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- W2896250702 abstract "In this paper, we introduce the concepts of upper and lower rough hyper fuzzy ideals (filters) in a hyperlattice and their basic properties are discussed. Let $theta$ be a hyper congruence relation on $L$. We show that if $mu$ is a fuzzy subset of $L$, then $overline{theta}( )=overline{theta}( )$ and $overline{theta}(mu^*) =overline{theta}((overline{theta}(mu))^*)$, where $ $ is the least hyper fuzzy ideal of $L$ containing $mu$ and $$mu^*(x) = sup{alpha in [0, 1]: x in I( mu_{alpha} )}$$ for all $x in L$. Next, we prove that if $mu $ is a hyper fuzzy ideal of $L$, then $mu$ is an upper rough fuzzy ideal. Also, if $theta$ is a $wedge-$complete on $L$ and $mu $ is a hyper fuzzy prime ideal of $L$ such that $overline{theta}(mu)$ is a proper fuzzy subset of $L$, then $mu$ is an upper rough fuzzy prime ideal. Furthermore, let $theta$ be a $vee$-complete congruence relation on $L$. If $mu $ is a hyper fuzzy ideal, then $mu$ is a lower rough fuzzy ideal and if $mu $ is a hyper fuzzy prime ideal such that $underline{theta}(mu)$ is a proper fuzzy subset of $L$, then $mu$ is a lower rough fuzzy prime ideal." @default.
- W2896250702 created "2018-10-26" @default.
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- W2896250702 date "2018-07-07" @default.
- W2896250702 modified "2023-09-22" @default.
- W2896250702 title "On Rough Sets and Hyperlattices" @default.
- W2896250702 doi "https://doi.org/10.23755/rm.v34i0.350" @default.
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