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Journal articles on the topic 'Intuitionistic Fuzzy Metric Space'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Kargın, Abdullah. "Intuitionistic Fuzzy Partial Metric Spaces." Adıyaman University Journal of Science 15, no. 1 (2025): 77–97. https://doi.org/10.37094/adyujsci.1635359.

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Fuzzy logic is a theory that is used as an alternative to classical structures in both application and algebraic fields. The fixed point theorem is a theorem widely used in mathematics, especially in metric spaces and partial metric spaces. The fixed point theorem is used on classical metric structures, but it is also widely used on fuzzy metric spaces, fuzzy partial metric spaces and intuitionistic fuzzy metric spaces. In this paper, intuitionistic fuzzy partial metric spaces are defined, their basic properties and examples are obtained. For it, open ball, convergent sequence, and Cauchy sequ

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2

Ishtiaq, Umar, Doha A. Kattan, Khaleel Ahmad, Tania A. Lazăr, Vasile L. Lazăr, and Liliana Guran. "On Intuitionistic Fuzzy Nb Metric Space and Related Fixed Point Results with Application to Nonlinear Fractional Differential Equations." Fractal and Fractional 7, no. 7 (2023): 529. http://dx.doi.org/10.3390/fractalfract7070529.

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This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, intuitionistic fuzzy quasi-Sb-metric space, intuitionistic fuzzy pseudo-Sb-metric space, intuitionistic fuzzy quasi-N-metric space and intuitionistic fuzzy pseudo Nb fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo Nb fuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fraction

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3

Onbaşıoğlu, Şuara, and Banu Pazar Varol. "Intuitionistic Fuzzy Metric-like Spaces and Fixed-Point Results." Mathematics 11, no. 8 (2023): 1902. http://dx.doi.org/10.3390/math11081902.

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The objective of this paper is to describe the concept of intuitionistic fuzzy metric-like spaces. This space is an extension of metric-like spaces and fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We discuss convergence sequences, contractive mapping and some fixed-point theorems in intuitionistic fuzzy metric-like space. We also give explanations, examples and counterexamples to validate the superiority of these results. Our results provide a substantial extension of several important results from fuzzy metric-like spaces.

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Altanji, Mohamed, Annamalai Santhi, Vediyappan Govindan, Shyam Sundar Santra, and Samad Noeiaghdam. "Fixed-Point Results Related to b-Intuitionistic Fuzzy Metric Space." Journal of Function Spaces 2022 (May 12, 2022): 1–15. http://dx.doi.org/10.1155/2022/9561906.

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In this study, we contribute to the terminological debate about various fixed-point results’ use of the term intuitionistic fuzzy b-metric space in defining the structure based on fuzzy sets. As a predominant result, we give an adequate condition for a sequence to be Cauchy in the intuitionistic fuzzy b-metric space. Subsequently, we simplify the proofs of manifold fixed-point theorems in the intuitionistic fuzzy b-metric spaces under the prominent contraction conditions. Also, we give a satisfactory condition for a solution to Cauchy in the intuitionistic fuzzy b-metric spaces.

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Lohani, Q. M. Danish. "Intuitionistic Fuzzy 2-Metric Space and Some Topological Properties." International Journal of Artificial Life Research 2, no. 3 (2011): 59–73. http://dx.doi.org/10.4018/jalr.2011070107.

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The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metric space.

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6

Hussain, Aftab, Hamed Al Sulami, and Umar Ishtiaq. "Some New Aspects in the Intuitionistic Fuzzy and Neutrosophic Fixed Point Theory." Journal of Function Spaces 2022 (March 3, 2022): 1–14. http://dx.doi.org/10.1155/2022/3138740.

