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Journal articles on the topic 'Fermatean Fuzzy sets'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Senapati, Tapan, and Ronald R. Yager. "Fermatean fuzzy sets." Journal of Ambient Intelligence and Humanized Computing 11, no. 2 (2019): 663–74. http://dx.doi.org/10.1007/s12652-019-01377-0.

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Nakkhasen, Warud, Teerapan Jodnok, and Ronnason Chinram. "Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals." AIMS Mathematics 9, no. 12 (2024): 35800–35822. https://doi.org/10.3934/math.20241698.

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<p>The concept of Fermatean fuzzy sets was introduced by Senapati and Yager in 2019 as a generalization of fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. In this article, we apply the notions of Fermatean fuzzy left (resp., right) hyperideals and Fermatean fuzzy (resp., generalized) bi-hyperideals in semihypergroups to characterize intra-regular semihypergroups, such as $ S $ is an intra-regular semihypergroup if and only if $ \mathcal{L}\cap\mathcal{R}\subseteq \mathcal{L}\circ\mathcal{R} $, for every Fermatean fuzzy left hyperideal $ \mathcal{L} $ and Fermatean fuzz

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V. Chitra. "Fermatean Picture Fuzzy Sets." Advances in Nonlinear Variational Inequalities 28, no. 1s (2024): 390–99. https://doi.org/10.52783/anvi.v28.2441.

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This paper introduces the concept of the Fermatean Picture Fuzzy Set (FPFS). We define several operations on these set. Additionally, we establish the concepts of images and preimages within the context of FPFS. Finally, we extend our discussion to the Fermatean Picture fuzzy topological space and define the properties using the theorems.

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Prasad, Archana Kumari, Mahima Thakur, Jyoti Pandey Bajpai, and Samajh Singh Thakur. "MAPPINGS ON FERMATEAN FUZZY SOFT CLASSES." South East Asian J. of Mathematics and Mathematical Sciences 20, no. 01 (2024): 197–210. http://dx.doi.org/10.56827/seajmms.2024.2001.15.

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This paper defined mappings on Fermatean fuzzy soft classes and established some results related to images and inverse images of Fermatean fuzzy soft sets under these mappings. Further Fermatean fuzzy soft continuous , Fermatean fuzzy soft open and Fermatean fuzzy soft closed mappings in Fermatean fuzzy soft topological spaces are created and established some theorems related their properties and characterizations.

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I., Silambarasan. "New operators for Fermatean fuzzy sets." Annals of Communications in Mathematics 3, no. 2 (2020): 116–31. https://doi.org/10.5281/zenodo.10046474.

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In this paper, we define some new operators[(A@B), (A$B), (A#B), (A∗ B), (A → B)] of Fermatean fuzzy sets. Then we discuss several properties of these operators. Further we prove necessity and possibility operators of Fermatean fuzzy sets and investigates the algebraic properties. Finally, we have identified and proved several of these properties, particularly those involving the operator A → B defined as Fermatean fuzzy implication with other operators.

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Gunjan, Manish Kumar, Amal Kumar Adak, and Davood Darvishi Salookolaei. "Fermatean Fuzzy Artinian and Noetherian Rings." Asian Research Journal of Mathematics 21, no. 5 (2025): 179–90. https://doi.org/10.9734/arjom/2025/v21i5933.

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This paper introduces and investigates the concepts of Fermatean fuzzy Artinian and Noetherian rings,extending classical ring-theoretic chain conditions into the framework of Fermatean fuzzy logic. We define Fermatean fuzzy left ideals and characterize the notions of Fermatean fuzzy left Artinian and Noetherian rings via descending and ascending chain conditions, respectively. We establish several structural properties, including the behavior of Fermatean fuzzy level subsets under ring homomorphisms, and the finiteness of the image sets of membership and non-membership degrees in Fermatean fuz

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Ruan, Chuanyang, and Lin Yan. "Fermatean Probabilistic Hesitant Fuzzy Power Bonferroni Aggregation Operators with Dual Probabilistic Information and Their Application in Green Supplier Selection." Axioms 13, no. 9 (2024): 602. http://dx.doi.org/10.3390/axioms13090602.

