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Journal articles on the topic 'Intuitionistic Fuzzy Ideal'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Alhaleem, Nour Abed, and Abd Ghafur Ahmad. "Intuitionistic fuzzy normed prime and maximal ideals." AIMS Mathematics 6, no. 10 (2021): 10565–80. http://dx.doi.org/10.3934/math.2021613.

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<abstract><p>Motivated by the new notion of intuitionistic fuzzy normed ideal, we present and investigate some associated properties of intuitionistic fuzzy normed ideals. We describe the intrinsic product of any two intuitionistic fuzzy normed subsets and show that the intrinsic product of intuitionistic fuzzy normed ideals is a subset of the intersection of these ideals. We specify the notions of intuitionistic fuzzy normed prime ideal and intuitionistic fuzzy normed maximal ideal, we present the conditions under which a given intuitionistic fuzzy normed ideal is considered to be

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2

Derseh, Beza Lamesgin, Berhanu Assaye Alaba, and Yohannes Gedamu Wondifraw. "t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra." International Journal of Mathematics and Mathematical Sciences 2022 (September 23, 2022): 1–13. http://dx.doi.org/10.1155/2022/5101293.

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In this article, we apply the concept of a t -intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the t -intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a t -intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a t -intuitionistic fuzzy PMS-ideal is provided. The t -intui

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3

G., Muhiuddin A. Mahboob and M. Balamurugan. "Hesitant anti-intuitionistic fuzzy soft commutative ideals of BCK-algebras." Annals of Communications in Mathematics 3, no. 2 (2020): 158–70. https://doi.org/10.5281/zenodo.10044331.

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In this paper, the notions of hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals of BCI-algebras and hesitant anti-intuitionistic fuzzy soft subcommutative ideals of BCK-algebras are introduced and their related properties are investigate. Relations between a hesitant anti-intuitionistic fuzzy soft ideals and hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals are discussed. Conditions for a hesitant anti-intuitionistic fuzzy soft ideal to be a hesitant anti-intuitionistic fuzzy soft BCIcommutative ideal are provided. Finally, it is proved that a hesitant anti-intuitioni

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4

Lee, Jeong-Gon, Mohammad Fozouni, Kul Hur, and Young Bae Jun. "A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets." Mathematics 8, no. 6 (2020): 993. http://dx.doi.org/10.3390/math8060993.

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In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar

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5

Sharma, Poonam Kumar. "Generalizations of prime intuitionistic fuzzy ideals of a lattice." Notes on Intuitionistic Fuzzy Sets 30, no. 1 (2024): 26–55. http://dx.doi.org/10.7546/nifs.2024.30.1.26-55.

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As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.

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6

Jun, Young, Eun Roh, and Mehmet Öztürk. "Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows." Mathematics 6, no. 9 (2018): 149. http://dx.doi.org/10.3390/math6090149.

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The concepts of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are introduced, and several properties are investigated. Characterizations of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are obtained, and relations between a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and an intuitionistic fuzzy ideal are discussed. Conditions for an intuitionistic fuzzy ideal to be a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are provided, and relations between a positive implicative ( ∈ , ∈)-intu

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7

Abed Alhaleem, Nour, and Abd Ghafur Ahmad. "Intuitionistic anti fuzzy normed ideals." Notes on Intuitionistic Fuzzy Sets 27, no. 1 (2021): 60–71. http://dx.doi.org/10.7546/nifs.2021.27.1.60-71.

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In this paper, we introduce the notion of intuitionistic anti fuzzy normed subrings and intuitionistic anti fuzzy normed ideals and various properties of intuitionistic anti fuzzy normal subrings and ideals are examined. Also, we prove that the intersection of two intuitionistic anti fuzzy normed ideals is also an intuitionistic anti fuzzy normed ideal. Besides, we define the anti level subsets and identify the relationship between these sets and intuitionistic anti fuzzy normed ideals. In addition, we define the anti-image of intuitionistic anti fuzzy normed ideals and discuss the inverse ima

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8

A. Ibrahim and C. Shajitha Begum. "Intuitionistic Fuzzy WI-Ideals of Lattice Wajsberg Algebras." International Journal of Fuzzy Mathematical Archive 15, no. 01 (2018): 07–17. http://dx.doi.org/10.22457/ijfma.v15n1a2.