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In this manuscript, we use the concepts of continuous t-norms and continuous t-conorms to introduce some definitions, in which intuitionistic fuzzy rectangular metric spaces, intuitionistic fuzzy rectangular metric-like spaces, intuitionistic fuzzy rectangular b-metric spaces, intuitionistic fuzzy rectangular b-metric-like spaces, neutrosophic rectangular metric spaces, neutrosophic rectangular metric-like spaces, neutrosophic rectangular b-metric spaces, and neutrosophic rectangular b-metric-like spaces are included. Continuous t-norms and continuous t-conorms are used to generalize the proba

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Ishtiaq, Umar, Salha Alshaikey, Muhammad Bilal Riaz, and Khaleel Ahmad. "Fixed point results in intuitionistic fuzzy pentagonal controlled metric spaces with applications to dynamic market equilibrium and satellite web coupling." PLOS ONE 19, no. 8 (2024): e0303141. http://dx.doi.org/10.1371/journal.pone.0303141.

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This manuscript contains several new spaces as the generalizations of fuzzy triple controlled metric space, fuzzy controlled hexagonal metric space, fuzzy pentagonal controlled metric space and intuitionistic fuzzy double controlled metric space. We prove the Banach fixed point theorem in the context of intuitionistic fuzzy pentagonal controlled metric space, which generalizes the previous ones in the existing literature. Further, we provide several non-trivial examples to support the main results. The capacity of intuitionistic fuzzy pentagonal controlled metric spaces to model hesitation, ca

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8

Wong, Koon Sang, Zabidin Salleh, and Habibulla Akhadkulov. "Exploring Fixed Points and Common Fixed Points of Contractive Mappings in Complex-Valued Intuitionistic Fuzzy Metric Spaces." International Journal of Analysis and Applications 22 (May 27, 2024): 91. http://dx.doi.org/10.28924/2291-8639-22-2024-91.

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The current manuscript aims to introduce complex-valued intuitionisitic fuzzy metric spaces as a fresh perspective on complex-valued fuzzy metric spaces and intuitionistic fuzzy metric spaces. Existence together with distinctiveness of the fixed points within maps with diverse contractive criteria in this novel space are established. Additionally, our work yields a few common fixed-point findings for intuitionistic fuzzy Banach contraction on this newly introduced space. The outcomes presented in this study go beyond the existing literature, adding to the growing body of knowledge in this fiel

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9

Uddin, Fahim, Umar Ishtiaq, Khalil Javed, et al. "A New Extension to the Intuitionistic Fuzzy Metric-like Spaces." Symmetry 14, no. 7 (2022): 1400. http://dx.doi.org/10.3390/sym14071400.

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In this manuscript, we introduce the concept of intuitionistic fuzzy controlled metric-like spaces via continuous t-norms and continuous t-conorms. This new metric space is an extension to intuitionistic fuzzy controlled metric-like spaces, controlled metric-like spaces and controlled fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We prove some fixed-point theorems and we present non-trivial examples to illustrate our results. We used different techniques based on the properties of the considered spaces notably the symmetry of the metric. Moreover, we present an application to no

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10

Khan, Vakeel, and Rahaman Ashadul. "Statistical convergence in intuitionistic fuzzy G-metric spaces with order n." Filomat 38, no. 8 (2024): 2785–812. https://doi.org/10.2298/fil2408785k.

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Mohiudddine and Alotaibi [25] introduced the notion of intuitionistic generalized fuzzy metric space to extend the generalized fuzzy metric space. Choi et al.[Structure for 1-Metric Spaces and Related Fixed Point Theorems, arXiv preprint arXiv:1804.03651, (2018)] has recently proposed the notion of 1-metric as a generalized notion of the distance function. Employing the idea in this paper, we first put forth the notion of Intuitionistic fuzzy G-metric space with order n as a generalization of intuitionistic fuzzy metric space. We describe some properties of this novel space and construct examp

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11

Güner, Elif, Vildan Çetkin, and Halis Aygün. "On Intuitionistic Fuzzy 2-Metric Spaces." ITM Web of Conferences 22 (2018): 01024. http://dx.doi.org/10.1051/itmconf/20182201024.

