Abstract
Following Bhakat and Das [21], Dudek et. al. [47], Ma and Zhan [106] defined (∈, ∈ Vq)-fuzzy ideals in semirings. In this chapter we have studied properties of these fuzzy ideals. In Section 1, we look at (α,β)-fuzzy ideals, and show that a fuzzy left (right) ideal of a semiring is an (∈, ∈)-fuzzy left (right) ideal. Section 2 provides a characterization of (∈, ∈ Vq)-fuzzy left (right) ideals, quasi and bi-ideals of semirings. Section 3 presents characterizations of regular semirings involving these ideals and Section 4 contains characterizations of regular and intra regular semirings by these ideals. Section 5 presents a study of (∈, ∈ Vq)-fuzzy k-ideals, k-quasi-ideals and k-bi-ideals of semirings. A study of k-regular and k-intra regular semirings in this context is separately made in Sections 6 and 7.
Throughout this chapter R is a semiring with zero element.
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© 2012 Springer-Verlag GmbH Berlin Heidelberg
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Ahsan, J., Mordeson, J.N., Shabir, M. (2012). (∈, ∈ Vq)-Fuzzy Ideals in Semirings. In: Fuzzy Semirings with Applications to Automata Theory. Studies in Fuzziness and Soft Computing, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27641-5_6
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DOI: https://doi.org/10.1007/978-3-642-27641-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27640-8
Online ISBN: 978-3-642-27641-5
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