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In the present paper, we introduce the notions of intuitionistic fuzzy WI-ideal and intuitionistic fuzzy lattice ideal of lattice Wajsberg algebras. We show that every intuitionistic fuzzy WI-ideal of lattice Wajsberg algebra is an intuitionistic fuzzy lattice ideal of lattice Wajsberg algebra. Also, we discuss its converse part. Further, we obtain every intuitionistic fuzzy lattice ideal is an intuitionistic fuzzy WI-ideal in lattice H-Wajsberg algebra. Moreover, we discuss some characterizations of intuitionistic fuzzy WI-ideal.

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9

Dr. M.Palanivelrajan, Dr M. Palanivelrajan, and S. Nandakumar S.Nandakumar. "Intuitionistic Fuzzy Primary And Semiprimary Ideal." Indian Journal of Applied Research 1, no. 5 (2011): 159–60. http://dx.doi.org/10.15373/2249555x/feb2012/59.

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10

Xin, Xiaolong, Rajab Borzooei, Mahmood Bakhshi, and Young Jun. "Intuitionistic Fuzzy Soft Hyper BCK Algebras." Symmetry 11, no. 3 (2019): 399. http://dx.doi.org/10.3390/sym11030399.

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Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision-making problem. Maji et al. also introduced the notion of intuitionistic fuzzy soft sets in the paper [P.K. Maji, R. Biswas and A.R. Roy, Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9 (2001), no. 3, 677–692]. The aim of this manuscript is to apply the notion of intuitionistic fuzzy soft set to hyper BCK algebras. The notions of intuitionistic fuzzy soft hyper BCK ideal, intuitionistic fuzzy soft weak hyper BCK i

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11

Balamurugan, Manivannan, Nazek Alessa, Karuppusamy Loganathan, and M. Sudheer Kumar. "Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making." Mathematics 11, no. 21 (2023): 4471. http://dx.doi.org/10.3390/math11214471.

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In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fu

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12

Sivakaminathan, S., B. Vasudevan та K. Gunasekaran. "Bipolar Intuitionistic Anti Fuzzy 𝛼-Ideal of A BP-Algebra". Indian Journal Of Science And Technology 18, № 6 (2025): 443–51. https://doi.org/10.17485/ijst/v18i6.3792.

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Objectives: The focus of this article is to present the idea of employing complement, union, and intersection and examine these fundamental operations in both bipolar intuitionistic anti fuzzy (BIAF) ideals. We investigate the conditions of BIAF ideal and BIAF α-ideal of a BP-algebra in this research work. Comparing the fuzzy set to a bipolar intuitionistic fuzzy set revealed a definite result. Therefore, the concept of bipolar intuitionistic fuzzy set was defined as a combination of intuitionistic fuzzy set and bipolar fuzzy set. It provides useful outcomes for problem analysis. Methods: We p

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13

Muhammad, Wedad Salman, Nada A. Laabi, and Asmaa Ali Zeyad. "On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces." European Journal of Theoretical and Applied Sciences 2, no. 1 (2024): 851–62. http://dx.doi.org/10.59324/ejtas.2024.2(1).75.

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The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intui

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14

Wedad, Salman Muhammad, A. Laabi Nada, and Ali Zeyad Asmaa. "On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces." European Journal of Theoretical and Applied Sciences 2, no. 1 (2024): 851–62. https://doi.org/10.59324/ejtas.2024.2(1).75.

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The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intui

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15

Sivakaminathan, S., K. Gunasekaran, and S. Nandakumar. "SOME OPERATIONS ON BIPOLAR INTUITIONISTIC FUZZY IDEAL AND BIPOLAR INTUITIONISTIC ANTI FUZZY IDEAL OF A BP-ALGEBRA." South East Asian J. of Mathematics and Mathematical Sciences 18, no. 02 (2022): 429–42. http://dx.doi.org/10.56827/seajmms.2022.1802.35.