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In this study, we first recall the notion of an intuitionistic fuzzy 2-metric space and fundamental definitions with several illustrative examples. Then we define the notion of δ−chainable space and (δ,λ)−uniform locally contractive mapping between intuitionistic fuzzy 2-metric spaces. After that, by using the proposed concepts, we obtain a few fixed point theorems of self-mappings defined on this spaces.

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12

Edan, Alaa J., and Sameer Q. Hasan. "On Intuitionistic Fuzzy Quasi Metric Space." Al-Mustansiriyah Journal of Science 33, no. 2 (2022): 64–69. http://dx.doi.org/10.23851/mjs.v33i2.1093.

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In this article the fixed point of intuitionistic fuzzy quasi metric space instabilities on two metrics dx(f, g) and Dx(f, g) on complicity space X have been studied and presented in details depended on (0,1]-fuzzy contractive map. The illustrative example is proposed to explain the present results using quick sort algorithm.

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13

Mehra, Seema. "Common Fixed Points of Weakly Compatible Mappings in ~-Chainable Intuitionistic Fuzzy Metric Spaces." International Journal of Engineering & Technology 1, no. 1 (2012): 14. http://dx.doi.org/10.14419/ijet.v1i1.24.

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The aim of this paper is to introduce the notion of~-chainable intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four weakly compatible mappings in this newly defined space. Our result is intuitionistic fuzzy version of Cho and Jung's [1] and Mukherjee's [9] results in ~-chainable fuzzy metric space.

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14

Amani E. Kadhm. "Some properties of intuitionistic fuzzy cone metric space." journal of the college of basic education 27, no. 110 (2022): 1225–35. http://dx.doi.org/10.35950/cbej.v27i110.5548.

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In this paper, we will study the concepts of continuous cross-sectional fuzzy conic and prove the Schauder fixed point theorem in "intuitive fuzzy conic metric spaces as a generalization of the fuzzy metric conic space and prove another version of the Schauder fixed point theorem in the intuitive fuzzy metric conic space as a generalization" of other types of point theorems fixed in the intuitively blurry conic metric space that other researchers are studying, as well as to the usual intuitively blurry conic metric space.

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15

Agrawal, Swati, P. L. Sanodia, Neeraj Malviya, and Jyoti Nema. "COINCIDENCE AND COMMON FIXED-POINT THEOREM USING COMPATIBLE MAPPING OF TYPE (P) ON INTUITIONISTIC FUZZY b-METRIC SPACES." South East Asian J. of Mathematics and Mathematical Sciences 20, no. 01 (2024): 469–80. http://dx.doi.org/10.56827/seajmms.2024.2001.36.

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16

Sewani, Godavari, A. D. Singh, Ruchi Singh, and Ramakant Bhardwaj. "Generalized Intuitionistic Fuzzy b-Metric Space." ECS Transactions 107, no. 1 (2022): 12415–34. http://dx.doi.org/10.1149/10701.12415ecst.

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In b-IFMS, the script consists of varied fixed point (FP) generalized results. It's a dominating outcome where an appropriate condition for a real sequence conferred to be cauchy within. Afterwards, results have been interpreted by way of manifold FP theorems in this pre-defined space with the exceptional contraction circumstances.

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17

A. Muraliraj and R. Thangathamizh. "SOME NEW FIXED POINT THEOREMS FOR ITERATED CONTRACTION MAPS IN INTUITIONISTIC FUZZY METRIC SPACE." Jnanabha 52, no. 01 (2022): 66–68. http://dx.doi.org/10.58250/jnanabha.2022.52108.

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We propose iterated contraction maps in intuitionistic fuzzy metric spaces and establish some novel fixed point theorems for intuitionistic fuzzy iterated contraction maps in intuionistic fuzzy metric spaces in this work.

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18

Manro, Saurabh, Sanjay Kumar, S. S. Bhatia, and Kenan Tas. "Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces." Journal of Applied Mathematics 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/189321.

