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Journal articles on the topic 'Complex fuzzy sets'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Ramot, D., R. Milo, M. Friedman, and A. Kandel. "Complex fuzzy sets." IEEE Transactions on Fuzzy Systems 10, no. 2 (2002): 171–86. http://dx.doi.org/10.1109/91.995119.

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P., Thirunavukarasu, and Suresh R. "Parameterized Soft Complex Fuzzy Sets." Journal of Progressive Research in Mathematics 4, no. 2 (2015): 303–8. https://doi.org/10.5281/zenodo.3980480.

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In this paper, we presents a new concept of parameterized soft complex fuzzy set (pscf-set) which is generalized from the innovative concept of a complex fuzzy set by adding phase term to the definition of fuzzy set. Various operators with examples of pscf-set provided in this paper. We then define a pscf-set aggregation operator.

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Dai, Songsong. "Linguistic Complex Fuzzy Sets." Axioms 12, no. 4 (2023): 328. http://dx.doi.org/10.3390/axioms12040328.

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Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this type of spatial directional information. To overcome this limitation, we first propose a novel concept called a linguistic complex fuzzy set (LCFS) to serve as an extension of the CFS. Then we put forward some basic operational laws for LCFSs. After that, we define three operators for LCFSs: the linguistic complex fuzzy weighted averaging (LCFWA) oper

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4

Dey, Asit, and Madhumangal Pal. "Multi-Fuzzy Complex Numbers and Multi-Fuzzy Complex Sets." International Journal of Fuzzy System Applications 4, no. 2 (2015): 15–27. http://dx.doi.org/10.4018/ijfsa.2015040102.

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This paper presents a method to construct more general fuzzy complex numbers and sets from ordinary fuzzy complex numbers by introduced the ordered sequences of membership functions. It is concluded that multi-fuzzy complex set is an extension of Buckley fuzzy complex set. Also, two types of multi-fuzzy complex numbers based on the forms and are investigated.

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Mu, Beining. "Fuzzy Julia Sets and Fuzzy Superior Julia Sets." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 375–80. http://dx.doi.org/10.54097/5c5hp748.

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This article examine the past study of fuzzy Mandelbrot set and fuzzy superior Mandelbrot set, then give the definition of fuzzy Julia sets and fuzzy superior Julia sets with the idea of utilizing membership functions to represent the escape velocity of Julia sets or superior Julia sets of each complex number in the definition of fuzzy Mandelbrot set and fuzzy superior Mandelbrot set inherited while the membership functions are selected to distinguish complex numbers with different escape velocity and same orbit. Then some examples of fuzzy Julia sets and fuzzy superior Julia sets are presente

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Alkouri, Abd Ulazeez, Mo'men Bany Amer, and Ibrahim Jawarneh. "Complex Bipolar Multi-Fuzzy Sets." Uncertainty 1, no. 1 (2024): 1–10. http://dx.doi.org/10.31559/uncertainty2024.1.1.1.

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Convey human being's information to a mathematical formula and vice versa by a proper tool, is considered a first step to solve the problem of assigning a membership degree (suitable value) of an object to a set by decision-makers. Different information with its periodic circumstances highlighted the need for an extra variable to be built into the mathematical tools. This extra variable adds a significant role to represent a special type of information that has the same data but with a different meaning in different time/levels/phases. However, the idea of extending the range of membership deg

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Pishtiwan O. Sabir. "Notes on Extension of Fuzzy Complex Sets." Tikrit Journal of Pure Science 22, no. 9 (2023): 88–93. http://dx.doi.org/10.25130/tjps.v22i9.880.

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The aim of this paper is to modify and improve the corresponding weakness results of multi-fuzzy complex numbers as an extension of fuzzy complex numbers, next we introduce and study the generalized multi-fuzzy complex numbers and get some results. Lastly, we discuss the derivative of functions mapping complex numbers into as an extension of fuzzy complex derivatives.

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Thirunavukarasu, Ashok Kumar, Suresh, and Lilly Merline. "EXTENDED THEORETICAL CONCEPT OF COMPLEX FUZZY SETS BY COMPLEX FUZZY SOFT HYPERGROUP, COMPLEX FUZZY SOFT HYPERRING." International Journal of Research -GRANTHAALAYAH 4, no. 7(SE) (2016): 62–69. http://dx.doi.org/10.29121/granthaalayah.v4.i7(se).2016.2629.