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The concept of a bipolar intuitionistic fuzzy ideal and bipolar intuitionistic anti fuzzy ideal are a new algebraic structure of BP-algebra and to use necessity and possibility operator. The purpose of this study is to implement the fuzzy set theory and ideal theory of a BP-algebra. The relation between the operation on bipolar intuitionistic fuzzy ideal and bipolar intuitionistic anti fuzzy ideal are established.

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16

Ramesh, D., B. Satyanarayana, and N. Srimannarayana. "Direct Product of Finite Interval-Valued Intuitionistic Fuzzy Ideals in BF-Algebra." International Journal of Engineering & Technology 7, no. 3.34 (2018): 631. http://dx.doi.org/10.14419/ijet.v7i3.34.19404.

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The present paper gives direct product of finite interval-valued intuitionistic fuzzy ideals. Furthermore, we add more useful results and also prove that, let be interval-valued intuitionistic fuzzy ideal of BF-algebra X. If and for any, then is an interval-valued intuitionistic fuzzy H-ideal of BF-algebra X.

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17

XU, ZESHUI, and HUI HU. "PROJECTION MODELS FOR INTUITIONISTIC FUZZY MULTIPLE ATTRIBUTE DECISION MAKING." International Journal of Information Technology & Decision Making 09, no. 02 (2010): 267–80. http://dx.doi.org/10.1142/s0219622010003816.

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The aim of this paper is to investigate the intuitionistic fuzzy multiple attribute decision-making problems where the attribute values are expressed in intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers. We introduce some notions, such as intuitionistic fuzzy ideal point, interval-valued intuitionistic fuzzy ideal point, the modules of intuitionistic fuzzy numbers, and interval-valued intuitionistic fuzzy numbers. We also introduce the cosine of the included angle between the attribute value vectors of each alternative and the intuitionistic fuzzy ideal point, and th

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18

Kim, Kyung Ho, and Young Bae Jun. "Intuitionistic fuzzy interior ideals of semigroups." International Journal of Mathematics and Mathematical Sciences 27, no. 5 (2001): 261–67. http://dx.doi.org/10.1155/s0161171201010778.

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We consider the intuitionistic fuzzification of the concept of interior ideals in a semigroupS, and investigate some properties of such ideals. For any homomorphismffrom a semigroupSto a semigroupT, ifB=(μB,γB)is an intuitionistic fuzzy interior ideal ofT, then the preimagef−1(B)=(f−1(μB),f−1(γB))ofBunderfis an intuitionistic fuzzy interior ideal ofS.

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19

Saikia, Pradip, and Helen K. Saikia. "Intuitionistic Fuzzy N-subgroup and Intuitionistic Fuzzy Ideal." International Journal of Mathematics Trends and Technology 57, no. 6 (2018): 418–21. http://dx.doi.org/10.14445/22315373/ijmtt-v57p557.

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20

Elnair, Mohamed. "More Results on Intuitionistic Fuzzy Ideals of BE-algebras." European Journal of Pure and Applied Mathematics 17, no. 1 (2024): 426–34. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.5030.

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This paper explores the intuitionistic fuzzy ideals in BE-algebras and establishes several new results related to their structure. We investigate the fundamental concepts and properties of intuitionistic fuzzy ideals and provide characterizations of an intuitionistic fuzzy ideal in BE-algebras. Our study focuses on examining the fundamental concepts and properties of these ideals and provides characterizations of intuitionistic fuzzy ideals in BE-algebras.

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21

S, Sivakaminathan, Vasudevan B та Gunasekaran K. "Bipolar Intuitionistic Anti Fuzzy 𝛼-Ideal of A BP-Algebra". Indian Journal of Science and Technology 18, № 6 (2025): 443–51. https://doi.org/10.17485/IJST/v18i6.3792.

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<strong>Objectives:</strong> The focus of this article is to present the idea of employing complement, union, and intersection and examine these fundamental operations in both bipolar intuitionistic anti fuzzy (BIAF) ideals. We investigate the conditions of BIAF ideal and BIAF α-ideal of a BP-algebra in this research work. Comparing the fuzzy set to a bipolar intuitionistic fuzzy set revealed a definite result. Therefore, the concept of bipolar intuitionistic fuzzy set was defined as a combination of intuitionistic fuzzy set and bipolar fuzzy set. It provides useful outcomes for pro

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22

SHARMA, P. K., HEM LATA, and NITIN BHARADWAJ. "Intuitionistic Fuzzy Prime Radical and Intuitionistic Fuzzy Primary Ideal Of $\Gamma$-Ring." Creative Mathematics and Informatics 32, no. 1 (2022): 69–86. http://dx.doi.org/10.37193/cmi.2023.01.08.