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In the realm of management decision-making, the selection of green suppliers has long been a complex issue. Companies must take a holistic approach, evaluating potential suppliers based on their capabilities, economic viability, and environmental impact. The decision-making process, fraught with intricacies and uncertainties, urgently demands the development of a scientifically sound and efficient method for guidance. Since the concept of Fermatean fuzzy sets (FFSs) was proposed, it has been proved to be an effective tool for solving multi-attribute decision-making (MADM) problems in complicat

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Sahoo, Laxminarayan. "Some Score Functions on Fermatean Fuzzy Sets and Its Application to Bride Selection Based on TOPSIS Method." International Journal of Fuzzy System Applications 10, no. 3 (2021): 18–29. http://dx.doi.org/10.4018/ijfsa.2021070102.

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The aim of this paper is to propose some score functions for the fruitful ranking of fermatean fuzzy sets (FFSs) and fermatean fuzzy TOPSIS method based on proposed score functions. fermatean fuzzy sets proposed by Senapati and Yager can handle uncertain information more easily in the process of multi-criteria decision making (MCDM). In this paper, the authors have proposed three newly improved score functions for effective ranking of fermatean fuzzy sets. Here, they have applied the proposed score function to calculate the separation measure of each alternative from the positive and negative

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Gonul Bilgin, Nazmiye, Dragan Pamučar, and Muhammad Riaz. "Fermatean Neutrosophic Topological Spaces and an Application of Neutrosophic Kano Method." Symmetry 14, no. 11 (2022): 2442. http://dx.doi.org/10.3390/sym14112442.

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The main objective of this paper is to redefine the concept of Fermatean neutrosophic sets as well as to introduce topological structure on Fermatean neutrosophic sets. The idea of Fermatean neutrosophic sets is the hybrid model of Fermatean fuzzy sets and neutrosophic sets to utilize key features of these structures. Topological data analysis for indeterminate and uncertain information is a rapidly developing field. Motivated by this recent trend, the idea of Fermatean neutrosophic topology is proposed, which is an extension of neutrosophic topology and Fermatean fuzzy topology. Some fundamen

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10

Garg, Harish, Gulfam Shahzadi, and Muhammad Akram. "Decision-Making Analysis Based on Fermatean Fuzzy Yager Aggregation Operators with Application in COVID-19 Testing Facility." Mathematical Problems in Engineering 2020 (August 18, 2020): 1–16. http://dx.doi.org/10.1155/2020/7279027.

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This research article is devoted to establish some general aggregation operators, based on Yager’s t-norm and t-conorm, to cumulate the Fermatean fuzzy data in decision-making environments. The Fermatean fuzzy sets (FFSs), an extension of the orthopair fuzzy sets, are characterized by both membership degree (MD) and nonmembership degree (NMD) that enable them to serve as an excellent tool to represent inexact human opinions in the decision-making process. In this article, the valuable properties of the FFS are merged with the Yager operator to propose six new operators, namely, Fermatean fuzzy

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Areen, Areen, Areen Al .., Hamzeh .., Belal .., and Rawan Almarashdeh. "Intuitionistic Possibility Fermatean Fuzzy Soft Sets." International Journal of Neutrosophic Science 24, no. 1 (2024): 131–46. http://dx.doi.org/10.54216/ijns.240212.

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In this study, we introduce a new concept by making Possibility Fermatean fuzzy soft sets into a more general concept, namely Intuitionistic Possibility Fermatean fuzzy soft sets. We present examples of the application of this theory to a decision-making problem. From a theoretical point of view, we review the basic properties of this model and define the operations essential to its framework. Comprehensive definitions of complement, union, and intersection, as well as AND and OR operations are meticulously presented. As a transition from theory to practical application within this innovative

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Saeed, Muhammad, Imrana Shafique, and Hatıra G¨unerhan. "Fundamentals of Fermatean Neutrosophic Soft Set with Application in Decision Making Problem." International Journal of Mathematics, Statistics, and Computer Science 3 (January 5, 2025): 294–312. https://doi.org/10.59543/ijmscs.v3i.10625.

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The classical set theory based on crisp sets is not able to deal with uncertainties which is a common feature of various real-world problems. This problem is solved using modified forms of sets such as fuzzy sets, Intuitionistic fuzzy sets, neutrosophic sets, soft sets and hypersoft sets and others along with their hybrids. In this paper, a modified hybrid of soft set named Fermatean Neutrosophic Soft set ($FrNSS$) is established. Basic entities of set theory including subsets, null set, universal set along with different operators are defined. With respect to these operators, the algebraic st

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Fahmi, Aliya, A. Khan, T. Abdeljawad, M. A. S. hassan, and D. K. Almutairid. "Einstein Aggregation Operators with Cubic Fermatean Fuzzy Sets." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5891. https://doi.org/10.29020/nybg.ejpam.v18i2.5891.

