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Journal articles on the topic 'INTUITIONISTIC FUZZY SET'

Author: Grafiati

Published: 16 January 2024

Last updated: 25 July 2025

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1

Jeon, Joung Kon, Young Bae Jun, and Jin Han Park. "Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy precontinuity." International Journal of Mathematics and Mathematical Sciences 2005, no. 19 (2005): 3091–101. http://dx.doi.org/10.1155/ijmms.2005.3091.

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A characterization of intuitionistic fuzzyα-open set is given, and conditions for an IFS to be an intuitionistic fuzzyα-open set are provided. Characterizations of intuitionistic fuzzy precontinuous (resp.,α-continuous) mappings are given.

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Kareem Mnahi, Afakar. "On Intuitionistic Fuzzy Minimal Semi-preopen Set." University of Thi-Qar Journal of Science 6, no. 3 (2017): 19–24. http://dx.doi.org/10.32792/utq/utjsci/v6i3.27.

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In this paper, we introduce the concept of intuitionistic fuzzy minimal open sets on intuitionistic fuzzy topological space. We introduce the concepts of closure and interior defined by intuitionistic fuzzy minimal open set and intuitionistic fuzzy minimal closed set. We also introduce a intuitionistic fuzzy minimal semi-preopen and intuitionistic fuzzy minimal semi-preclosed. We also redefine the concepts of closure and interior by intuitionistic fuzzy minimal semi-preopen set and intuitionistic fuzzy minimal semi-preclosed set and we introduce the concept of intuitionistic fuzzy minimal semi

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3

Szmidt, Eulalia, and Janusz Kacprzyk. "A Fuzzy Set Corresponding to an Intuitionistic Fuzzy Set." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 05 (1998): 427–35. http://dx.doi.org/10.1142/s0218488598000343.

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We propose a new approach to find a fuzzy set which corresponds to a given intuitionistic fuzzy set (Atanassov, 1986) in a certain sense. This will help extend a huge array of fuzzy properties, models, etc. available to the case of intuitionistic fuzzy sets.

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Pratama, Dian. "STRUKTUR IMAGE DAN PRE-IMAGE HOMOMORFISMA PADA TRANSLASI RING FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 11, no. 1 (2020): 59. http://dx.doi.org/10.20884/1.jmp.2020.12.1.1937.

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A set that is characterized by membership function and a non-membership function with the sum of both at intervals of 0 to 1 is called intuitionistik fuzzy set.. When it’s applied in ring’s theory, it will called intuitionistic fuzzy ring. In this research,if the topics is membership fuction and non-membership function then there are translates operator. This operator only changes the values of the membership and non-membership function while the properties are fixed. This journal discussed the structure of image ad pre-image homomorphism of translates on intuitionistic fuzzy rings. The result

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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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Priya, Arora, and P. Tomar V. "Selecting the Best Project using Generalized Parametric Fuzzy Entropy Measure on Intuitionistic Fuzzy Sets." Indian Journal of Science and Technology 16, no. 30 (2023): 2276–86. https://doi.org/10.17485/IJST/v16i30.637.

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Abstract Objectives: To develop a new parametric measure of entropy for Intuitionistic Fuzzy Sets and to study its application in selecting the best project for a company. Methods: We have used five-point Likert scale to determine the feedback of different projects and devised a method based on parametric intuitionistic fuzzy entropy to select the best project for the company. Findings: In this study, a parametric measure of entropy is being proposed for intuitionistic fuzzy sets. It is a generalized version of entropy for intuitionistic fuzzy sets. Properties of the proposed entropy have also

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Roh, Eun Hwan, Eunsuk Yang, and Young Bae Jun. "Intuitionistic Fuzzy Ordered Subalgebras in Ordered BCI-algebras." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1342–58. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4832.

