On complex fuzzy multisets

Authors

  • Idris Muhammadu Adamu
    Department of Mathematics, Federal University Dutse, P.M.B. 7156 Dutse, Jigawa State, Nigeria
  • Musa Balarabe
    Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
  • Abdussamad Tanko Imam
    Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
  • Maryam Aliyu
    Basic Science Units, Maryam Abacha American University-Kano, Nigeria
  • Yakubu Nasallah
    Department of Foundation Courses and Remedial Studies, Binyaminu Usman Polytechnic, Hadejia, Jigawa State, Nigeria

Keywords:

Fuzzy sets, Complex fuzzy sets, Multisets, Complex fuzzy multisets

Abstract

This article proposes a mathematical structure called complex fuzzy multisets (CFMSs), which integrates the multiplicity feature of fuzzy multisets with the complex-valued membership grades of complex fuzzy sets. In this framework, each membership grade is expressed as reiφ, with r ∈ [0, 1] and φ ∈ [0, 2π), enabling simultaneous representation of membership intensity, phase information, and multiple occurrences of elements. We provide a formal definition of CFMSs and establish fundamental operations, including inclusion, complement, intersection, union, Cartesian product, rotation, and reflection. The algebraic analysis proves that CFMSs satisfy involution, idempotence, commutativity, associativity, distributivity, De Morgan's laws, and absorption, thereby forming a distributive lattice with an involution. Additionally, we define the image and inverse image of CFMSs under mappings. This work lays a rigorous foundation for further theoretical development and potential applications in multi-source data fusion, periodic signal processing, and reasoning under uncertainty with repeated observations.   

Dimensions

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Table 1

Published

2026-08-31

How to Cite

On complex fuzzy multisets. (2026). African Scientific Reports, 5(3), 505. https://doi.org/10.46481/asr.2026.5.3.505

Issue

Volume 5, Issue 3, December 2026 (In progress)

Section

MATHEMATICS AND STATISTICS SECTION
Copyright & Licensing

Copyright (c) 2026 Idris Muhammadu Adamu, Musa Balarabe, Abdussamad Tanko Imam, Maryam Aliyu, Yakubu Nasallah

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On complex fuzzy multisets. (2026). African Scientific Reports, 5(3), 505. https://doi.org/10.46481/asr.2026.5.3.505

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