Implicative Ideals and Fuzzy Implicative Ideals of a Distributive Implication Groupoid |
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| Authors: | Ravi Kumar BANDARU and K. P. SHUM |
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| Affiliation: | Department of Engineering Mathematics, GITAM University, Hyderabad Campus, Andhra Pradesh 502329, India;Institute of Mathematics, Yunnan University, Yunnan 650091, P. R. China |
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| Abstract: | We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient conditions for an ideal (fuzzy ideal) to be an implicative ideal (fuzzy implicative ideal) is given. By using the concept of level sets, we will characterize the fuzzy implicative ideals of a distributive implication groupoid. Finally, an extension property for fuzzy implicative ideals is given. |
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| Keywords: | implication groupoids distributive implication groupoids fuzzy ideals implicative ideals fuzzy implicative ideals. |
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