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In this paper, we apply the concept of an intuitionistic fuzzy set to ordered subalgebras in ordered BCI-algebras in the sense of intuitionistic fuzzy point. We introduce the notion of an intuitionistic fuzzy (ordered) subalgebra in ordered BCI-algebras, and investigate some related properties. We provide relations between an intuitionistic fuzzy ordered subalgebra and an intuitionistic fuzzy subalgebra. We give characterizations of an intuitionistic fuzzy (ordered) subalgebra. Finally, we provide relations between a $q_{(t,s)}$-level set of intuitionistic fuzzy set and an intuitionistic fuzzy

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8

Bashir, Maruah, Abdul Razak Salleh, and Shawkat Alkhazaleh. "Possibility Intuitionistic Fuzzy Soft Set." Advances in Decision Sciences 2012 (March 13, 2012): 1–24. http://dx.doi.org/10.1155/2012/404325.

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Possibility intuitionistic fuzzy soft set and its operations are introduced, and a few of their properties are studied. An application of possibility intuitionistic fuzzy soft sets in decision making is investigated. A similarity measure of two possibility intuitionistic fuzzy soft sets has been discussed. An application of this similarity measure in medical diagnosis has been shown.

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9

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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10

Anjan, Mukherjee, Kanti Das Ajoy, and Saha Abhijit. "MORE ON INTERVAL-VALUED INTUITIONISTIC FUZZY SOFT MULTI SETS." Advances in Vision Computing: An International Journal (AVC) 2, no. 2 (2015): 01–21. https://doi.org/10.5281/zenodo.3591661.

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In 2013, Mukherje et al. developed the concept of interval-valued intuitionistic fuzzy soft multi set as a mathematical tool for making descriptions of the objective world more realistic, practical and accurate in some cases, making it very promising. In this paper we define some operations in interval-valued intuitionistic fuzzy soft multi set theory and show that the associative, distribution and De Morgan’s type of results hold in interval-valued intuitionistic fuzzy soft multi set theory for the newly defined operations in our way. Also, we define the necessity and possibility operat

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Jana, Chiranjibe, and Madhumangal Pal. "Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem." International Journal of Fuzzy System Applications 7, no. 3 (2018): 32–55. http://dx.doi.org/10.4018/ijfsa.2018070103.

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This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipo

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Singh, Shiva Raj, Surendra Singh Gautam, and Abhishekh . "An Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems." MATEMATIKA 34, no. 1 (2018): 49–58. http://dx.doi.org/10.11113/matematika.v34.n1.890.

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In general most of real life problem of decision making involve imprecise parameters. In recent past the major emphasis of research workers in this area have been to develop the reliable models to deal with such imprecision and vagueness effectively. Several theories have been developed such as fuzzy set theory, interval valued fuzzy set, intuitionistic fuzzy set, and interval valued intuitionistic fuzzy set, rough set and soft set. The primary objectives of all the above developed theories are to deal with various kinds of uncertainty, imprecision and vagueness but unfortunately every theory

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Wijaya, Ongky Denny, Abdul Rouf Alghofari, Noor Hidayat, and Mohamad Muslikh. "The Properties of Intuitionistic Anti Fuzzy Module t-norm and t-conorm." CAUCHY 7, no. 2 (2022): 207–19. http://dx.doi.org/10.18860/ca.v7i2.13351.

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Zadeh have introduced fuzzy set in 1965 and Atanassov have introduced intuitionistic fuzzy set in 1986 in theirs paper. Now, many of researcher connecting intuitionistic fuzzy set with algebraic structure. We interested to combine some concepts over intuitionistic fuzzy set, module of a ring, t-norm, t-conorm, and intuitionistic anti fuzzy. In this paper, we discusses about intuitionistic anti fuzzy module t-norm and t-conorm (IAFMTC) and their properties with respect to module homomorphism, maps, pre-image, and anti-image from intuitionistic fuzzy sets. We have investigate all properties of I

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Gosain, Anjana, and Sonika Dahiya. "An effective fuzzy clustering algorithm with outlier identification feature." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 2417–28. http://dx.doi.org/10.3233/jifs-201858.

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DKIFCM (Density Based Kernelized Intuitionistic Fuzzy C Means) is the new proposed clustering algorithm that is based on outlier identification, kernel functions, and intuitionist fuzzy approach. DKIFCM is an inspiration from Kernelized Intuitionistic Fuzzy C Means (KIFCM) algorithm and it addresses the performance issue in the presence of outliers. It first identifies outliers based on density of data and then clusters are computed accurately by mapping the data to high dimensional feature space. Performance and effectiveness of various algorithms are evaluated on synthetic 2D data sets such

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15

Zhang, Haidong, Lan Shu, and Shilong Liao. "Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/287314.

