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The characterization of Γ-modules in terms of fuzzy soft Γ-submodules

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Abstract

In this paper, we focus on combining the theories of fuzzy soft sets with Γ-modules, and establishing a new framework for fuzzy soft Γ-submodules. The main contributions of the paper are 3-fold. First, we present the concepts of (R, S)-bi-Γ-submodules, quasi-Γ-submodules and regular Γ-modules. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in this paper. Second, several new kinds of generalized fuzzy soft Γ-submodules are proposed, and related properties and mutual relationships are also investigated. Third, we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules, and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Min Zhou

  2. Department of Mathematics, Hubei University for Nationalities, Enshi, 445000, China

    Da-jing Xiang & Jian-ming Zhan

Authors
  1. Min Zhou
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  2. Da-jing Xiang
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  3. Jian-ming Zhan
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Correspondence to Jian-ming Zhan.

Additional information

Supported by the National Natural Science Foundation of China (61175055), the Innovation Term of Higher Education of Hubei Province, China (T201109), the Natural Science Foundation of Hubei Province (2012FFB01101) and the Natural Science Foundation of Education Committee of Hubei Province (D20131903).

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Zhou, M., Xiang, Dj. & Zhan, Jm. The characterization of Γ-modules in terms of fuzzy soft Γ-submodules. Appl. Math. J. Chin. Univ. 28, 217–239 (2013). https://doi.org/10.1007/s11766-013-2923-2

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  • DOI: https://doi.org/10.1007/s11766-013-2923-2

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