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Journal articles on the topic 'Soft Fuzzy Quotient Group'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Dr., S. V. Manemaran *1 &. Dr. R. Nagarajan2. "APPLICATIONS OF STEP N-FUZZY FACTOR GROUP UNDER FUZZY VERSION." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 7 (2019): 105–17. https://doi.org/10.5281/zenodo.3354318.

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In this paper, we define the notion of Step N-Fuzzy Soft subgroup and investigate the condition under which a Fuzzy Soft subgroup is Step N-Fuzzy Soft subgroup. We introduce the notion of Step N-Fuzzy Soft cosets and establish their algebraic properties. We also initiate the study of Step N-Fuzzy Soft normal subgroups and quotient group with respect to Step N-Fuzzy Soft normal subgroup and prove some of their various group theoretic properties.

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S., Subramanian, and Seethalakshmi E. "CERTAIN APPLICATIONS OF P- FUZZY SOFT STRUCTURES." International Journal of Applied and Advanced Scientific Research 2, no. 2 (2017): 294–98. https://doi.org/10.5281/zenodo.1115610.

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In this paper, we investigate the notion of P-fuzzy soft intersection groups which is a generalization of that fuzzy soft groups is provided. By introducing the notion soft fuzzy cosets, soft fuzzy quotient groups based on P-fuzzy soft intersection ideals are established. Finally, isomorphism theorems of   P-fuzzy soft intersection groups related to invariant fuzzy soft sets are discussed.

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Dehghan, O. R. "Quotient bipolar fuzzy soft sets of hypervector spaces and bipolar fuzzy soft sets of quotient hypervector spaces." Journal of Algebraic Hyperstructures and Logical Algebras 4, no. 2 (2023): 67–90. http://dx.doi.org/10.61838/kman.jahla.4.2.5.

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In this paper, two related quotient structures are investigated utilizing the concept of coset. At first, a new hypervector space F/V = (F/V,\circ,\circledcirc,K) is created, which is composed of all cosets of a bipolar fuzzy soft set (F;A) over a hypervector space V . Then it will be shown that dim F/V = dim V/W, where the quotient hypervector space V/W includes all cosets of an especial subhyperspace W of V. Also, three bipolar fuzzy soft sets over the quotient hypervector space V/W are presented and in this way some new bipolar fuzzy soft hypervector spaces are defined.

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Tarmizi, Mahfuz, and Saman Abdurrahman. "GRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 13, no. 1 (2019): 1. http://dx.doi.org/10.20527/epsilon.v13i1.1240.

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A Quotient group is a set which contains coset members and satisfies group definition. These cosets are formed by group and its normal subgroup. A set which contains fuzzy coset members is also called a quotient group. These fuzzy cosets are formed by a group and its fuzzy normal subgroup. The purpose of this research is to explain quotient groups induced by fuzzy normal subgroups and isomorphic between them. This research construct sets which contain fuzzy coset members, define an operation between fuzzy cosets and prove these sets under an operation between fuzzy coset satisfy group definiti

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Feng, Feng, Hamido Fujita, Young Bae Jun, and Madad Khan. "Decomposition of Fuzzy Soft Sets with Finite Value Spaces." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/902687.

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The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Usingt-level soft sets, we define level equivalent relations and show that

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Karyati, Karyati, and Rifki Chandra Utama. "FUZZY RINGS AND ITS PROPERTIES." Jurnal Sains Dasar 5, no. 1 (2017): 32. http://dx.doi.org/10.21831/jsd.v5i1.12662.

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Abstract One of algebraic structure that involves a binary operation is a group that is defined an un empty set (classical) with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and

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SEZGİN, ASLIHAN, ALEYNA İLGİN, FATIMA ZEHRA KOCAKAYA, ZEYNEP HARE BAŞ, BEYZA ONUR, and FİLİZ ÇITAK. "A REMARKABLE CONTRIBUTION TO SOFT INT-GROUP THEORY VIA A COMPREHENSIVE VIEW OF SOFT COSETS." Journal of Science and Arts 24, no. 4 (2024): 905–34. https://doi.org/10.46939/j.sci.arts-24.4-a13.

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This paper aims to expand soft int-group theory by analyzing its many aspects and structural properties regarding soft cosets and soft quotient groups, which are crucial concepts of the theory. All the characteristics of soft cosets are given in accordance with the properties of classical cosets in abstract algebra, and many interesting analogous results are obtained. It is proved that if an element is in the e-set, then its soft left and right cosets are the same and equal to the soft set itself. The main and remarkable contribution of this paper to the theory is that the relation between the

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8

lakshmi, S. Maha, and A. Solai raju. "Hesitant Fuzzy Soft Group." International Journal of Mathematics Trends and Technology 54, no. 5 (2018): 404–14. http://dx.doi.org/10.14445/22315373/ijmtt-v54p549.