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In this paper, we develop the initial theory of complex fuzzy soft hypergroup by introducing the novel concept of complex fuzzy soft hypergroup, complex fuzzy soft hyperring. Consequently, a major part of this work is dedicated to extend the theory of complex fuzzy soft set, complex fuzzy hypergroup. Complex fuzzy soft quasihypergroup, complex fuzzy soft semihypergroup and complex fuzzy soft subhypergroup also discussed in this paper.

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Hu, Bo, Lvqing Bi, Songsong Dai, and Sizhao Li. "Distances of complex fuzzy sets and continuity of complex fuzzy operations." Journal of Intelligent & Fuzzy Systems 35, no. 2 (2018): 2247–55. http://dx.doi.org/10.3233/jifs-172264.

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Tamir, Dan E., and Abraham Kandel. "Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes." International Journal of Computers Communications & Control 6, no. 3 (2011): 562. http://dx.doi.org/10.15837/ijccc.2011.3.2135.

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Complex fuzzy sets, classes, and logic have an important role in applications, such as prediction of periodic events and advanced control systems, where several fuzzy variables interact with each other in a multifaceted way that cannot be represented effectively via simple fuzzy operations such as union, intersection, complement, negation, conjunction and disjunction. The initial formulation of these terms stems from the definition of complex fuzzy grade of membership. The problem, however, with these definitions are twofold: 1) the complex fuzzy membership is limited to polar representation w

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Al-Qudah, Yousef, and Nasruddin Hassan. "Operations on complex multi-fuzzy sets." Journal of Intelligent & Fuzzy Systems 33, no. 3 (2017): 1527–40. http://dx.doi.org/10.3233/jifs-162428.

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Alolaiyan, Hanan, Halimah A. Alshehri, Muhammad Haris Mateen, Dragan Pamucar та Muhammad Gulzar. "A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups". Entropy 23, № 8 (2021): 992. http://dx.doi.org/10.3390/e23080992.

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A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define α,β-complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic

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Kumar, Tanuj, and Rakesh Kumar Bajaj. "On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies." Journal of Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/972198.

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We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzz

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Imtiaz, Aneeza, Umer Shuaib, Hanan Alolaiyan, Abdul Razaq та Muhammad Gulistan. "On Structural Properties of ξ -Complex Fuzzy Sets and Their Applications". Complexity 2020 (2 грудня 2020): 1–13. http://dx.doi.org/10.1155/2020/2038724.

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Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α , δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investi

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Wattanasiripong, Nuttapong, Nuchanat Tiprachot, and Somsak Lekkoksung. "On Tripolar Complex Fuzzy Sets and Their Application in Ordered Semigroups." International Journal of Analysis and Applications 23 (June 9, 2025): 139. https://doi.org/10.28924/2291-8639-23-2025-139.

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The tripolar complex fuzzy set is a generalization of the tripolar fuzzy sets. In this paper, we introduce the notion of tripolar complex fuzzy sets in ordered semigroups. The concepts of tripolar complex fuzzy subsemigroups and tripolar complex fuzzy left (right, two-sided) ideals are introduced. Some algebraic properties of such tripolar complex fuzzy subsemigroups and their tripolar complex fuzzy ideals are studied. We characterize subsemigroup and left (resp., right, two-sided) ideals by using tripolar complex fuzzy subsemigroups and tripolar complex fuzzy left (resp., right, two-sided) id

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Xu, Yingying, Haifeng Song, Lei Du, and Songsong Dai. "Complex-Valued Migrativity of Complex Fuzzy Operations." Journal of Mathematics 2022 (April 6, 2022): 1–6. http://dx.doi.org/10.1155/2022/1813717.