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In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in $\Gamma$-rings. We also characterise intuitionistic fuzzy primary ideal of $\Gamma$-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of $\Gamma$-rings.

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23

Amigo, Royyan, Noor Hidayat, and Vira Hari Krisnawati. "Multipolar Intuitionistic Fuzzy Ideal in B-Algebras." CAUCHY 7, no. 2 (2022): 293–301. http://dx.doi.org/10.18860/ca.v7i2.14003.

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In this paper, we study with the definition of B-algebras, commutative B-algebras and fuzzy ideal in B-algebras. We consider the terminology of multipolar intuitionistic fuzzy ideal. We propose about multipolar intuitionistic fuzzy ideal in B-algebras and some related properties. Then, we discuss about theorems and propositions which contain some conditions for a multipolar intuitionistic fuzzy set become a multipolar intuitionistic fuzzy ideal in B-algebras.

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24

Abdul-Ghani, Samaher Adnan, Shuker Mahmood Khalil, Mayadah Abd Ulrazaq, and Abu Firas Muhammad Jawad Al-Musawi. "New Branch of Intuitionistic Fuzzification in Algebras with Their Applications." International Journal of Mathematics and Mathematical Sciences 2018 (July 10, 2018): 1–6. http://dx.doi.org/10.1155/2018/5712676.

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The intuitionistic fuzzification in ρ-algebras about the concepts of ideals and subalgebras given with several related characterizations is considered. Some new concepts like intuitionistic fuzzy ρ-ideal (IFρi), intuitionistic fuzzy ρ-subalgebra (IFρs), ρ-homomorphism, and intuitionistic fuzzy ρ¯-ideal (IFρ¯i) are introduced and some of their descriptions are given in this work. Further, we show some applications on the family of all intuitionistic fuzzy ρ-subalgebras IFρS(R) in ρ-algebra like the binary relations ≈μ, ≈ν and Γr on IFρS(R). Also, their equivalence classes are given and studied.

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25

Thomas, K. V., and Latha S. Nair. "Quotient of Ideals of an Intuitionistic Fuzzy Lattice." Advances in Fuzzy Systems 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/781672.

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The concept of intuitionistic fuzzy ideal of an intuitionistic fuzzy lattice is introduced, and its certain characterizations are provided. We defined the quotient (or residual) of ideals of an intuitionistic fuzzy sublattice and studied their properties.

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26

R. G. Keerthana , K. R. Sobha. "Intuitionistic Fuzzy Magnified Translation of Intuitionistic Weak Fuzzy d-Ideals of d-Subalgebra." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 2645–49. http://dx.doi.org/10.52783/tjjpt.v44.i4.1331.

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In this paper, we discuss intuitionistic fuzzy magnified translation of intuitionistic weak fuzzy d-ideals of d-subalgebra. Here we also investigate about some of its properties in detail by using the concepts of intuitionistic weak fuzzy d-ideal.

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27

Oner, Tahsin, Hashem Bordbar, Neelamegarajan Rajesh, and Akbar Rezaei. "SBE-Algebras via Intuitionistic Fuzzy Structures." Mathematics 12, no. 24 (2024): 4038. https://doi.org/10.3390/math12244038.

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The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understanding the behavior of intuitionistic fuzzy logic in this algebraic structure. The study further establishes a bidirectional relationship between subalgebras, ideals, filters, and their respective level sets on Sheffer stroke BE-algebras, demonstrating that the level set of an intuitionistic fuzzy SBE-subalgebra, ideal, or filter is itself a subalgeb

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28

Mandal, Debabrata. "A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings." International Journal of Fuzzy System Applications 10, no. 3 (2021): 1–17. http://dx.doi.org/10.4018/ijfsa.2021070101.