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The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical examp

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16

Ganai, Suhail Ahmad, Nitin Bhardwaj, and Riyaz Ahmad Padder. "Improving Decision-Making Under Uncertainty: A Comparative Study of Fuzzy Set Extensions." Multidisciplinary Journal of Engineering Sciences 2 (July 5, 2023): 1–21. https://doi.org/10.5281/zenodo.8118017.

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Fuzzy sets have revolutionized decision-making by providing a mathematical tool for modeling uncertainty and imprecision. However, traditional fuzzy sets may not be sufficient in certain situations, leading to the development of extensions such as Type-2 fuzzy sets, Intuitionistic fuzzy sets, and Type-2 intuitionistic fuzzy sets. This paper provides an overview of these sets, comparing and contrasting them using operations of union, intersection, and distance measures. Additionally, a new distance measure is proposed for Type-2 intuitionistic fuzzy sets, which is demonstrated with a numerical

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17

G.Prasannavengeteswari, Dr.B.Vasudevan, Dr.K.Gunasekaran, and Dr.S.Nandakumar. "Some properties of primary interval-valued intuitionistic fuzzy M group." International Journal of Recent Research in Mathematics Computer Science and Information Technology 11, no. 2 (2024): 23–31. https://doi.org/10.5281/zenodo.14209095.

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<strong>Abstract:</strong> The concept of interval-valued intuitionistic fuzzy M group is extended by introducing primary interval-valued intuitionistic fuzzy M group using this concept primary interval-valued intuitionistic fuzzy M group is defined. We also proved some properties of the above are established. <strong>Keywords:</strong> Intuitionistic fuzzy set, Interval-valued intuitionistic fuzzy set, Primary interval-valued intuitionistic fuzzy M group. <strong>Title:</strong> Some properties of primary interval-valued intuitionistic fuzzy M group <strong>Author:</strong> G.Prasannavengetes

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18

Alshehri, Noura, and Muhammad Akram. "Intuitionistic Fuzzy Planar Graphs." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/397823.

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Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomor

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19

S., Sheik Dhavudh, and Srinivasan R. "LEVEL OPERATORS ON INTUITIONISTIC L-FUZZY SETS." International Journal of Scientific Research and Modern Education 1, no. 2 (2016): 114–18. https://doi.org/10.5281/zenodo.163677.

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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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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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Yunianti, Dwi Nur, Noor Hidayat, Raden Sulaiman, and Abdul Rouf Alghofari. "Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach." European Journal of Pure and Applied Mathematics 16, no. 4 (2023): 2198–207. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4939.

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In this paper, we introduce collection of intuitionistic fuzzy sets as a new concept of intuitionistic fuzzy sets. In ordinary, universal set in intuitionistic fuzzy sets is classical set. So in this paper, we generalize the universal set as a collection or family of intuitionistic fuzzy sets. We also present intersection and union operation on collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan’s laws properties.

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Lupiáñez, Francisco Gallego. "On Covering Properties in Intuitionistic Fuzzy Topological Spaces: A survey." PROOF 4 (November 6, 2024): 69–74. http://dx.doi.org/10.37394/232020.2024.4.5.

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We show here some results on covering properties in intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set. D. Çoker constructed the fundamental theory on intuitionistic fuzzy topological spaces, and D. Çoker and other mathematicians studied compactness, connectedness, continuity, separation, convergence and paracompactness in intuitionistic fuzzy topological spaces. Finally, G.-J Wang and Y.Y. He showed that every intuitionistic fuzzy set may be regarded as an L-fuzzy set for some appropria

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G. Shanmugam. "New algebraic structures such as q-rung interval-valued intuitionistic fuzzy set applied to logarithm operator and its extension." Communications on Applied Nonlinear Analysis 32, no. 3 (2024): 539–49. http://dx.doi.org/10.52783/cana.v32.2015.

