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Interval valued L-fuzzy cosets of nearrings and isomorphism theorems

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Abstract

In this paper, we study homomorphic images of interval valued L-fuzzy ideals of a nearring. If \(f:N_1\rightarrow N_2\) is an onto nearring homomorphism and \(\hat{\mu }\) is an interval valued L-fuzzy ideal of \(N_2\) then we prove that \(f^{-1}(\hat{\mu })\) is an interval valued L-fuzzy ideal of \(N_1\). If \(\hat{\mu }\) is an interval valued L-fuzzy ideal of \(N_1\) then we show that \(f(\hat{\mu })\) is an interval valued L-fuzzy ideal of \(N_2\) whenever \(\hat{\mu }\) is invariant under \(f\) and interval valued t-norm is idempotent. Finally, we define interval valued L-fuzzy cosets and prove isomorphism theorems.

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Acknowledgments

We thank the anonymous referees and the editor for their constructive comments and suggestions which has improved the paper. All authors acknowledge Manipal University for the encouragement. The second author acknowledges St. Joseph Engineering College, Mangalore, India for the encouragement.

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Authors and Affiliations

  1. Department of Mathematics, Manipal Institute of Technology, Manipal University, Manipal, Karnataka, 576104, India

    Syam Prasad Kuncham, B. Jagadeesha & Babushri Srinivas Kedukodi

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  1. Syam Prasad Kuncham
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  2. B. Jagadeesha
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  3. Babushri Srinivas Kedukodi
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Correspondence to Babushri Srinivas Kedukodi.

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Kuncham, S.P., Jagadeesha, B. & Kedukodi, B.S. Interval valued L-fuzzy cosets of nearrings and isomorphism theorems. Afr. Mat. 27, 393–408 (2016). https://doi.org/10.1007/s13370-015-0348-1

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