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The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and ca

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29

Muhiuddin, G., D. Al-Kadi, K. P. Shum, and A. M. Alanazi. "Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory." Advances in Fuzzy Systems 2021 (January 23, 2021): 1–10. http://dx.doi.org/10.1155/2021/8869931.

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In the present paper, using Lukaswize triple-valued logic, we introduce the notion of α , β -intuitionistic fuzzy soft ideal of BCK / BCI -algebras, where α and β are the membership values between an intuitionistic fuzzy soft point and intuitionistic fuzzy set. Moreover, intuitionistic fuzzy soft ideals with thresholds are introduced, and their related properties are investigated.

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30

Amigo, Royyan, Noor Hidayat, and Vira Hari Krisnawati. "Multipolar Intuitionistic Fuzzy Positive Implicative Ideal in B-Algebras." CAUCHY: Jurnal Matematika Murni dan Aplikasi 9, no. 1 (2024): 26–35. http://dx.doi.org/10.18860/ca.v9i1.23164.

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In this paper, we start with the concept of B-algebras, commutative B-algebras and fuzzy ideal in B-algebras. We also study about multipolar intuitionistic fuzzy ideal. We explain the notion of multipolar intuitionistic fuzzy positive implicative ideal in B-algebras and some characterizes. In addition, we examine some theorems and proportions which contain the conditions for a multipolar intuitionistic fuzzy set become a multipolar intuitionistic fuzzy positive implicative ideal in B-algebras. One of the result is a multipolar intuitionistic fuzzy set (l,s) over commutative B-algebra X is a mu

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31

Kang, Kyung Tae, Seok-Zun Song, and Young Bae Jun. "Multipolar Intuitionistic Fuzzy Set with Finite Degree and Its Application in BCK/BCI-Algebras." Mathematics 8, no. 2 (2020): 177. http://dx.doi.org/10.3390/math8020177.

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When events occur in everyday life, it is sometimes advantageous to approach them in two directions to find a solution for them. As a mathematical tool to handle these things, we can consider the intuitionistic fuzzy set. However, when events are complex and the key to a solution cannot be easily found, we feel the need to approach them for hours and from various directions. As mathematicians, we wish we had the mathematical tools that apply to these processes. If these mathematical tools were developed, we would be able to apply them to algebra, topology, graph theory, etc., from a close poin

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Saleem, Kholoud W., Abir K. Salib, and Abrahim A. A.Tentush. "SEMIGROUPS IN TERMS OF INTUITIONISTIC FUZZY BI-IDEALS." EPH - International Journal of Applied Science 7, no. 1 (2021): 23–30. http://dx.doi.org/10.53555/eijas.v7i1.73.

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Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play a

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Seo, Young Joo, Hee Sik Kim, Young Bae Jun, and Sun Shin Ahn. "Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras." Mathematics 8, no. 8 (2020): 1373. http://dx.doi.org/10.3390/math8081373.

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In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzz

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Hidayahningrum, Syafitri, Noor Hidayat та Marjono Marjono. "An η-Intuitionistic Fuzzy Rings Structure". JTAM (Jurnal Teori dan Aplikasi Matematika) 7, № 1 (2023): 231. http://dx.doi.org/10.31764/jtam.v7i1.11833.

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In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the

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35

Davvaz, Bijan, and Wieslaw A. Dudek. "Intuitionistic fuzzyHv-ideals." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–11. http://dx.doi.org/10.1155/ijmms/2006/65921.

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The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we apply the concept of intuitionistic fuzzy sets toHv-rings. We introduce the notion of an intuitionistic fuzzyHv-ideal of anHv-ring and then some related properties are investigated. We state some characterizations of intuitionistic fuzzyHv-ideals. Also we investigate some natural equivalence relations on the set of all intuitionistic fuzzyHv-ideals of anHv-ring.

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Lata, Hem, та P. K. Sharma. "On the translational invariant intuitionistic fuzzy subset of a Γ-ring". Notes on Intuitionistic Fuzzy Sets 28, № 1 (2022): 11–22. http://dx.doi.org/10.7546/nifs.2022.28.1.11-22.

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In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we p

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37

Macodi, Amila, and Archie G. Dorig. "On Intuitionistic Fuzzy Implicative Hyper GR-ideals." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 2221–34. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5344.