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This paper consists of main two sections. In the first section, we prove a common fixed point theorem in modified intuitionistic fuzzy metric space by combining the ideas of pointwiseR-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions. In the second section, we prove common fixed point theorems in modified intuitionistic fuzzy metric space from the class of compatible continuous mappings to noncompatible and discontinuous mappings. Lastly, as an application, we prove fixed point theorems using weakly reciprocally continuous noncompatible self-mappings o

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19

Manandhar, K. B., K. Jha, and Y. J. Cho. "Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using Compatible Mappings of Type (K)." Bulletin of Society for Mathematical Services and Standards 10 (June 2014): 53–58. http://dx.doi.org/10.18052/www.scipress.com/bsmass.10.53.

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In this paper, we introduce the notion of compatible mappings of type (K) in intuitionistic fuzzy metric space and obtain a common fixed point theorem for self mappings on complete intuitionistic fuzzy metric space with example. Our result generalizes and improves other similar results in literature.

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20

Dr., Kanchan Mishra. "Implementation of Common Soft Fixed Point with Intuitionistic Soft Fuzzy Metric Space." 'Journal of Research & Development' 15, no. 11 (2023): 145–52. https://doi.org/10.5281/zenodo.8046459.

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In this article, we define compatible mappings of type (K) in intuitionistic fuzzy metric space and prove a general Soft fixed point theorem with an application to self mappings on a full intuitionistic fuzzy metric space. Our conclusion broadens and enhances earlier, related findings in the literature.

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21

Esi, Ayhan, Vakeel A. Khan, Mobeen Ahmad, and Masood Alam. "Some Results on Wijsman Ideal Convergence in Intuitionistic Fuzzy Metric Spaces." Journal of Function Spaces 2020 (November 10, 2020): 1–8. http://dx.doi.org/10.1155/2020/7892913.

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In the present work, we study and extend the notion of Wijsman J –convergence and Wijsman J ∗ –convergence for the sequence of closed sets in a more general setting, i.e., in the intuitionistic fuzzy metric spaces (briefly, IFMS). Furthermore, we also examine the concept of Wijsman J ∗ –Cauchy and J –Cauchy sequence in the intuitionistic fuzzy metric space and observe some properties.

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22

Park, Jin Han. "Intuitionistic fuzzy metric spaces." Chaos, Solitons & Fractals 22, no. 5 (2004): 1039–46. http://dx.doi.org/10.1016/j.chaos.2004.02.051.

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23

Kattan, Doha, Amjad Owaidh Alzanbaqi, and Sahidul Islam. "Contraction Mappings in Intuitionistic Fuzzy Rectangular Extended B-Metric Spaces." Mathematical Problems in Engineering 2022 (April 23, 2022): 1–21. http://dx.doi.org/10.1155/2022/1814291.

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In this study, we present the notion of intuitionistic fuzzy rectangular extended b-metric spaces as a generalization of intuitionistic fuzzy metric spaces and intuitionistic fuzzy rectangular b-metric spaces. Some well-known fixed-point results in metric fixed-point theory are generalized in the sense of intuitionistic fuzzy rectangular extended b-metric spaces. Several nontrivial examples and an application to nonlinear fractional differential equations are also imparted in this work to examine the validity of given results.

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Park, Jong-Seo, Young-Chel Kwun, and Jin-Han Park. "Some Properties on Intuitionistic Fuzzy Metric Space." International Journal of Fuzzy Logic and Intelligent Systems 10, no. 2 (2010): 152–56. http://dx.doi.org/10.5391/ijfis.2010.10.2.152.

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25

Tripathi, Namrata, and Anil Rajput. "Noncompatible Mappings in Intuitionistic Fuzzy Metric Space." Journal of Advanced Studies in Topology 3, no. 4 (2012): 62. http://dx.doi.org/10.20454/jast.2012.291.

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26

Ishtiaq, Umar, Khalil Javed, Fahim Uddin, Manuel de la Sen, Khalil Ahmed, and Muhammad Usman Ali. "Fixed Point Results in Orthogonal Neutrosophic Metric Spaces." Complexity 2021 (August 9, 2021): 1–18. http://dx.doi.org/10.1155/2021/2809657.