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The study goals are to address the compound, multi-criteria decision-making tests associated with choosing the ideal scope for electric vehicle charging stations. This difficulty ascends due to the interaction of numerous quantitative and qualitative issues and the uncertainty characteristic in such assessments. Aliya et al. [37] introduced the concept of the cubic fermatean fuzzy sets, including their operational laws and score function. We develop the three aggregation operators including CFEFWA, CFEFOWA, and CFEFHWA operators with the cubic fermatean fuzzy set. Furthermore, uncertainty usua

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Ejegwa, P. A., G. Muhiuddin, E. A. Algehyne, J. M. Agbetayo, and D. Al-Kadi. "An Enhanced Fermatean Fuzzy Composition Relation Based on a Maximum-Average Approach and Its Application in Diagnostic Analysis." Journal of Mathematics 2022 (May 30, 2022): 1–12. http://dx.doi.org/10.1155/2022/1786221.

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The idea of composition relations on Fermatean fuzzy sets based on the maximum-extreme values approach has been investigated and applied in decision making problems. However, from the perspective of the measure of central tendency, this approach is not reliable because of the information loss occasioned by the use of extreme values. Based on this limitation, we introduce an enhanced Fermatean fuzzy composition relation with a better performance rating based on the maximum-average approach. An easy-to-follow algorithm based on this approach is presented with numerical computations. An applicati

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Palanikumar, Murugan, Nasreen Kausar, Harish Garg, Shams Forruque Ahmed, and Cuauhtemoc Samaniego. "Robot sensors process based on generalized Fermatean normal different aggregation operators framework." AIMS Mathematics 8, no. 7 (2023): 16252–77. http://dx.doi.org/10.3934/math.2023832.

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<abstract><p>Novel methods for multiple attribute decision-making problems are presented in this paper using Type-Ⅱ Fermatean normal numbers. Type-Ⅱ Fermatean fuzzy sets are developed by further generalizing Fermatean fuzzy sets and neutrosophic sets. The Type-Ⅱ Fermatean fuzzy sets with basic aggregation operators are constructed. The concept of a Type-Ⅱ Fermatean normal number is compatible with both commutative and associative rules. This article presents a new proposal for Type-Ⅱ Fermatean normal weighted averaging, Type-Ⅱ Fermatean normal weighted geometric averaging, Type-Ⅱ g

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Xu, Changlin, and Juhong Shen. "Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets." Journal of Intelligent & Fuzzy Systems 41, no. 6 (2021): 5847–63. http://dx.doi.org/10.3233/jifs-201557.

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Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures

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Chitra, V., and B. Maheswari. "Picture Logic Operators and Implications on Fermatean Picture Fuzzy Sets." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 193–207. https://doi.org/10.56557/ajomcor/2025/v32i29215.

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Fermatean Picture Fuzzy sets (FPFS) represent an advanced extension of Picture Fuzzy sets and Pythagorean Picture Fuzzy sets, aimed at enhancing uncertainty modeling through the principles of Fermatean geometry. FPFS deliver heightened precision and adaptability rendering them highly applicable to complex decision-making, voting analysis and computational intelligence tasks. This work details the mathematical formulation of FPFS which explores their fundamental operations and demonstrates their practical relevance via numerical examples. The results highlight the efficacy of FPFS as a dynamic

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Sahoo, Laxminarayan. "Similarity measures for Fermatean fuzzy sets and its applications in group decision-making." Decision Science Letters 11, no. 2 (2022): 167–80. http://dx.doi.org/10.5267/j.dsl.2021.11.003.

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The intention of this paper is to propose some similarity measures between Fermatean fuzzy sets (FFSs). Firstly, we propose some score based similarity measures for finding similarity measures of FFSs and also propose score based cosine similarity measures between FFSs. Furthermore, we introduce three newly scored functions for effective uses of Fermatean fuzzy sets and discuss some relevant properties of cosine similarity measure. Fermatean fuzzy sets introduced by Senapati and Yager can manipulate uncertain information more easily in the process of multi-criteria decision making (MCDM) and g

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Akram, Muhammad, Syed Muhammad Umer Shah, Mohammed M. Ali Al-Shamiri, and S. A. Edalatpanah. "Fractional transportation problem under interval-valued Fermatean fuzzy sets." AIMS Mathematics 7, no. 9 (2022): 17327–48. http://dx.doi.org/10.3934/math.2022954.

