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On derivations of linguistic truth-valued lattice implication algebras

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Abstract

Algebraic characters of linguistic truth-valued lattice implication algebras (L-LIAs) are focused in this paper. Concretely, the concept of derivation coming from analytic theory is introduced in L-LIAs, and then some properties of derivations are given in L-LIAs. Subsequently, some special derivations (such as isotone deri-vation, embedding derivation, isomorphism derivation and regular derivation) are discussed in L-LIAs along with the relations among them. The relations between derivations and lattice implication homomorphisms are also investigated in L-LIAs. At the end, the derivations of some algebraic substructures are described in L-LIAs.

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Acknowledgments

This work is partially supported by the Natural Science Foundation of China (Grant Nos. 61175055, 61100046 and 61305074), the Science and Technology Research Project of the Education Department of Henan Province (Grant No. 13B110383), the Application basic research plan project of Sichuan Province (No. 2015JY0120) and the Scientific Research Fund of Sichuan Provincial Education Department (14ZA0245 and 15ZB0270). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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Authors and Affiliations

  1. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Hua Zhu & Yang Xu

  2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, People’s Republic of China

    Hua Zhu

  3. College of Mathematics and Information Sciences, Neijiang Normal University, Neijiang, 641000, Sichuan, People’s Republic of China

    Yi Liu

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  1. Hua Zhu
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  2. Yi Liu
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  3. Yang Xu
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Correspondence to Hua Zhu.

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Zhu, H., Liu, Y. & Xu, Y. On derivations of linguistic truth-valued lattice implication algebras. Int. J. Mach. Learn. & Cyber. 9, 611–620 (2018). https://doi.org/10.1007/s13042-016-0551-x

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