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Complex fuzzy sets (CFSs), as an important extension of fuzzy sets, have been investigated in the literature. Operators of CFSs are of high importance. In addition, α − migrativity for various fuzzy operations on [0, 1] has been well discussed, where α is a real number and α ∈ 0,1 . Thus, this paper studies α − migrativity for binary functions on the unit circle of the complex plane O , where α is a complex number and α ∈ O . In particular, we show that a binary function is α − migrativity for all α ∈ O if and only if it is α − migrativity for all α ∈ 0,1 ∪ O ¯ , where O ¯ is the boundary poin

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Guo, Wenping, Lvqing Bi, Bo Hu, and Songsong Dai. "Cosine Similarity Measure of Complex Fuzzy Sets and Robustness of Complex Fuzzy Connectives." Mathematical Problems in Engineering 2020 (July 22, 2020): 1–9. http://dx.doi.org/10.1155/2020/6716819.

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Complex fuzzy set (CFS), as a generalization of fuzzy set (FS), is characterized by complex-valued membership degrees. By considering the complex-valued membership degree as a vector in the complex unit disk, we introduce the cosine similarity measures between CFSs. Then, we investigate some invariance properties of the cosine similarity measure. Finally, the cosine similarity measure is applied to measure the robustness of complex fuzzy connectives and complex fuzzy inference.

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18

Ma, Shengquan, and Shenggang Li. "Complex Fuzzy Set-Valued Complex Fuzzy Measures and Their Properties." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/493703.

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LetF*(K)be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance onF*(K), fuzzy complex number-valued measure onF*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous from above, autocontionuous from below, and autocontinuity of the defined fuzzy complex number-valued measures. Properties of fuzzy complex number-valued measures are studied in detail.

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Dai, Songsong. "Quaternionic Fuzzy Sets." Axioms 12, no. 5 (2023): 490. http://dx.doi.org/10.3390/axioms12050490.

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A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, int

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20

Luqman, Anam, Muhammad Akram, Ahmad N. Al-Kenani, and José Carlos R. Alcantud. "A Study on Hypergraph Representations of Complex Fuzzy Information." Symmetry 11, no. 11 (2019): 1381. http://dx.doi.org/10.3390/sym11111381.

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The paradigm shift prompted by Zadeh’s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representatio

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Imtiaz, Aneeza, Umer Shuaib, Abdul Razaq та Muhammad Gulistan. "Image development in the framework of ξ – complex fuzzy morphisms". Journal of Intelligent & Fuzzy Systems 40, № 3 (2021): 4425–37. http://dx.doi.org/10.3233/jifs-201261.

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The study of complex fuzzy sets defined over the meet operator (ξ – CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ – CFS and propose the notion of complex fuzzy subgroups defined over ξ – CFS (ξ – CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concept

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22

Yasin Ali, Md, and Abedul Hadi. "Correlation Coefficients of Complex Fuzzy Sets and Their Application." GANIT: Journal of Bangladesh Mathematical Society 44, no. 2 (2024): 28–38. https://doi.org/10.3329/ganit.v44i2.78530.

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Complex fuzzy set (CFS) is an extension of the fuzzy set (FS) which can deal with ambiguity by allowing a complex-valued membership degree of an element of a universal set. A host of researchers studied the complex fuzzy sets in theoretical and practical due to their amplitude term and phase term membership degrees. At present, various applications of fuzzy correlation and correlation coefficients have emerged by numerous researchers. But most of the works are related to real fuzzy data. In this article, we introduce the concept of the correlation coefficient of the complex fuzzy sets and some

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Galarza, Fredy Canizares, Marcos Lalama Flores, Diego Palma Rivero, and Mohammad Abobala. "On Weak Fuzzy Complex Pythagoras Quadruples." International Journal of Neutrosophic Science 22, no. 2 (2023): 108–13. http://dx.doi.org/10.54216/ijns.220209.

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In this work, we study the generating of Pythagoras quadruples in the sets of weak fuzzy complex integers and anti-weak fuzzy complex integers, where we present sufficient and necessary conditions for generating Pythagoras quadruples in the mentioned sets. Also, we present many examples to clarify our work's validity and novelty.

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Khalaf, Mohammed M., Sayer Obaid Alharbi, and Wathek Chammam. "Similarity Measures between Temporal Complex Intuitionistic Fuzzy Sets and Application in Pattern Recognition and Medical Diagnosis." Discrete Dynamics in Nature and Society 2019 (July 1, 2019): 1–16. http://dx.doi.org/10.1155/2019/3246439.