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We introduce the interval-valued intuitionistic fuzzy set used with the q-rung logarithimic operator (q-LIVIFS). A q-rung interval-valued intuitionistic fuzzy set may be developed by expanding the Pythagorean interval-valued fuzzy set (PIVFS). We discuss the q-logarithimic operator applied to interval-valued intuitionistic fuzzy weighted averaging (q-LIVIFWA), interval-valued intuitionistic fuzzy weighted geometric (q-LIVIFWG), extended q-logarithimic operator applied to interval-valued intuitionistic fuzzy weighted averaging (q-ELIVIFWA), and extended q-logarithimic operator applied to interv

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Attaullah, Sultan Alyobi, Mohammed Alharthi, and Yasser Alrashedi. "Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information." Axioms 13, no. 9 (2024): 610. http://dx.doi.org/10.3390/axioms13090610.

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In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hy

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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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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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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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Sivasankari, H., and J. Subhashini. "Intuitionistic Fuzzy Binary Soft Sets and Its Properties." Indian Journal Of Science And Technology 17, no. 35 (2024): 3636–42. http://dx.doi.org/10.17485/ijst/v17i35.1161.

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Objective : The objective of Intuitionistic fuzzy binary soft sets is to extend the existing frameworks of binary soft sets and Intuitionistic fuzzy sets to accommodate both uncertainty and ambiguity in decision-making processes. This extension aims to provide a more flexible, representation of real-world data and phenomena, allowing for analysis and reasoning. Specifically, the objective involves defining the fundamental structures of Intuitionistic fuzzy binary soft sets over two initial universal sets, U1 and U2. Method: Reviewing the existing literature on binary soft sets, Intuitionistic

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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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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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Guangpeng Ta and Zengtai Gong. "The Shadowed Set, Intuitionistic Fuzzy Set and their Three-way Decision." Journal of Mathematics and Informatics 22 (2022): 09–22. http://dx.doi.org/10.22457/jmi.v22a02206.

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The theory of three-way decision provides an effective tool for decision-making under uncertainty and incomplete information when a two-way decision is difficult to make. In this paper, we try to transform an intuitionistic fuzzy set into a pessimistic shadowed set or an optimistic shadowed set by using two intuitionistic fuzzy parameters and the classical shadowed set. Accordingly, the pessimistic three-way decision or the optimistic three-way decision of intuitionistic fuzzy set are investigated by means of the proposed shadowed sets. In addition, a method to calculate the thresholds by the

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Thumbakara, Rajesh K. "On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes." Journal of Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/793824.

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Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.

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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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Pratama, Dian. "IMAGE DAN PRE-IMAGE TRANSLASI PADA GRUP FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 8, no. 2 (2016): 41. http://dx.doi.org/10.20884/1.jmp.2016.8.2.2886.

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A intuitionistic fuzzy set in is set gives a membership function and a non-membership function (the complement of membership function) for each with the sum worth one. When it’s applied in group’s theory, it will called intuitionistic fuzzy group with conditions membership function is fuzzy subgroup and non-membership function is anti-fuzzy subgroup. In this research, the operator will be given a fuzzy set is called fuzzy translation operator. This operator is a mapping imposed on membership functions (fuzzy subset) to interval [ 0,1]. This research will discuss the properties homomorphism of

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Saeed, Tareq. "Intuitionistic fuzzy variational inequalities and their applications." AIMS Mathematics 9, no. 12 (2024): 34289–310. https://doi.org/10.3934/math.20241634.

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<p>In this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set $ {K\subseteq \mathbb{R}}^{n} $ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterization of intuitionistic convex fuzzy mappings is also discussed. Different types of intuitionistic convex (concave) fuzzy mappings are defined and their properties are investigated. Then, we discuss some applications of intuitionistic fuzzy convex mappings in fuzzy optimization. Additionally,

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Mostafavi, Marzieh. "Z_2-graded intuitionistic L-fuzzy q-deformed quantum subspaces of A_q." Notes on Intuitionistic Fuzzy Sets 28, no. 2 (2022): 93–112. http://dx.doi.org/10.7546/nifs.2022.28.2.93-112.

