Complex fuzzy sets with applications in signals

Ma, Xueling; Zhan, Jianming; Khan, Madad; Zeeshan, Muhammad; Anis, Saima; Awan, Abdul Sami

doi:10.1007/s40314-019-0925-2

Cited by 30 publications

(13 citation statements)

References 23 publications

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“…Hu et al [18] introduced the orthogonality relation of complex fuzzy sets and discussed its applications in signals and systems. Ma et al [30] proposed an algorithm based on complex fuzzy sets for the identi…cation of a high degree of resemblance with the reference signal. Zeeshan et al [55] proposed a distance function of complex fuzzy soft sets and applied it to signal processing.…”

Section: Introductionmentioning

confidence: 99%

Denoising Data in Signal Processing under the Complex Fuzzy Environment

Khan

Rehman

Anis

et al. 2022

Preprint

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In this paper, we have established some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we introduced the basic results of complex fuzzy sets with their examples such as complex fuzzy union, complex fuzzy intersection, complex fuzzy complement, complex fuzzy Cartesian product, complex fuzzy bounded sum, complex fuzzy bounded difference, complex fuzzy algebraic sum, and complex fuzzy algebraic product. We established a new algorithm for the application of a complex fuzzy set in denoising data. We employed CFSs in data denoising using Fast Fourier transform since the phase term of CFS is periodic and performs like a Fast Fourier transform. We introduced a novel methodology for exploiting a CFS to develop a new model of the matrix, in which we identified a reference signal and removed noise from a specific signal.

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Section: Introductionmentioning

confidence: 99%

Denoising Data in Signal Processing under the Complex Fuzzy Environment

Khan

Rehman

Anis

et al. 2022

Preprint

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“…The notion of complex dual hesitant FS was presented by Ur Rehman et al [43]. Ma et al [44] interpreted CFS with applications in signals.…”

Section: Introductionmentioning

confidence: 99%

Bipolar Complex Fuzzy Hamacher Aggregation Operators and Their Applications in Multi-Attribute Decision Making

et al. 2021

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On the basis of Hamacher operations, in this manuscript, we interpret bipolar complex fuzzy Hamacher weighted average (BCFHWA) operator, bipolar complex fuzzy Hamacher ordered weighted average (BCFHOWA) operator, bipolar complex fuzzy Hamacher hybrid average (BCFHHA) operator, bipolar complex fuzzy Hamacher weighted geometric (BCFHWG) operator, bipolar complex fuzzy Hamacher ordered weighted geometric (BCFHOWG) operator, and bipolar complex fuzzy Hamacher hybrid geometric (BCFHHG) operator. We present the features and particular cases of the above-mentioned operators. Subsequently, we use these operators for methods that can resolve bipolar complex fuzzy multiple attribute decision making (MADM) issues. We provide a numerical example to authenticate the interpreted methods. In the end, we compare our approach with existing methods in order to show its effectiveness and practicality.

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“…The CFS is characterized by a complex-valued function, i.e., (r k )e i2π(ξ (r k )) and satisfied the condition: 0 ≤ (r k ), ξ (r k ) ≤ 1. The notion related to CFSs was also proposed in [52,53]. As mentioned above, though the CFSs have many advantages, however, there are some situations where it is difficult or impossible to solve the issue by using only complex-valued membership function.…”

Section: Introductionmentioning

confidence: 99%

Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications

Kamacı

2021

Complex Intell. Syst.

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In this paper, the concept of complex linear Diophantine fuzzy set (CLDFS), which is obtained by integrating the phase term into the structure of the linear Diophantine fuzzy set (LDFS) and thus is an extension of LDFS, is introduced. In other words, the ranges of grades of membership, non-membership, and reference parameters in the structure of LDFS are extended from the interval [0, 1] to unit circle in the complex plane. Besides, this set approach is proposed to remove the conditions associated with the grades of complex-valued membership and complex-valued non-membership in the framework of complex intuitionistic fuzzy set (CIFS), complex Pythagorean fuzzy set (CPyFS), and complex q-rung orthopair fuzzy set (Cq-ROFS). It is proved that each of CIFS, CPyFS, and Cq-ROFS is a CLDFS, but not vice versa. In addition, some operations and relations on CLDFSs are derived and their fundamental properties are investigated. The intuitive definitions of cosine similarity measure (CSM) and cosine distance measure (CDM) between two CLDFSs are introduced and their characteristic principles are examined. An approach based on CSM is proposed to tackle medical diagnosis issues and its performance is tested by dealing with numerical examples. Finally, a comparative study of the proposed approach with several existing approaches is created and its advantages are discussed.

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Complex fuzzy sets with applications in signals

Cited by 30 publications

References 23 publications

Denoising Data in Signal Processing under the Complex Fuzzy Environment

Denoising Data in Signal Processing under the Complex Fuzzy Environment

Bipolar Complex Fuzzy Hamacher Aggregation Operators and Their Applications in Multi-Attribute Decision Making

Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications

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