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This work addresses the issue of similarity measures between two temporal complex Atanassov’s intuitionistic fuzzy sets, many measures of similarity between complex Atanassov’s intuitionistic fuzzy sets. What was proposed before did not consider the abstention group influence, which may lead to counterintuitive results in some cases. A new structure of temporal complex Atanassov’s intuitionistic fuzzy sets is obtained. This set is formally generalized from a conventional Atanassov’s intuitionistic complex fuzzy sets. Here we analyze the limitations of the existing similarity measures. Then, a

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Al-Sharoa, Doaa. "(α1, 2, β1, 2)-complex intuitionistic fuzzy subgroups and its algebraic structure". AIMS Mathematics 8, № 4 (2023): 8082–116. http://dx.doi.org/10.3934/math.2023409.

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<abstract> <p>A complex intuitionistic fuzzy set is a generalization framework to characterize several applications in decision making, pattern recognition, engineering, and other fields. This set is considered more fitting and coverable to Intuitionistic Fuzzy Sets (IDS) and complex fuzzy sets. In this paper, the abstraction of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$) complex intuitionistic fuzzy sets and (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups were introduced regarding to the concept of complex intuitionistic fuzzy sets. Besides, we show that

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Balamurugan, Manivannan, Thukkaraman Ramesh, Anas Al-Masarwah, and Kholood Alsager. "A New Approach of Complex Fuzzy Ideals in BCK/BCI-Algebras." Mathematics 12, no. 10 (2024): 1583. http://dx.doi.org/10.3390/math12101583.

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The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the concept of a complex fuzzy subalgebra in a BCK/BCI-algebra and explore their properties. Furthermore, we discuss the modal and level operators of these complex fuzzy subalgebras, highlighting their importance in BCK/BCI-algebras. We study various operations, and the laws of a complex fuzzy system, including union, intersection, complement, simple

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Alharbi, Abeer Ali, and Dilshad Alghazzawi. "Some Characterizations of Certain Complex Fuzzy Subgroups." Symmetry 14, no. 9 (2022): 1812. http://dx.doi.org/10.3390/sym14091812.

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The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (ρ,η)-complex fuzzy sets, (ρ,η)-complex fuzzy subgroupoid, (ρ,η)-complex fuzzy subgroups and describe important examples of the symmetric group under (ρ,η)-complex fuzzy sets. Additionally, we discuss the conjugacy class of the group with respect to (ρ,η)-complex fuzzy normal subgroups. We define (ρ,η)-complex fuzzy cosets and elaborate upon the certain operation of this analog to group theoretic operation. We prove that factors

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Al-harshni, Ahad Abdullah, та Dilshad Alghazzawi. "Algebraic Properties of ω , θ -Complex Fuzzy Subgroups". Mathematical Problems in Engineering 2022 (29 вересня 2022): 1–8. http://dx.doi.org/10.1155/2022/1426724.

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This paper defined the notion of ω , θ -complex fuzzy sets, ω , θ -complex fuzzy subgroupoid, and ω , θ -complex fuzzy subgroups and described important examples under ω , θ -complex fuzzy sets. Additionally, we discussed the conjugacy class of group with respect to ω , θ -complex fuzzy normal subgroups. We define ω , θ -complex fuzzy cosets and elaborate the certain operation of this analog to group theoretic operation. We prove that factor group with regard to ω , θ -complex fuzzy normal subgroup forms a group and establishes an ordinary homomorphism from group to its factor group with regar

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Hu, Bo, Lvqing Bi, Songsong Dai, and Sizhao Li. "The approximate parallelity of complex fuzzy sets." Journal of Intelligent & Fuzzy Systems 35, no. 6 (2018): 6343–51. http://dx.doi.org/10.3233/jifs-181131.

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Lloret-Climent, Miguel, Sergio Pérez-Gonzaga, Josep-Lluis Usó-Doménech, and Josué-Antonio Nescolarde-Selva. "Fuzzy Structure of Complex Belief Systems: Fuzzy Relations and Fuzzy Belief Sets." Cybernetics and Systems 46, no. 6-7 (2015): 452–69. http://dx.doi.org/10.1080/01969722.2015.1038475.

