Generated Fuzzy Ideals in Semirings
Keywords:
Semirings; arbitrary intersection; level subsets; strong level subsets; generated fuzzy ideals.Abstract
This study offers a comprehensive characterization of fuzzy left ideals, fuzzy right ideals, fuzzy ideals, fuzzy bi-ideals, fuzzy interior ideals, and fuzzy quasi-ideals within the context of semirings. These fuzzy structures are analyzed using level subsets and strong level subsets. Additionally, we introduce the generated fuzzy left ideal, fuzzy right ideal, fuzzy ideal, fuzzy bi-ideal, fuzzy interior ideal, and fuzzy quasi-ideals by a fuzzy set in semirings, with or without a multiplicative identity. Furthermore, the work presents an expression for generating fuzzy left ideal, fuzzy right ideal, fuzzy ideal, fuzzy bi-ideal, fuzzy interior ideal, and fuzzy quasi-ideals in terms of left ideal, right ideal, ideal, bi-ideal, interior ideal, and quasi-ideal generated by level subsets and strong level subsets of the given fuzzy set.
References
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J. S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science. Addison-Wesley Longman Ltd (1992).
