.org/10.1007/s40815-023-01582-2

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