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<abstract><p>The concept of an interval-valued Fermatean fuzzy set (IVFFS), an extension of Fermatean fuzzy sets, is a more resilient and reliable tool for dealing with uncertain and incomplete data in practical applications. The purpose of this paper is to define a triangular interval-valued Fermatean fuzzy number (TIVFFN) and its arithmetic operations. Fractional transportation problems (FTPs) have important implications for cost reduction and service improvement in logistics and supply management. However, in practical problems, the parameters in the model are not precise due to

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20

Wadei, Wadei, M. M.Kaviyarasu, and Rajeshwari M. "Operations on Translation of Fermatean Neutrosophic INK-Algebra." International Journal of Neutrosophic Science 25, no. 4 (2025): 135–46. https://doi.org/10.54216/ijns.250411.

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This paper investigates the theoretical basis of fermatean neutrosophic sets, which were first introduced by Smarandache, to clarify the relationship between single-valued fermatean neutrosophic sets and their role as specific subsets in the wider context of fermatean neutrosophic sets, particularly in science and engineering. This study investigates fermatean neutrosophic INK-ideals within INK-algebras using the translation concept, which is proposed as an extension of intuitionistic fuzzy sets. First, translation fermatean neutrosophic INKalgebras are presented and their fundamental features

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Aruchsamy, Revathy, Inthumathi Velusamy, Krishnaprakash Sanmugavel, Prasantha Bharathi Dhandapani, and Kavikumar Ramasamy. "Generalization of Fermatean Fuzzy Set and Implementation of Fermatean Fuzzy PROMETHEE II Method for Decision Making via PROMETHEE GAIA." Axioms 13, no. 6 (2024): 408. http://dx.doi.org/10.3390/axioms13060408.

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The Fermatean fuzzy set, in contrast to other generalizations of fuzzy sets like PFS and IFS, has a wide range of acceptance for both MF and NMF. In light of this, the Fermatean fuzzy set performs as an efficient, flexible, and comprehensive representation in situations that lack certainty. Here, the weaker forms of Fermatean fuzzy sets are introduced, and their traits are analyzed. Decomposition and continuity of the Fermatean fuzzy α-open set are also accustomed. With the goal of safeguarding our green environment, hiring the best supplier is of the utmost significance in the construction in

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Fahmi, Aliya, Muhammad Arshad Shehzad Hassan, Aziz Khan, Thabet Abdeljawad, and D. K. Almutairi. "A Bipolar Fermatean Fuzzy Hamacher Approach to Group Decision-Making for Electric Waste." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5691. https://doi.org/10.29020/nybg.ejpam.v18i1.5691.

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The paper introduces advanced aggregation operators based on Hamacher operational laws for Bipolar Fermatean Fuzzy sets, addressing complex decision-making problems. In addition, a score function is utilized to evaluate and rank alternatives within the Bipolar Fermatean Fuzzy decision framework, offering a quantitative measure of each alternative’s performance based onthe aggregation results. This score function helps simplify decision-making, particularly in cases involving complex uncertainty and multiple criteria. The proposed operators include the Bipolar Fermatean Fuzzy-Hamacher weighted

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Niu, Wenyao, Yuan Rong, Liying Yu, and Lu Huang. "A Novel Hybrid Group Decision Making Approach Based on EDAS and Regret Theory under a Fermatean Cubic Fuzzy Environment." Mathematics 10, no. 17 (2022): 3116. http://dx.doi.org/10.3390/math10173116.

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Intercity railway is an important system for the development of urban agglomeration, and the site selection of the Line Management Department of Intercity Railway (LMDIR) is a significant task for the railway department when constructing intercity railways. Owing to the complexity and uncertainty during the selection process, we constructed a multiple expert multi-criteria decision making (MEMCDM) method to provide a rational decision support model for a railway management department in the Fermatean cubic fuzzy set context. In this regard, an innovative extension called Fermatean cubic fuzzy

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Akram, Muhammad, Syed Muhammad Umer Shah, Mohammed M. Ali Al-Shamiri, and S. A. Edalatpanah. "Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets." AIMS Mathematics 8, no. 1 (2022): 924–61. http://dx.doi.org/10.3934/math.2023045.

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<abstract><p>Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work

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Akram, Muhammad, G. Muhiuddin, and Gustavo Santos-García. "An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets." Mathematical Biosciences and Engineering 19, no. 7 (2022): 7201–31. http://dx.doi.org/10.3934/mbe.2022340.