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In this paper, assuming that ⟨L, ≤〉 is a lattice set with a few specific conditions, intuitionistic L-fuzzy subalgebras, intuitionistic L-fuzzy subcoalgebras and intuitionistic L-fuzzy left (right) coideals are defined and the properties of intuitionistic L-fuzzy subcoalgebras under homomorphisms of coalgebras are investigated. Duality of intuitionistic L-fuzzy subalgebras and duality of intuitionistic L-fuzzy subcoalgebras are also discussed. Intuitionistic L-fuzzy subbialgebras as well as intuitionistic L-fuzzy Hoph subalgebras are studied. Intuitionistic L-fuzzy quantum subsets of k_q[x, y]

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Ebrahimnejad, Ali, Amal Kumar Adak, and Ezzatallah Baloui Jamkhaneh. "Eigenvalue of Intuitionistic Fuzzy Matrices Over Distributive Lattice." International Journal of Fuzzy System Applications 8, no. 1 (2019): 1–18. http://dx.doi.org/10.4018/ijfsa.2019010101.

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In this article, the concepts of intuitionistic fuzzy complete and complete distributive lattice are introduced and the relative pseudocomplement relation of intuitionistic fuzzy sets is defined. The concepts of intuitionistic fuzzy eigenvalue and eigenvector of an intuitionistic fuzzy matrixes are presented and proved that the set of intuitionistic fuzzy eigenvectors of a given intuitionistic fuzzy eigenvalue form an intuitionistic fuzzy subspace. Also, the authors obtain an intuitionistic fuzzy maximum matrix of a given intuitionistic fuzzy eigenvalue and eigenvector and give some properties

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Sen, Dilip Kumar, Saurav Datta, and S. S. Mahapatra. "Sustainable supplier selection in intuitionistic fuzzy environment: a decision-making perspective." Benchmarking: An International Journal 25, no. 2 (2018): 545–74. http://dx.doi.org/10.1108/bij-11-2016-0172.

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Purpose The purpose of this paper is to attempt supplier selection considering economic, environmental and social sustainability issues. Design/methodology/approach Subjective human judgment bears some kind of vagueness and ambiguity; fuzzy set theory has immense potential to overcome this. Owing to the advantage of intuitionistic fuzzy numbers set over classical fuzzy numbers set; three decision-making approaches have been applied here in intuitionistic fuzzy setting (namely, intuitionistic-TOPSIS, intuitionistic-MOORA and intuitionistic-GRA) to facilitate supplier selection in sustainable su

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BUSTINCE, H., and P. BURILLO. "PERTURBATION OF INTUITIONISTIC FUZZY RELATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 01 (2001): 81–103. http://dx.doi.org/10.1142/s0218488501000648.

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In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations afterward obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another also intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the con

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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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Derseh, Beza Lamesgin, Yohannes Gedamu Wondifraw, and Berhanu Assaye Alaba. "On t-Intuitionistic Fuzzy PMS-Subalgebras of a PMS Algebra." International Journal of Fuzzy System Applications 12, no. 1 (2023): 1–22. http://dx.doi.org/10.4018/ijfsa.317103.

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In this paper, the authors extend the concept of a t-intuitionistic fuzzy set to PMS-subalgebras of PMS-algebras. The authors define the t-intuitionistic fuzzy PMS-subalgebra of a PMS-algebra and show that any intuitionistic fuzzy PMS-subalgebra of a PMS-algebra is a t-intuitionistic fuzzy PMS-subalgebra. The authors provide the condition for an intuitionistic fuzzy set in a PMS-algebra to be a t-intuitionistic fuzzy PMS-subalgebra. The authors use their (α,β) level cuts to characterize the t-intuitionistic fuzzy PMS-subalgebras of PMS-algebra. The authors investigate whether the homomorphic i

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Van Dinh, Nguyen, and Nguyen Xuan Thao. "Some Measures of Picture Fuzzy Sets and Their Application." Journal of Science and Technology: Issue on Information and Communications Technology 3, no. 2 (2017): 35. http://dx.doi.org/10.31130/jst.2017.49.

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To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and di

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Sayed, Osama Rashed, Nabil Hasan Sayed, and Gui-Xiu Chen. "Suitable interval-valued intuitionistic fuzzy topological spaces." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 879–89. http://dx.doi.org/10.3233/jifs-202757.

