| Summary: | The concept of fuzzy multiset is well established in dealing with many real life problems. It is possible to find various applications of algebraic hypercompositional structures in natural, technical and social sciences, where symmetry, or the lack of symmetry, is clearly specified and laid out. In this paper, we use fuzzy multisets to introduce the concept of fuzzy multi-<inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>v</mi> </msub> </semantics> </math> </inline-formula>-ideals as a generalization of fuzzy <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>v</mi> </msub> </semantics> </math> </inline-formula>-ideals. Moreover, we introduce the concept of generalized fuzzy multi-<inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>v</mi> </msub> </semantics> </math> </inline-formula>-ideals as a generalization of generalized fuzzy <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>v</mi> </msub> </semantics> </math> </inline-formula>-ideals. Finally, we investigate the properties of these new concepts and present different examples.
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