Affiliations: [a] Department of Mathematics, Abdul Wali Khan University Mardan, KP, Pakistan
| [b] Department of Electronics Engineering, University of Engineering and Technology, Taxila, Sub Campus Chakwal | [c] Department of Mathematics, Govt. College Palai Malakand, KP, Pakistan
| [d] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
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Corresponding author. Muhammad Farooq, Department of Mathematics, Abdul Wali Khan University Mardan, 23200, KP, Pakistan. Tel.: +92 345 93 33 950; E-mail: [email protected].
Abstract: Fuzzy set theory and Rough set theory are two useful mathematical tools for dealing with uncertainty and provides a general mathematical framework for dealing with uncertainty. In this paper, we introduce the notions of hyperideals of hyperquantales. The notions of (upper, lower) rough hyperideals of hyperquantales are given. Furthermore the notions of fuzzy hyperideals of hyperquantales are introduce and investigate their properties. Then, we introduce the concept of prime fuzzy hyperideals and establish relationships between these hyperideals and prime fuzzy hyperideals of hyperquantales. Finally we define rough upper (lower) fuzzy hyperideals of hyperquantales and investigate several related properties.