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In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued i

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Kurfia, Mustika Ana, Noor Hidayat та Corina Karim. "η-Intuitionistic Fuzzy Soft Groups". CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, № 3 (2022): 354–61. http://dx.doi.org/10.18860/ca.v7i3.14555.

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In this research, we present the idea of the intuitionistic fuzzy soft group defined on the intuitionistic fuzzy soft set. The main purpose of this research is to create a new concept, which is an intuitionistic fuzzy group. To achieve this, we combine the concept of intuitionistic fuzzy group and intuitionistic fuzzy soft group. As the main result, we prove the correlation between the intuitionistic fuzzy soft group and intuitionistic fuzzy soft group along with some properties of intuitionistic fuzzy soft groups. Also, we prove some properties of a subgroup of an intuitionistic fuzzy soft gr

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Khan, Muhammad Jabir, Poom Kumam, Peide Liu, Kumam, and Ashraf. "A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System." Mathematics 7, no. 8 (2019): 742. http://dx.doi.org/10.3390/math7080742.

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The basic idea underneath the generalized intuitionistic fuzzy soft set is very constructive in decision making, since it considers how to exploit an extra intuitionistic fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is redefined and clarified by F. Feng. In this paper, we introduced a method to solve decision making problems using an adjustable weighted soft discernibility matrix in a generalized intuitionistic fuzzy soft set. We define the threshold functions like mid-threshold, top-bottom-threshold, bottom-bottom-thr

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Buvaneswari, R., and K. Umamaheswari. "Bondage and non-bondage sets in regular intuitionistic fuzzy graphs." Notes on Intuitionistic Fuzzy Sets 29, no. 3 (2023): 318–24. http://dx.doi.org/10.7546/nifs.2023.29.3.318-324.

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The concept of strong edges in domination set and its properties are discussed. The increasing or reducing domination numbers using cardinality are also studied. Bondage $(\alpha(G))$ and non-bondage $(\alpha_K(G))$ sets are defined in regular intuitionistic fuzzy graph. The properties of bondage and non-bondage number of intuitionistic fuzzy graph analyzed. A minimum $2$-bondage set $X$ of an intuitionistic fuzzy graph (IFG) $G$ is a bondage set of regular intuitionistic fuzzy graph in $G$.

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Jawad, Muhammad, Niat Nigar, Sarka Hoskova-Mayerova, Bijan Davvaz, and Muhammad Haris Mateen. "Fundamental theorems of group isomorphism under the framework of complex intuitionistic fuzzy set." AIMS Mathematics 10, no. 1 (2025): 1900–1920. https://doi.org/10.3934/math.2025088.

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<p>Algebraic homomorphisms are essential mathematical structures that sustain operations across algebraic systems such as groups, rings, and fields. These mappings not only preserve the validity of algebraic operations but also make it easier to investigate structural similarities and equivalences across distinct algebraic entities. In this article, we establish the group isomorphism under the complex intuitionistic fuzzy set, an extended form of the complex fuzzy set that adds the complex degree of non-membership functions, which plays a significant role in the decision-making process.

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Zhao, Feng, Hao Hao, and Hanqiang Liu. "Robust intuitionistic fuzzy clustering with bias field estimation for noisy image segmentation." Intelligent Data Analysis 26, no. 5 (2022): 1403–26. http://dx.doi.org/10.3233/ida-216058.

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The concept of intuitionistic fuzzy set has been found to be highly useful to handle vagueness in data. Based on intuitionistic fuzzy set theory, intuitionistic fuzzy clustering algorithms are proposed and play an important role in image segmentation. However, due to the influence of initialization and the presence of noise in the image, intuitionistic fuzzy clustering algorithm cannot acquire the satisfying performance when applied to segment images corrupted by noise. In order to solve above problems, a robust intuitionistic fuzzy clustering with bias field estimation (RIFCB) is proposed for

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Hayat, Khizar, Muhammad Ali, Bing-Yuan Cao, Faruk Karaaslan, and Xiao-Peng Yang. "Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods." Symmetry 10, no. 12 (2018): 753. http://dx.doi.org/10.3390/sym10120753.

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In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operato

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