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<abstract><p>This paper aims to propose a new decision-making approach retaining the fascinating traits of the conventional VIKOR method in the context of the enrich multidimensional complex Fermatean fuzzy $ N $-soft set. The VIKOR technique is contemplated as the most reliable decision-making approach among others which employs a strategy to identify the compromise solution with advantageous distance from the positive ideal solution possesses maximum majority utility and minimum individual regret. At the same time, the paramount characteristic of the complex Fermatean fuzzy $ N $

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Akram, Muhammad, Naila Ramzan, Anam Luqman, and Gustavo Santos-García. "An integrated MULTIMOORA method with 2-tuple linguistic Fermatean fuzzy sets: Urban quality of life selection application." AIMS Mathematics 8, no. 2 (2022): 2798–828. http://dx.doi.org/10.3934/math.2023147.

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<abstract><p>This article elaborates the enormous theory of MULTIMOORA (multi-objective optimization ratio analysis plus full multiplicative form) method to build up a new outranking approach for the innovative extension of fuzzy set theory, namely, 2-tuple linguistic Fermatean fuzzy sets (2TLFFSs). The main objective of the proposed work is to expand and present the components of MULTIMOORA method in 2-tuple linguistic Fermatean fuzzy framework. The resulted technique is named as 2-tuple linguistic Fermatean fuzzy MULTIMOORA method. This technique is designed to tackle the unclear

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Haq, Iftikhar Ul, Tanzeela Shaheen, Wajid Ali, et al. "Novel Fermatean Fuzzy Aczel–Alsina Model for Investment Strategy Selection." Mathematics 11, no. 14 (2023): 3211. http://dx.doi.org/10.3390/math11143211.

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For choosing the optimal option for multiple issues, the multiattribute decision-making (MADM) technique within a Fermatean fuzzy environment is a well-known and significant method. This paper presents a novel superiority inferiority ranking (SIR) approach for Fermatean fuzzy sets in group decision-making using multicriteria to reduce investment risk. This approach aims to evaluate the strategies for selecting the optimal investment company. The SIR method is depicted, and its effectiveness in decision-making is explored. In this manuscript, we develop new types of Aczel–Alsina operations on t

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M Sngeetha, T. Mummoorthy. "A Fermatean Fuzzy Environment is used in Transportation Problems to Extend a New Score Function." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 1002–20. https://doi.org/10.52783/cana.v32.4097.

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Since the economy and environment are in a state of instability. In a transportation difficulty, it is no longer possible to determine supply, demand, and transportation costs. This work aims to explore transportation, including supply, demand, and transportation costs expressed as FFNs. However, Pythagorean fuzzy numbers or generalized fuzzy numbers are used as the parameters in each of these recommendations. It is simpler to deal with uncertain data when making decisions because of the innovative idea of Fermatean fuzzy sets. For the first time, we have overcome the transportation problem wi

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Zhan, Mengyao, and Mu Zhang. "The Extended TOPSIS Method for MAGDM with Probabilistic Hesitant Fermatean Fuzzy Linguistic Term Set." Journal of Risk Analysis and Crisis Response 15, no. 2 (2025): 14. https://doi.org/10.54560/jracr.v15i2.663.

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To tackle the uncertainties in language-based evaluation and the limitations of traditional methods in capturing expert preferences within complex decision-making scenarios, this study introduces an extended TOPSIS method for MAGDM with PHFFLTSs. This novel method leverages the advantages of probabilistic linguistic term sets, hesitant fuzzy linguistic term sets, and Fermatean fuzzy sets by constructing a probabilistic hesitant Fermatean fuzzy linguistic term decision matrix. This matrix enables experts to articulate their confidence in various linguistic terms while retaining a hesitant stanc

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Shanthi, S. Anita, and K. G. Basavaraju. "Estimating the overall efficiency of storage batteries in Fermatean picture fuzzy environment." E3S Web of Conferences 405 (2023): 02028. http://dx.doi.org/10.1051/e3sconf/202340502028.

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Electricity storage devices play a very vital role in eﬃcient energy management. Storage technologies vary depending on the speciﬁc needs and applications. Battery is a electric storage system which converts chemical energy into electrical energy and possess some speciﬁc parameters that characterize them. Here, four types of storage batteries are evaluated based on their eﬃciency, cost, life span and energy density properties using COPRAS and ARAS methods on Fermatean picture fuzzy sets. Firstly a decision matrix is constructed using Fermatean picture fuzzy sets and it is normalized. Entropy m

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Broumi, Said, S. krishna Prabha, and Vakkas Uluçay. "Interval-Valued Fermatean Neutrosophic Shortest Path Problem via Score Function." Neutrosophic Systems with Applications 11 (October 13, 2023): 1–10. http://dx.doi.org/10.61356/j.nswa.2023.83.