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The influx of researches on hyperstructure theory has encouraged many researchers to introduce new algebras. Notable among these is the work of Indangan and Petalcorin who introduced hyper GR-algebra and that of Macodi and Petalcorin who studied fuzzification of hyper GR-algebra. Macodi extended the fuzzification of hyper GR-algebra into intuitionistic fuzzification and introduced the concept of an intuitionistic fuzzy hyper GR-ideal. Following the works of Macodi and Petalcorin, this paper established an intuitionistic fuzzy implicative hyper GR-ideal and obtained its characterization using l

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Dr., M. Mary Jansi Rani, and Sudhalakshmi P. "INTUITIONISTIC M-FUZZY IDEALS OF SEMIGROUPS." International Journal of Computational Research and Development 2, no. 2 (2017): 47–49. https://doi.org/10.5281/zenodo.848247.

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Davvaz, Bijan, Fatema F. Kareem, and Wisam K. Awad. "Cubic intuitionistic structures of a semigroup in KU-algebra." Mathematica Montisnigri 56 (2023): 63–75. http://dx.doi.org/10.20948/mathmontis-2023-56-7.

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An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.

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Thamir, Riyam, Walaa Hasan Ashour, Mohammed Jassim Tuamah, and Hasan Ali Naser. "Intuitionistic Fuzzy Soft HX Ideals." Journal of Education for Pure Science- University of Thi-Qar 11, no. 1 (2021): 77–87. http://dx.doi.org/10.32792/jeps.v11i1.93.

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In this paper we defined the concept of intuitionistic fuzzy soft HX ideal of HX ring and prove some results about them, after that we study some types of intuitionistic fuzzy soft HX ideal of HX ring and prove some results about them. Also, we study the image and pre image of intuitionistic fuzzy soft HX ideal of HX ring and prove some results about them.

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41

Pratama, Dian. "KERNEL DAN SIFATNYA PADA TRANSLASI NAIK DAN TURUN RING FUZZY INTUITIONISTIK." Mathline : Jurnal Matematika dan Pendidikan Matematika 7, no. 1 (2022): 40–52. http://dx.doi.org/10.31943/mathline.v7i1.257.

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Intuitionistic fuzzy ring is a generalized of ring combined with intuitionistic fuzzy sets. It also has impact on ideal so it become intuitionistic fuzzy ideal. The existence of the generalization process, needs to be studied about the properties of kernel at ring homomorphism in which we know that the kernel of a ring homomorphism is ideal. In addition, the study of fuzzy sets there are operators that are subject to membership and non membership functions. One of the known operators is up translates. This research examines the structure of the kernel at homomorphism rings in fuzzy intuitionis

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42

Achik, S., I. Bakhadach, M. Oukessou, and S. Melliani. "Intuitionistic fuzzy Nakayama’s Lemma." Notes on Intuitionistic Fuzzy Sets 30, no. 4 (2024): 309–22. https://doi.org/10.7546/nifs.2024.30.4.309-322.

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Drawing upon Atanassov's pioneering work on intuitionistic fuzzy sets [1], this paper presents the concept of intuitionistic fuzzy Nakayama's Lemma, offering a natural extension to Rajesh Kumar et al.'s fuzzy Nakayama's Lemma [8]. Additionally, we define the intuitionistic fuzzy Jacobson radical and explore the product of an intuitionistic fuzzy ideal and intuitionistic fuzzy submodule. Finally, we conclude by introducing the sum of two intuitionistic fuzzy submodules.

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A., Alphonse Anitha, M. Mary Jansi Rani Dr., and S. Katrin Lydia Dr. "INTUITIONISTIC FUZZY TRANSLATION OF BV- ALGEBRAS." International Journal of Advanced Trends in Engineering and Technology (IJATET) 6, no. 2 (2021): 38–41. https://doi.org/10.5281/zenodo.5758687.

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In this paper, we introduced the concept of Intuitionistic Fuzzy translations to Intuitionistic Fuzzy BV-Algebras. We investigated some of their properties in detail by using the concepts of Intuitionistic fuzzy BV- Ideal and Intuitionistic fuzzy BV-subalgebra.

