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A unified algorithm for finding \(k\)-IESFs in linguistic truth-valued lattice-valued propositional logic

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Abstract

As a symbolic approach for computing with words, linguistic truth-valued lattice-valued propositional logic \(\fancyscript{L}_{V(n\times 2)}P(X)\) can represent and handle both imprecise and incomparable linguistic value-based information. Indecomposable extremely simple form (IESF) is a basic concept of \(\alpha \)-resolution automated reasoning in lattice-valued logic based in lattice implication algebra (LIA). In this paper we establish a unified method for finding the structure of \(k\)-IESF in \(\fancyscript{L}_{V(n\times 2)}P(X)\). Firstly, some operational properties of logical formulae in \(L_6P(X)\) are studied, and some rules are obtained for judging whether a given logical formula is a \(k\)-IESF, which are used to contrive an algorithm for finding \(k\)-IESF in \(L_6P(X)\). Then, all the results are extended into \(\fancyscript{L}_{V(n\times 2)}P(X)\). Finally, a unified algorithm for finding all \(k\)-IESFs in \(\fancyscript{L}_{V(n\times 2)}P(X)\) is proposed. This work provides theoretical foundations and algorithms for \(\alpha \)-resolution automated reasoning in linguistic truth-valued lattice-valued logic based in linguistic truth-valued LIAs and formal tools for symbolic natural language processing.

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grant No. 61305074, 61175055, 61100046 and 61105059).

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Authors and Affiliations

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

    Xingxing He & Yang Xu

  2. School of Computing and Mathematics, University of Ulster, Northern Ireland, UK

    Jun Liu & Shuwei Chen

Authors
  1. Xingxing He
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  2. Yang Xu
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  3. Jun Liu
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  4. Shuwei Chen
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Correspondence to Xingxing He.

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Communicated by C.-S. Lee.

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He, X., Xu, Y., Liu, J. et al. A unified algorithm for finding \(k\)-IESFs in linguistic truth-valued lattice-valued propositional logic. Soft Comput 18, 2135–2147 (2014). https://doi.org/10.1007/s00500-013-1188-2

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