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Contemporary mathematical techniques have been crafted to address the uncertainty of numerous real-world settings, including Fermatean neutrosophic fuzzy set theory. Fermatean neutrosophic fuzzy set is an extension of combining Fermatean and neutrosophic sets. Fermatean neutrosophic set was developed to enable the analytical management of ambiguous data from relatively typical real-world decision-making scenarios. Decision-makers find it challenging to determine the degree of membership (MG) and non-membership (NG) with sharp values due to the insufficient data provided. Intervals MG and NG ar

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admin, admin, Hamzeh Zureigat, Belal Batiha, Areen Al Al-khateeb, and Abedallah Al Al-shboul. "Fermatean Neutrosophic Soft Set." International Journal of Neutrosophic Science 25, no. 3 (2025): 469–88. http://dx.doi.org/10.54216/ijns.250339.

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This paper aims to introduce a new concept which is Fermatean Neutrosophic Soft Set (FNSS), which is a combination of the Neutrosophic soft sets and Fermatean Fuzzy Sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of FNSS is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the most attractive laptop based on a computer simulation report. Finally, a comparative analysis between the initiated FNSS model an

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Zhou, Liang, Sadhna Chaudhary, Mukesh Kumar Sharma, Arvind Dhaka, and Amita Nandal. "Artificial Neural Network Dual Hesitant Fermatean Fuzzy Implementation in Transportation of COVID-19 Vaccine." Journal of Organizational and End User Computing 35, no. 2 (2023): 1–23. http://dx.doi.org/10.4018/joeuc.321169.

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This article, in order to address impreciseness, initiated the notion of dual hesitant fermatean fuzzy sets (DHFFSs), as a generalization of the combination of dual hesitant fuzzy set (DHFS), dual hesitant Pythagorean fuzzy set (DHPFS) and Fermatean fuzzy set (FFS). The authors defined the fundamental set of operations for DHFFS. Additionally, the authors have also proposed two ranking functions and an accuracy function for the ordering of this novel set. In order to facilitate the pragmatic implementation of DHFFS in optimization, the authors formulated three types of transportation problem w

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Bhatia, Mansi, H. D. Arora, and Anjali Naithani. "Some New Correlation Coefficient Measures Based on Fermatean Fuzzy Sets using Decision Making Approach in Pattern Analysis and Supplier Selection." International Journal of Mathematical, Engineering and Management Sciences 8, no. 2 (2023): 245–63. http://dx.doi.org/10.33889/ijmems.2023.8.2.015.

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Fermatean fuzzy set (FFS) is an effective tool to depict expert reasoning information in the decision‐making process than fuzzy sets (FS), intuitionistic fuzzy sets (IFS), and Pythagorean fuzzy sets (PFS). Keeping in mind the importance of correlation coefficient and application in medical diagnosis, decision making and pattern recognition, several studies on correlation coefficient measures have been proposed in the literature. As there does not exist any study concerning correlation coefficient measures for FFS, in this communication, we propose novel entropy-correlation measures for Fermate

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Althuniyan, Najla, Abedallah Al-shboul, Sarah Aljohani, et al. "Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution." Axioms 14, no. 5 (2025): 381. https://doi.org/10.3390/axioms14050381.

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This study addresses the challenge of effectively modeling uncertainty and hesitation in complex decision-making environments, where traditional fuzzy and vague set models often fall short. To overcome these limitations, we propose the Fermatean neutrosophic vague soft set (FNVSS), an advanced extension that integrates the concepts of neutrosophic sets with Fermatean membership functions into the framework of vague sets. The FNVSS model enhances the representation of truth, indeterminacy, and falsity degrees, providing greater flexibility and resilience in capturing ambiguous and imprecise inf

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Shahzadi, Gulfam, Anam Luqman, and Mohammed M. Ali Al-Shamiri. "The Extended MOORA Method Based on Fermatean Fuzzy Information." Mathematical Problems in Engineering 2022 (September 29, 2022): 1–15. http://dx.doi.org/10.1155/2022/7595872.