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A., Alphonse Anitha, M. Mary Jansi Rani Dr., and S. Katrin Lydia Dr. "INTUITIONISTIC FUZZY MULTIPLICATION OF BV - ALGEBRAS." International Journal of Engineering Research and Modern Education (IJERME) 6, no. 2 (2021): 46–49. https://doi.org/10.5281/zenodo.5758698.

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In this paper, we introduced the concept of Intuitionistic Fuzzy multiplication to Intuitionistic Fuzzy BV-Algebras. We investigated some of their properties in detail by using the concepts of Intuitionistic fuzzy BV- Ideal and Intuitionistic fuzzy BV-subalgebra.

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Guo, Jian. "Hybrid Multiattribute Group Decision Making Based on Intuitionistic Fuzzy Information and GRA Method." ISRN Applied Mathematics 2013 (September 4, 2013): 1–10. http://dx.doi.org/10.1155/2013/146026.

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Hybrid multiple attribute group decision making involves ranking and selecting competing courses of action available using attributes to evaluate the alternatives. The decision makers assessment information can be expressed in the form of real number, interval-valued number, linguistic variable, and the intuitionistic fuzzy number. All these evaluation information can be transformed to the form of intuitionistic fuzzy numbers. A combined GRA with intuitionistic fuzzy group decision-making approach is proposed. Firstly, the hybrid decision matrix is standardized and then transformed into an int

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Khan, Hidayat Ullah, Nor Haniza Sarmin, Asghar Khan, Faiz Muhammad Khan, and Muhammad Taj. "Intuitionistic fuzzy interior ideal of semigroup based on intuitionistic fuzzy point." Matrix Science Mathematic 1, no. 2 (2017): 22–26. http://dx.doi.org/10.26480/msmk.02.2017.22.26.

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Rajesh, Neelamegarajan, Tahsin Oner, Aiyared Iampan, and Ibrahim Senturk. "Intuitionistic Fuzzy Structures on Sheffer Stroke UP-algebras." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5627. https://doi.org/10.29020/nybg.ejpam.v18i1.5627.

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The study defines an intuitionistic fuzzy SUP-subalgebra and a level set of an intuitionistic fuzzy UP-structure on Sheffer stroke UP-algebras. It appears that these concepts are integral to understanding the behavior of neutrosophic logic within the framework of Sheffer stroke UP-algebras. The study establishes a relationship between UP-subalgebras and level sets on Sheffer stroke UP-algebras. Specifically, it proves that the level set of intuitionistic fuzzy SUP-subalgebras on this algebra is its subalgebra, and vice versa. It is stated that the family of all intuitionistic fuzzy SUP-subalge

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Bandaru, Ravi Kumar, Rajesh Neelamegarajan, Tahsin Oner, and Amal S. Alali. "A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras." Axioms 14, no. 5 (2025): 347. https://doi.org/10.3390/axioms14050347.

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This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for understanding the interaction between intuitionistic logic and Sheffer stroke BCK-algebras. The paper establishes a connection between subalgebras and level sets in the framework of Sheffer stroke BCK-algebras, demonstrating that the level set of intuitionistic fuzzy SBCK-subalgebras corresponds precisely to their subalgebras, and conversely. Additionall

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Roszkowska, Ewa, Bartłomiej Jefmański, and Marta Kusterka-Jefmańska. "On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights." Entropy 24, no. 8 (2022): 1081. http://dx.doi.org/10.3390/e24081081.

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In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membe

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Julatha, Pongpun, та Aiyared Iampan. "On inf -Hesitant Fuzzy Γ -Ideals of Γ -Semigroups". Advances in Fuzzy Systems 2022 (17 січня 2022): 1–8. http://dx.doi.org/10.1155/2022/9755894.

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The notions of an inf -hesitant fuzzy Γ -ideal and a sup , inf -hesitant fuzzy Γ -ideal, which are a generalization of an interval-valued fuzzy Γ -ideal, of a Γ -semigroup are introduced and some properties are investigated. Characterizations of the notions are provided in terms of sets, fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and hesitant fuzzy sets. Furthermore, characterizations of a Γ -ideal of a Γ -semigroup are given in terms of inf -hesitant and sup , inf -hesitant fuzzy Γ -ideals.

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