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Abuhijleh, Eman A., Mourad Massa’deh, Amani Sheimat, and Abdulazeez Alkouri. "Complex Fuzzy Groups Based on Rosenfeld’s Approach." WSEAS TRANSACTIONS ON MATHEMATICS 20 (August 4, 2021): 368–77. http://dx.doi.org/10.37394/23206.2021.20.38.

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Complex fuzzy sets (CFS) generalize traditional fuzzy sets (FS) since the membership functions of CFS reduces to the membership functions of FS. FS values are always at [0, 1], unlike CFS which has values in the unit disk of C. This paper merges notion and concept in group theory and presents the notion of a complex fuzzy subgroup of a group. This proposed idea represents a more general and better optional mathematical tool as one of the approaches in the fuzzy group. However, this research defines the notion of complex fuzzy subgroupiod, complex fuzzy normal subgroup, and complex fuzzy left(r

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Ibrahim, Hariwan Z., Tareq M. Al-shami, Murad Arar, and M. Hosny. "Complex nth power root fuzzy sets: Theory, and applications for multi-attribute decision making in uncertain environments." PLOS One 20, no. 5 (2025): e0319757. https://doi.org/10.1371/journal.pone.0319757.

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The newly introduced nth power root fuzzy set is a useful tool for expressing ambiguity and vagueness. It has an improved ability to manage uncertain situations compared to intuitionistic fuzzy set and Pythagorean fuzzy set theories, making nth power root fuzzy sets applicable in various everyday decision-making contexts. The notions of nth power root fuzzy sets and complex fuzzy sets are integrated in this study to offer complex nth power root fuzzy sets (CnPR-FSs), explaining its fundamental ideas and useful applications. The proposed CnPR-FS integrates the advantages of nth power root fuzzy

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Ali, Md Yasin. "SOME TRIGONOMETRIC SIMILARITY MEASURES OF COMPLEX FUZZY SETS WITH APPLICATION." Ural Mathematical Journal 9, no. 1 (2023): 18. http://dx.doi.org/10.15826/umj.2023.1.002.

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Similarity measures of fuzzy sets are applied to compare the closeness among fuzzy sets. These measures have numerous applications in pattern recognition, image processing, texture synthesis, medical diagnosis, etc. However, in many cases of pattern recognition, digital image processing, signal processing, and so forth, the similarity measures of the fuzzy sets are not appropriate due to the presence of dual information of an object, such as amplitude term and phase term. In these cases, similarity measures of complex fuzzy sets are the most suitable for measuring proximity between objects wit

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Jun, Young Bae, and Xiao Long Xin. "Complex Fuzzy Sets with Application in BCK/BCI-Algebras." Bulletin of the Section of Logic 48, no. 3 (2019): 173–85. http://dx.doi.org/10.18778/0138-0680.48.3.02.

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As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left (right) reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image (preimage) of a complex subalgebra and a complex left (right) reduced ideal.

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Alqaraleh, Sahar M., Abd Ulazeez M. J. S. Alkouri, Mourad Oqla Massa'deh, Adeeb G. Talafha, and Anwar Bataihah. "Bipolar Complex Fuzzy Soft Sets and Their Application." International Journal of Fuzzy System Applications 11, no. 1 (2022): 1–23. http://dx.doi.org/10.4018/ijfsa.285551.

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We introduce a new computational model to solve efficient problems. This research generalizes the concept of bipolar fuzzy soft sets (BFSS) to the realm of complex numbers. However, the ranges of positive and negative values membership BFSS functions are extended to unit disk instead of [0, 1] and [-1, 0] respectively. The main benefit of bipolar complex fuzzy soft sets BCFSSs appears in the ability to transfer bipolar fuzzy soft information to a mathematical formula without losing the full meaning of information that may appear from different phases. Some basic operations and theorems on BCFS

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Ravi, Shanker Kumar. "A Mathematical Analysis of Functions Mapping Complex Numbers to Fuzzy Sets: Properties and Applications." MATHEMATICS EDUCATION LIX, no. 1, March 2025 (2025): 40–57. https://doi.org/10.5281/zenodo.15554852.

