How can a mathematical framework represent uncertainty, repeated observations, and phase information at the same time?
This study introduces complex fuzzy multisets, a new mathematical structure that combines the multiplicity feature of fuzzy multisets with the complex-valued membership grades used in complex fuzzy sets.
In the proposed framework, each membership grade is expressed in complex form, allowing both membership intensity and phase information to be represented while also permitting multiple occurrences of the same element.
The researchers provide a formal definition of complex fuzzy multisets and develop several fundamental operations, including inclusion, complement, intersection, union, Cartesian product, rotation, and reflection.
The study also establishes important algebraic properties of the new framework.
Complex fuzzy multisets were shown to satisfy involution, idempotence, commutativity, associativity, distributivity, De Morganβs laws, and absorption.
These properties demonstrate that the proposed structure forms a distributive lattice with an involution.
The researchers further define the image and inverse image of complex fuzzy multisets under mathematical mappings.
By combining multiplicity, complex-valued membership, and phase information within a single framework, the study provides a foundation for representing more complicated forms of uncertain and repeated information.
The proposed framework may support future applications in areas such as multi-source data fusion, periodic signal processing, and reasoning under uncertainty involving repeated observations.
The authors also identify opportunities for further theoretical development and practical validation of the framework.
π Read the full article here:
https://doi.org/10.46481/asr.2026.5.3.505
Published in: African Scientific Reports