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Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metr

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27

Gupta, Vishal, Ashima Kanwar, and Rahul Shukla. "Topological Properties and Fixed Point Results for Modified Intuitionistic Generalized Fuzzy Metric Spaces." International Journal of Analysis and Applications 23 (April 28, 2025): 102. https://doi.org/10.28924/2291-8639-23-2025-102.

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The principle originality inside the paper is to establish the concept of modified intuitionistic generalized fuzzy metric space and its fundamental topological properties. Moreover, we give the steps for proving some coupled coincidence point results for mapping with contractive condition in partial ordered modified intuitionistic generalized fuzzy metric space. Furthermore, an illustration is proved in the support of our main result.

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Gupta, Vishal, Anju, and Rahul Shukla. "Fixed Point Results in Complex Valued Modified Intuitionistic Fuzzy Metric Space with Applications." International Journal of Analysis and Applications 23 (May 8, 2025): 105. https://doi.org/10.28924/2291-8639-23-2025-105.

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The aims is to introduce complex-valued modified intuitionistic fuzzy metric spaces as a fresh perspective on complex-valued FMS and modified intuitionistic fuzzy metric spaces. Additionally, our work yields a fixed and common fixed point result on this newly introduced space. Our research outcomes are exemplified through examples that are included in this paper to help readers better grasp our findings. Our paper concludes with a discussion of how our findings can be applied to the problem of determining the existence of a unique solution for Fredholm integral equations.

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Abu-Donia, Hassan, Hany Atia, and Omnia Khater. "Fixed point theorem for compatible mappings in intuitionistic fuzzy 3-metric spaces." Thermal Science 24, Suppl. 1 (2020): 371–76. http://dx.doi.org/10.2298/tsci20371a.

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In this paper, we introduced the concept of weak compatible of type (?) and asymptotically regular defined on intuitionistic fuzzy 3-metric space and proved the uniqueness and existence the fixed point theorem for five mappings from a complete intuitionistic fuzzy 3-metric space into itself under weak compatible of type (?) and asymptotically regular. The used definitions and theorem show the practice of our main idea.

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Abu-Donia, Hassan, Hany Atia, and Omnia Khater. "Fixed point theorem for compatible mappings in intuitionistic fuzzy 3-metric spaces." Thermal Science 24, Suppl. 1 (2020): 371–76. http://dx.doi.org/10.2298/tsci20s1371a.

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In this paper, we introduced the concept of weak compatible of type (?) and asymptotically regular defined on intuitionistic fuzzy 3-metric space and proved the uniqueness and existence the fixed point theorem for five mappings from a complete intuitionistic fuzzy 3-metric space into itself under weak compatible of type (?) and asymptotically regular. The used definitions and theorem show the practice of our main idea.

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31

Muraliraj, A., and R. Thangathamizh. "RATIONAL TYPE INTUITIONISTIC FUZZY CONTRACTION RESULTS IN INTUITIONISTIC FUZZY METRIC SPACES WITH AN APPLICATION." jnanabha 54, no. 01 (2024): 122–33. http://dx.doi.org/10.58250/jnanabha.2024.54116.

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The purpose of this study is to propose a new idea of rational type intuitionistic fuzzy contraction mappings in intuitionistic fuzzy metric spaces. We show several fixed point results in intuitionistic fuzzy metric spaces under rational type intuitionistic fuzzy contraction conditions, with detailed examples to back up our claims. This revolutionary idea will be crucial in the theory of intuitionistic fuzzy fixed point outcomes and can be applied to other contractive type mappings in the setting of intuitionistic fuzzy metric spaces. Furthermore, to support our work, we offer an application o

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32

Debnath, Shyamal, Vishnu Narayan Mishra, and Jayanta Debnath. "On statistical convergent sequence spaces of intuitionistic Fuzzy numbers." Boletim da Sociedade Paranaense de Matemática 36, no. 1 (2018): 235. http://dx.doi.org/10.5269/bspm.v36i1.30880.

