Abstract
Theories of fuzzy set and rough set are powerful mathematical tools for modelling various types of uncertainty. In this paper, we introduce the notions of bi-hyperideal, fuzzy bi-hyperideals of hyperquantales and their related properties is given. Furthermore we introduce the notion of generalized rough fuzzy bi-hyperideals. Moreover, we will describe the set-valued homomorphism and strong set-valued homomorphism of hyperquantales and some related properties will be study.
Highlights
The theory of rough sets was introduced by Pawlak [15,16], to deal with uncertain knowledge in information systems
Fuzzy bi-hyperideal of hyperquantale we introduce the notion of fuzzy bi-hyperideal of hyperquantale and investigate some related properties
Let F be a strong set-valued homomorphism and let f be a fuzzy bi-hyperideal of Q2
Summary
The theory of rough sets was introduced by Pawlak [15,16], to deal with uncertain knowledge in information systems. The theory of fuzzy sets has been developed fast and has many applications in many branches of sciences. Luo and Wang in [25], studied roughness and fuzziness in quantales. Davvaz et al in [6] applied Atanassov’s intuitionistic fuzzy set theory to quantales. In [29, 30], Saqib and Shabir studied relationship between generalized rough sets and quantale by using fuzzy ideals of quantale. In [26], Khan et al introduced the notions of hyperideals and fuzzy hyperideals of hyperquantales. We will introduce the notions of generalized rough fuzzy bi-hyperideal in hyperquantales and some new properties will be obtain
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