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Very True Operators on Quasi-pseudo-MV Algebras

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Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1074))

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Abstract

In this paper, we introduce the notion of very true operator on a quasi-pseudo-MV algebra (qpMV-algebra, for short) and investigate the new algebraic structure qpMV\(_{vt}\)-algebra which will generalize psMV\(_{vt}\)-algebra defined in [10]. First we discuss some properties of very true operator on a qpMV-algebra. Next we define the dual notion very false operator on a qpMV-algebra and prove that there exists a one-to-one correspondence between very true operators and very false operators on any qpMV-algebra. Finally, some cases of qpMV\(_{vt}\)-algebras with truth-depressing hedges are given.

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References

  1. Botur, M., Svrcek, F.: Very true on CBA fuzzy logic. Math. Slovaca. 60(4), 435–446 (2010)

    Article  MathSciNet  Google Scholar 

  2. Chajda, I., Kolarik, M.: Very true operators in effect algebras. Soft. Comput. 16(7), 1213–1218 (2012)

    Article  Google Scholar 

  3. Chen, W.J., Dudek, W.A.: Quantum computational algebra with a non-commutative generalization. Math. Slovaca. 66(1), 1–16 (2016)

    Article  MathSciNet  Google Scholar 

  4. Chen, W.J., Davvaz, B.: Some classes of quasi-pseudo-MV algebras. Logic J. IGPL. 24(5), 655–673 (2016)

    Article  MathSciNet  Google Scholar 

  5. Chen, W.J., Dudek, W.A.: Ideals and congruences in quasi-pseudo-MV algebras. Soft. Comput. 22(12), 3879–3889 (2018)

    Article  Google Scholar 

  6. Ciungu, L.C.: Very true pseudo-BCK algebras. Soft Comput. (2019). https://doi.org/10.1007/s00500-019-03859-x

  7. Georgescu, G., Iorgulescu, A.: Pseudo MV algebras. Mult.-Valued Log. 6, 95–135 (2001)

    MathSciNet  MATH  Google Scholar 

  8. Hajek, P.: On very true. Fuzzy Sets Syst. 124, 329–333 (2001)

    Article  MathSciNet  Google Scholar 

  9. Ledda, A., Konig, M., Paoli, F., Giuntini, R.: MV algebras and quantum computation. Studia Log. 82, 245–270 (2006)

    Article  MathSciNet  Google Scholar 

  10. Leustean, I.: Non-commutative Lukasiewicz propositional logic. Arch. Math. Logic 45, 191–213 (2006)

    Article  MathSciNet  Google Scholar 

  11. Liu, J.M., Chen, W.J.: A non-communicative generalization of quasi-MV algebras. In: 2016 IEEE International Conference on Fuzzy Systems, pp. 122–126. FUZZ-IEEE (2016)

    Google Scholar 

  12. Rachunek, J., Salounova, D.: Truth values on generalizations of some commutative fuzzy structures. Fuzzy Sets Syst. 157, 3159–3168 (2006)

    Article  MathSciNet  Google Scholar 

  13. Vychodil, V.: Truth-depressing hedges and BL-logic. Fuzzy Sets Syst. 157, 2074–2090 (2006)

    Article  MathSciNet  Google Scholar 

  14. Wang, J.T., Xin, X.L., Jun, Y.B.: Very true operators on equality algebras. J. Comput. Anal. Appl. 24(3) (2018)

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, Jinan, 250022, Shandong, China

    Guoqing Yang & Wenjuan Chen

  2. College of Science and Engineering, University of Minnesota, Twin Cities, USA

    Anran Chen

Authors
  1. Guoqing Yang
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  2. Wenjuan Chen
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  3. Anran Chen
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Corresponding author

Correspondence to Wenjuan Chen .

Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, The University of Aizu, Aizu-Wakamatsu, Fukushima, Japan

    Yong Liu

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Lipo Wang

  3. Computer Science and Mathematics, University of Sao Paulo, Ribeirao Preto, Brazil

    Liang Zhao

  4. School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China

    Zhengtao Yu

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Yang, G., Chen, W., Chen, A. (2020). Very True Operators on Quasi-pseudo-MV Algebras. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_84

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