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In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.

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33

Kanwal, Shazia, and Akbar Azam. "Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions." Advances in Fuzzy Systems 2018 (October 21, 2018): 1–6. http://dx.doi.org/10.1155/2018/1989423.

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The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete metric space in association with the Hausdorff metric. Furthermore, the technique of Meir-Keeler (shortly, M-K) contraction is applied to obtain common fixed point of intuitionistic fuzzy compatible maps and fixed points of Kannan type intuitionistic fuzzy set-valued contractive mappings. Our results generalize M-K type fixed point theorem along with its various generalizations. Some nontrivial ex

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34

Ben Amma, Bouchra, Said Melliani, and Lalla Saadia Chadli. "The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations." International Journal of Differential Equations 2019 (July 21, 2019): 1–13. http://dx.doi.org/10.1155/2019/9210641.

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In this paper, we consider intuitionistic fuzzy partial functional differential equations with local and nonlocal initial conditions using the Banach fixed point theorem. A new complete intuitionistic fuzzy metric space is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems. We use the level-set representation of intuitionistic fuzzy functions and define the solution to an intuitionistic fuzzy partial functional differential equation problem through a corresponding parametric problem and further develop theoretical results on the existence

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Gupta, Vishal, and Ashima Kanwar. "Unified Fixed Point Theorems on ∈−Chainable Fuzzy Metric Space and Modified Intuitionistic Fuzzy Metric Space." Applied Mathematics & Information Sciences 10, no. 6 (2016): 2283–91. http://dx.doi.org/10.18576/amis/100631.

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Sharma, Sushil, and Prashant Tilwankar. "Some Fixed Point Theorems in intuitionistic fuzzy metric spaces." Tamkang Journal of Mathematics 42, no. 4 (2011): 405–14. http://dx.doi.org/10.5556/j.tkjm.42.2011.683.

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The aim of this paper is to prove some common fixed point theorems by using the property ($S$-$B$) and the notion of R-weak commutativity of type $(S_p)$ in intuitionistic fuzzy metric spaces. We first formulate the definition of R-weakly commuting mappings of type $(S_p)$ in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem.

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37

Shojaei, H. "Notes And Examples On Intuitionistic Fuzzy Metric Space." Journal of Mathematics and Computer Science 08, no. 03 (2014): 187–92. http://dx.doi.org/10.22436/jmcs.08.03.01.

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Tiwari, A., C. K. Ganteda, and R. Sandhya. "ABSORBING MAP IN COMPLETE INTUITIONISTIC FUZZY METRIC SPACE." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9009–17. http://dx.doi.org/10.37418/amsj.9.11.5.

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Dwivedi, Pradeep Kumar. "Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space." IOSR Journal of Mathematics 4, no. 6 (2013): 59–64. http://dx.doi.org/10.9790/5728-0465964.

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PRANJALI, SHARMA, and DIWAN SHAILESH DHAR. "COMMON FIXED POINTS IN INTUITIONISTIC FUZZY METRIC SPACE." i-manager’s Journal on Mathematics 5, no. 3 (2016): 32. http://dx.doi.org/10.26634/jmat.5.3.8226.

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Mursaleen, M., Q. M. Danish Lohani, and S. A. Mohiuddine. "Intuitionistic fuzzy 2-metric space and its completion." Chaos, Solitons & Fractals 42, no. 2 (2009): 1258–65. http://dx.doi.org/10.1016/j.chaos.2009.03.025.

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42

Yue, Chen, H. M. Abu-Donia, H. A. Atia, et al. "Weakly compatible fixed point theorem in intuitionistic fuzzy metric spaces." AIP Advances 13, no. 4 (2023): 045113. http://dx.doi.org/10.1063/5.0147488.

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This study presents fundamental theorems, lemmas, and mapping definitions. There are three types of mappings: binary operators, compatible mappings, and sequentially continuous mappings. The symbols used to represent fuzzy metric spaces are intuitive. Icons were also used to prescribe a shared, linked fixed point in intuitionistic fuzzy metric space for two compatible and sequentially continuous mappings that satisfy ϕ-contractive conditions. To accomplish this, finding the intersection of both mappings was necessary.