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The intelligent manufacturing system (IMS) is a framework that improves productivity by organizing the logical features involved in manufacturing. The procedure of intelligent manufacturing owns the capability to self-control the manufacturing of the products according to the specifications of design. Different IMSs are designed to deal with continuous changes in market which can adjust to make the modified environment easier. The central idea of this research article is to select an IMS that can adapt the updated situations faster than the existing competing systems and provide higher benefit

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Ruan, Chuanyang, Xiangjing Chen, and Lin Yan. "Fermatean Hesitant Fuzzy Multi-Attribute Decision-Making Method with Probabilistic Information and Its Application." Axioms 13, no. 7 (2024): 456. http://dx.doi.org/10.3390/axioms13070456.

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When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method

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Voskoglou, Michael Gr. "Q- Rung Orthopair Fuzzy Sets and Topological Spaces." Uncertainty 1, no. 1 (2024): 11–16. http://dx.doi.org/10.31559/uncertainty2024.1.1.2.

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The concept of q-rung orthopair fuzzy set, where q is a positive integer, introduced by Yager, is studied in the present paper and fundamental properties of it are examined. The concept of the 1-rung orthopair fuzzy set coincides with Atanassov&rsquo;s intuitionistic fuzzy set, a 2-rung orthopair fuzzy set is known as a Pythagorean fuzzy set, while a 3-rung orthopair fuzzy set is referred to as a Fermatean fuzzy set. Also the ordinary notion of topological space is extended in this work to a q-rung orthopair fuzzy environment, as well as the fundamental properties and concepts of convergen

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Hamadneh, Tareq, Hariwan Z. Ibrahim, Mayada Abualhomos, et al. "Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator." Symmetry 15, no. 8 (2023): 1617. http://dx.doi.org/10.3390/sym15081617.

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A significant addition to fuzzy set theory for expressing uncertain data is an n,m-th power root fuzzy set. Compared to the nth power root, Fermatean, Pythagorean, and intuitionistic fuzzy sets, n,m-th power root fuzzy sets can cover more uncertain situations due to their greater range of displayed membership grades. When discussing the symmetry between two or more objects, the innovative concept of an n,m-th power root fuzzy set over dual universes is more flexible than the current notion of an intuitionistic fuzzy set, a Pythagorean fuzzy set, and a nth power root fuzzy set. In this study, w

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Kumam, Wiyada, Konrawut Khammahawong, Muhammad Jabir Khan, Thanatporn Bantaojai, and Supak Phiangsungnoen. "Fermatean Fuzzy Divergences and Their Applications to Decision-making and Pattern Recognition." Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications 2, no. 1 (2023): 31–53. http://dx.doi.org/10.58715/ncao.2023.2.2.

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Fermatean fuzzy sets (FFS) generalized the Intuitionistic fuzzy set and Pythagorean fuzzy set in terms of more space available to choose orthopairs. The manuscript provides Chi-square and Canberra divergence measures for FFSs. Divergence measurements’ additional characteristics are looked into to ensure good performance. The entropy and dissimilarity measures from the suggested divergence measures are derived. A technique is developed to transform the real or fuzzy data into Fermatean fuzzy data. An empirically successful VIKOR method is extended for FFSs. The Australasian New Car Assessment P

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Verma, Rajkumar. "A Decision-Making Approach Based on New Aggregation Operators under Fermatean Fuzzy Linguistic Information Environment." Axioms 10, no. 2 (2021): 113. http://dx.doi.org/10.3390/axioms10020113.

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Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors i

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Arindam, Arindam, Said Broumi, Ranjan Kumar, and Jayanta Pratihar. "Fermatean Shortest Route Problem with Interval Fermatean Neutrosophic Fuzzy Arc Length: Formulation and a Modified Dijkstra’s Algorithm." International Journal of Neutrosophic Science 23, no. 3 (2024): 288–95. http://dx.doi.org/10.54216/ijns.230323.

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Dijkstra’s algorithm (DA) is a very popular approach for finding the shortest route (SR) in the shortest route problem (SRP). The SRP becomes a challenging and complex problem in real life scenarios. The Fermatean neutrosophic set is a mathematical model that combines Fermatean sets with neutrosophic sets. It can handle the unclear, ambiguous, inconsistent, confusing, and uncertain information that comes from real-world problems. Decision-makers face difficulty accurately determining the precise membership (MG) and non membership levels due to the lack of appropriate data available. The FNS ca

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A., Revathy, Inthumathi V., Krishnaprakash S., Anandakumar H., and Arifmohammed K. M. "The Characteristics of Circular Fermatean Fuzzy Sets and Multicriteria Decision-Making Based on the Fermatean Fuzzy t-Norm and t-Conorm." Applied Computational Intelligence and Soft Computing 2024 (February 10, 2024): 1–18. http://dx.doi.org/10.1155/2024/6974363.