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          <em> In this study, a thorough mathematical framework for analysing  functions that translate complex numbers to fuzzy sets is presented. This framework represents a unique function of complex analysis and fuzzy set theory. These kinds of functions are naturally produced in a variety of applications, such as quantum physics, control theory, and signal processing, where there is a coexistence of uncertainty and complex-valued systems. First, we will formally define fuzzy-valued functions over the complex domain, and then we will investigate the essen

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Alkouri, Abd Ulazeez, Eman A. Abuhijleh, Eman Almuhur, Ghada Alafifi, and Sana Abu-Ghurra. "Subgroups and Homomorphism Structures of Complex Pythagorean Fuzzy Sets." WSEAS TRANSACTIONS ON MATHEMATICS 23 (October 16, 2024): 614–26. http://dx.doi.org/10.37394/23206.2024.23.65.

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This research introduces the notion of complex Pythagorean fuzzy subgroup (CPFSG). Both complex fuzzy subgroup (CFSG) and complex intuitionistic fuzzy subgroup (CIFSG) have significance in assigning membership grades in the unit disk in the complex plane. CFSG has a limitation solved by CIFSG, while CIFSG deals with a limited range of values. The important novelty of the CPFSG lies in its ability to solve the above limitations simultaneously and gets a wider range of values to be engaged in CPFSG. This work has introduced and investigated CPFSG as a new algebraic structure via the conditions t

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Mahmood, Tahir, Ubaid Ur Rehman, Abdul Jaleel, Jabbar Ahmmad, and Ronnason Chinram. "Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making." Mathematics 10, no. 7 (2022): 1048. http://dx.doi.org/10.3390/math10071048.

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This article introduces the notion of bipolar complex fuzzy soft set as a generalization of bipolar complex fuzzy set and soft set. Furthermore, this article contains elementary operations for bipolar complex fuzzy soft sets such as complement, union, intersection, extended intersection, and related properties. The OR and AND operations for bipolar complex fuzzy soft set are also initiated in this study. Moreover, this study contains the decision-making algorithm and real-life examples to display the success and usability of bipolar complex fuzzy soft sets. Finally, the comparative study of in

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Liu, Mahmood, and Ali. "Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making." Information 11, no. 1 (2019): 5. http://dx.doi.org/10.3390/info11010005.

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In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of compl

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Bi, Lvqing, Zhiqiang Zeng, Bo Hu, and Songsong Dai. "Two Classes of Entropy Measures for Complex Fuzzy Sets." Mathematics 7, no. 1 (2019): 96. http://dx.doi.org/10.3390/math7010096.

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Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.

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Alkouri, Abd Ulazeez M., and Abdul Razak Salleh. "Complex Atanassov's Intuitionistic Fuzzy Relation." Abstract and Applied Analysis 2013 (2013): 1–18. http://dx.doi.org/10.1155/2013/287382.

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This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex A

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Ali, Zeeshan. "Analysis of BCK/BCI-Algebras Based on Bipolar Complex Intuitionistic Fuzzy Soft Ideals." Neutrosophic Systems with Applications 24 (December 1, 2024): 34–50. https://doi.org/10.61356/j.nswa.2024.24419.

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In this article, we design an informative and reliable technique of bipolar complex intuitionistic fuzzy soft sets with numerous operational laws by merging the model of soft sets, complex fuzzy sets, and bipolar intuitionistic fuzzy sets to handle imprecise data. In addition, an ideal in a BCK-algebra is derived based on bipolar complex intuitionistic fuzzy soft set theory are proposed which can capture the information of hesitancy, vagueness, and non-membership information within the circumstance of BCK-algebra. Moreover, we design union, intersection, AND, and OR based on bipolar complex in

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Gulistan, Muhammad, and Salma Khan. "Extentions of neutrosophic cubic sets via complex fuzzy sets with application." Complex & Intelligent Systems 6, no. 2 (2019): 309–20. http://dx.doi.org/10.1007/s40747-019-00120-8.

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Abstract In this paper, we propose that the complex neutrosophic cubic set (internal and external) show, which is a blend of complex fuzzy sets, neutrosophic sets, and cubic sets. We characterize a few set theoretic activities of internal complex neutrosophic sets, for example, union, intersection and complement, and a while later the operational principles. A few ideas identified with the structure of this model are clarified. We present some accumulation administrators and talk about some basic leadership issue with genuine model.

