ON COMPLEX INTUITIONISTIC FUZZY MULTISETS

Abstract

This paper introduces complex intuitionistic fuzzy multisets, a novel structure that combines complex-valued membership and non-membership grades with multiset multiplicities. We provide a formal definition and establish fundamental operations, including inclusion, complement, intersection, union, and Cartesian product, with examples to show how they work. We also define the concepts of image and inverse image under mappings. The framework extends both intuitionistic fuzzy multiset and complex intuitionistic fuzzy set theories, enabling the representation of elements with multiple simultaneous complex evaluations. Finally, we prove two key properties, the involution law and De Morgan's laws, demonstrating that the new structure behaves in a mathematically consistent way.