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When diverse decision makers are involved in the decision-making process, taking average of decision values might not reflect an accurate point of view. To overcome such a scenario, the circular Fermatean fuzzy (CFF) set, an advancement of the Fermatean fuzzy (FF) set, and the interval-valued Fermatean fuzzy set (IVFFS) are introduced in this current study. The proposed CFF set is a circle with a centre as association value (AV) and nonassociation value (NAV) with a radius at most equal to 2. It is built in such a way that it covers all the decision makers’ opinion value through a circle. Due

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Ashraf, Shahzaib, Attaullah, Muhammad Naeem, Asghar Khan, Noor Rehman, and M. K. Pandit. "Novel Information Measures for Fermatean Fuzzy Sets and Their Applications to Pattern Recognition and Medical Diagnosis." Computational Intelligence and Neuroscience 2023 (March 8, 2023): 1–19. http://dx.doi.org/10.1155/2023/9273239.

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Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in

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Xue, Yige, and Yong Deng. "Extending Set Measures to Orthopair Fuzzy Sets." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 30, no. 01 (2022): 63–91. http://dx.doi.org/10.1142/s0218488522500040.

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Yager have proposed the extending set measures to Pythagorean fuzzy sets, which is able to efficiently solve the problems of uncertain information representation in Pythagorean fuzzy environment. However, the Pythagorean fuzzy sets represent a limited range of fields, while the q-rung orthopair fuzzy sets can represent many fuzzy sets, including the Pythagorean fuzzy sets, Fermatean fuzzy sets, and intuitionistic fuzzy sets. In order to extend the extending set measures to Pythagorean fuzzy sets to a broader range, the paper proposes the extending set measures to orthopair fuzzy sets, which ca

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Wang, Huijuan, Xin Wang, and Lidong Wang. "Multicriteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms." Complexity 2019 (December 20, 2019): 1–19. http://dx.doi.org/10.1155/2019/5705907.

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The study is concerned with the representation and aggregation of complex uncertainty information. First, the concept of hesitant Fermatean 2-tuple linguistic sets (HF2TLSs) is introduced for characterizing an individual’s imprecision preferences and assessing information by combining 2-tuple linguistic terms and Fermatean fuzzy sets. The advantage of hesitant Fermatean 2-tuple linguistic information is that it can handle higher levels of uncertainty and express the decision-makers’ hesitancy. Second, we extend Bonferroni mean (BM) operators under the background of HF2TLSs for the sake of thei

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Satpal Singh, Satish Kumar. "An Innovative Distance Measure for Picture Fuzzy Sets and Applications in Medical Diagnosis and Pattern Analysis." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 1472–96. https://doi.org/10.52783/cana.v32.4171.

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In this paper, we proposed a novel distance measure and applied on picture fuzzy sets which have the various applications in uncertain problems that cannot be solved easily by fuzzy set, intuitionistic fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, ortho-pair fuzzy sets easily. We can explore these sets with the help of problems in the field of personnel selection, pattern analysis, medical diagnosis, or human voting etc. This field type of problem required the answer in the form of yes, no, refusal and abstain. The distance measures play an important role for comparing the picture

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Kirişci, Murat. "Risk Assessment for Breast Cancer with Integrated Group Decision-Making Method." Fundamentals of Contemporary Mathematical Sciences 6, no. 1 (2025): 1–18. https://doi.org/10.54974/fcmathsci.1374962.

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The most prevalent invasive malignancy in women is breast cancer. The second most common cause of cancer deaths in women, behind lung cancer, is breast cancer. It begins with developing a tiny tumor or mass and spreads from breast cells, primarily in the milk ducts (ductal carcinoma) or glands (lobular carcinoma). Every woman needs to be aware of her risk of developing breast cancer to be proactive about risk reduction measures and for better care of the disease, even though the causes of breast cancer are not fully known. Numerous variables that can either raise or decrease the likelihood of

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Deng, Zhan, and Jianyu Wang. "New distance measure for Fermatean fuzzy sets and its application." International Journal of Intelligent Systems 37, no. 3 (2021): 1903–30. http://dx.doi.org/10.1002/int.22760.

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S, Jeevaraj. "Ordering of interval-valued Fermatean fuzzy sets and its applications." Expert Systems with Applications 185 (December 2021): 115613. http://dx.doi.org/10.1016/j.eswa.2021.115613.

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