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Mahmood, Tahir, Muhammad Rehan Ali, Jabbar Ahmmad, Ubaid Ur Rehman, and Muhammad Hamza Farooq. "Bi-parametric Similarity Measures for Complex Hesitant Fuzzy Sets with Applications to Pattern Recognition and Medical Diagnosis." Computer and Decision Making: An International Journal 2 (February 13, 2025): 451–81. https://doi.org/10.59543/comdem.v2i.13493.

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The complex hesitant fuzzy sets which are the extension of hesitant fuzzy sets can incorporate Tamir’s complex fuzzy environment which makes them more appropriate to model the uncertainty and vagueness involved in real-life problems. Some of the traditional similarity measures may not capture all the information contained in the hesitant fuzzy set since such measures are often simple in handling fuzzy information. This study aims to propose new similarity measures under the notion of complex hesitant fuzzy sets. Moreover, we have delivered similarity measures and weighted similarity measures f

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Farooq, Adeel, Mohammed M. Ali Al-Shamiri, Mohammed M. Khalaf, and Umaira Amjad. "Decision-Making Approach with Complex Bipolar Fuzzy N-Soft Sets." Mathematical Problems in Engineering 2022 (February 21, 2022): 1–22. http://dx.doi.org/10.1155/2022/2635568.

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The primary aim of this article is to extend the bipolar fuzzy N -soft sets with the concern of pursuing the periodicity involved real-world problems and introduce a new multiskilled hybrid model, namely, complex bipolar fuzzy N -soft sets. The novel model possesses the parametric characteristics of the versatile N -soft set and enjoys the distinguished attributes of a complex bipolar fuzzy set to handle the double-sided periodic vague data. We illustrate that the innovative model assists as a proficient mechanism for grading-based parameterized two-dimensional bipolar fuzzy information. We pr

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A., Panneerselvam, and Vinotha R. "N-FUZZY COMPLEMENT OPERATIONS ON COMPLEX NUMBER." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2018): 277–82. https://doi.org/10.5281/zenodo.1256850.

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Dai, Songsong, Lvqing Bi, and Bo Hu. "Distance Measures between the Interval-Valued Complex Fuzzy Sets." Mathematics 7, no. 6 (2019): 549. http://dx.doi.org/10.3390/math7060549.

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Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems i

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Li, Chunshien, and Tai-Wei Chiang. "Function Approximation with Complex Neuro-Fuzzy System Using Complex Fuzzy Sets – A New Approach." New Generation Computing 29, no. 3 (2011): 261–76. http://dx.doi.org/10.1007/s00354-011-0302-1.

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Jan, Naeem, Jeonghwan Gwak, Younghoon Jeon, and Bushra Akram. "Investigation of Blockchain Technology by Using the Innovative Concepts of Complex Pythagorean Fuzzy Soft Information." Complexity 2022 (November 17, 2022): 1–18. http://dx.doi.org/10.1155/2022/2274684.

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A blockchain is a valuable and proficient type of digital ledger technology that involves of expanding list of records, called blocks, that are strongly connected simultaneously using cryptography. Further, complex Pythagorean fuzzy sets (CPFSs) are the generalized form of the intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), and complex intuitionistic fuzzy sets (CIFSs), used for evaluating the awkward and unreliable information in genuine life problems. In this analysis, we aim to diagnose the innovative idea of complex Pythagorean fuzzy soft relations (CPyFSRs) by using the

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Li, Sizhao, Xinyu Han, Lvqing Bi, Bo Hu, and Songsong Dai. "Complex fuzzy aggregation operations with complex weights." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 10999–1005. http://dx.doi.org/10.3233/jifs-202100.

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Complex fuzzy aggregation operation (CFAO) is a formalized definition of combining several complex fuzzy sets into a single complex fuzzy set. It extends classical fuzzy aggregation operation (FAO) to the complex-valued domain retaining classical real-valued weight. CFAO was initially defined with complex weight by Ramot et al. However, there has been virtually no progress in developing CFAO with complex weight. In this paper, we study the CFAOs with complex weight. We first discuss how to define complex weights meeting the restriction that the sum of weights is equal to 1. We give a new natur

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