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Hussain, Nawab, Nawal Alharbi, and Ghada Basendwah. "Fixed-Point Results with Applications in Generalized Neutrosophic Rectangular b-Metric Spaces." Axioms 13, no. 12 (2024): 818. http://dx.doi.org/10.3390/axioms13120818.

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In this paper, we introduce several new concepts: generalized neutrosophic rectangular b-metric-like spaces (GNRBMLSs), generalized intuitionistic rectangular b-metric-like spaces (GIRBMLSs), and generalized fuzzy rectangular b-metric-like spaces (GFRBMLSs). These innovative spaces can expand various topological spaces, including neutrosophic rectangular extended b-metric-like spaces, intuitionistic fuzzy rectangular extended b-metric-like spaces, and fuzzy rectangular extended b-metric-like spaces. Moreover, we establish Banach’s fixed point theorem and Ćirić’s quasi-contraction theorem with

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Kshama Pandey, Pranjali Sharma, Shailesh Dhar Diwan. "Intuitionistic Fuzzy Fixed Point Theory: Relation-Theoretic Approaches and Applications." Journal of Information Systems Engineering and Management 10, no. 16s (2025): 32–51. https://doi.org/10.52783/jisem.v10i16s.2558.

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This paper explores the concept of intuitionistic fuzzy R-φ- contractive mappings and establishes key results regarding the existence and uniqueness of fixed points in non-Archimedean intuitionistic fuzzy metric spaces. To illustrate the applicability of these findings, several examples are provided. Additionally, the main results are utilized to demonstrate the existence and uniqueness of solutions for Caputo fractional differential equations within the framework of intuitionistic fuzzy metric spaces.

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Li, Xia, Meifang Guo, and Yongfu Su. "On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces." Journal of Nonlinear Sciences and Applications 09, no. 09 (2016): 5441–48. http://dx.doi.org/10.22436/jnsa.009.09.12.

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Al-Qurashi, Maysaa, Mohammed Shehu Shagari, Saima Rashid, Y. S. Hamed, and Mohamed S. Mohamed. "Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions." AIMS Mathematics 7, no. 1 (2021): 315–33. http://dx.doi.org/10.3934/math.2022022.

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<abstract><p>In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every f

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García, Gonzalo. "Approximating intuitionistic fuzzy fractals by densifiability techniques." General Mathematics 29, no. 2 (2021): 3–21. http://dx.doi.org/10.2478/gm-2021-0011.

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Abstract We present a sequence of sets converging, under suitable conditions and respect to the Hausdorff intuitionistic fuzzy metric, to the attractor set of certain intuitionistic fuzzy iterated function systems. For this goal, we will introduce a fuzzy version of the so called α-dense curves which have been used by the author to approximate, with arbitrarily small and controlled error, the attractor set of certain (metric) iterated function systems. In this way, we relate the above mentioned concepts of the intuitionistic fuzzy metric spaces with the α-density theory.

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Park, Jong-Seo. "Some Properties and Theorems on Intuitionistic Fuzzy Metric Space." International Journal of Fuzzy Logic and Intelligent Systems 9, no. 2 (2009): 137–40. http://dx.doi.org/10.5391/ijfis.2009.9.2.137.

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Mohamed, S. Yahya, and A. Mohamed Ali. "Fixed Point Theorems in Intuitionistic Fuzzy Graph Metric Space." Annals of Pure and Applied Mathematics 17, no. 1 (2018): 57–65. http://dx.doi.org/10.22457/apam.v17n1a7.

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Samanta, T. K., Sumit Mohinta, and Iqbal H. Jebril. "On Fixed-Point Theorems in Intuitionistic Fuzzy Metric Space." International Journal of Open Problems in Computer Science and Mathematics 5, no. 2 (2012): 16–27. http://dx.doi.org/10.12816/0006102.

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