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

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

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Ullah, Aman, Muhammad Ibrahim, and Tareq Saeed. "Fuzzy cosets in AG-groups." AIMS Mathematics 7, no. 3 (2022): 3321–44. http://dx.doi.org/10.3934/math.2022185.

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<abstract><p>In this paper, the notion of fuzzy AG-subgroups is further extended to introduce fuzzy cosets in AG-groups. It is worth mentioning that if $ A $ is any fuzzy AG-subgroup of $ G $, then $ \mu_{A}(xy) = \mu_{A}(yx) $ for all $ x, \, y\in G $, i.e. in AG-groups each fuzzy left coset is a fuzzy right coset and vice versa. Also, fuzzy coset in AG-groups could be empty contrary to fuzzy coset in group theory. However, the order of the nonempty fuzzy coset is the same as the index number $ [G:A] $. Moreover, the notions of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the

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R.Nagarajan, R. Nagarajan, and S. Subramanian S.Subramanian. "Cyclic Fuzzy Neutrosopic Soft Group." International Journal of Scientific Research 3, no. 8 (2012): 234–44. http://dx.doi.org/10.15373/22778179/august2014/68.

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Sarala, N., and B. Suganya. "On Normal Fuzzy Soft Group." International Journal of Mathematics Trends and Technology 10, no. 2 (2014): 70–75. http://dx.doi.org/10.14445/22315373/ijmtt-v10p512.

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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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Masmali, Ibtisam, Umer Shuaib, Abdul Razaq, Areeba Fatima та Ghaliah Alhamzi. "On Fundamental Algebraic Characterizations of μ -Fuzzy Normal Subgroups". Journal of Function Spaces 2022 (19 травня 2022): 1–10. http://dx.doi.org/10.1155/2022/2703489.

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In this article, we present the study of μ -fuzzy subgroups and prove numerous fundamental algebraic attributes of this newly defined notion. We also define the concept of μ -fuzzy normal subgroup and investigate many vital algebraic characteristics of these phenomena. In addition, we characterize the quotient group induced by this particular fuzzy normal subgroup and establish a group isomorphism between the quotient groups G / κ μ and G / κ ∗ μ . Furthermore, we initiate the study of level subgroup, open level subgroup, and tangible subgroup of a μ -fuzzy subgroup and emphasize the significa

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S Mattam, Anju, and Dr Sasi Gopalan. "Factor Group of a Fuzzy Soft Group." IOSR Journal of Mathematics 10, no. 3 (2014): 09–16. http://dx.doi.org/10.9790/5728-10330916.

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Abdurrahman, Saman, Mochammad Idris, Faisal Faisal, Na’imah Hijriati, Threye Threye, and Aprida Siska Lestia. "LEVEL SOFT GROUP AND ITS PROPERTIES." BAREKENG: Jurnal Ilmu Matematika dan Terapan 19, no. 3 (2025): 2263–74. https://doi.org/10.30598/barekengvol19iss3pp2263-2274.

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In this paper, we present an application of fuzzy subset and fuzzy subgroup to a soft set and a soft group, thereby creating a soft set and a soft group within the same group. Furthermore, we refer to the soft and soft groups as level soft sets and level soft groups. We also found out the level of soft sets and the operations on soft sets, such as intersection, union, and subset. We also examine what conditions a fuzzy subgroup and a soft group must meet to form a level soft group. Moreover, we scrutinize the properties of operations on a soft set, specifically intersection, union, and AND, an

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Garg, Harish, Fathima Perveen P A, Sunil Jacob John, and Luis Perez-Dominguez. "Spherical Fuzzy Soft Topology and Its Application in Group Decision-Making Problems." Mathematical Problems in Engineering 2022 (April 26, 2022): 1–19. http://dx.doi.org/10.1155/2022/1007133.

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The spherical fuzzy soft set is a generalized soft set model, which is more realistic, practical, and accurate. It is an extended version of existing fuzzy soft set models that can be used to describe imprecise data in real-world scenarios. The paper seeks to introduce the new concept of spherical fuzzy soft topology defined on spherical fuzzy soft sets. In this work, we define some basic concepts including spherical fuzzy soft basis, spherical fuzzy soft subspace, spherical fuzzy soft interior, spherical fuzzy soft closure, and spherical fuzzy soft boundary. The properties of these defined se

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18

Wang, Jian-qiang, Xin-E. Li, and Xiao-hong Chen. "Hesitant Fuzzy Soft Sets with Application in Multicriteria Group Decision Making Problems." Scientific World Journal 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/806983.

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Soft sets have been regarded as a useful mathematical tool to deal with uncertainty. In recent years, many scholars have shown an intense interest in soft sets and extended standard soft sets to intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, and generalized fuzzy soft sets. In this paper, hesitant fuzzy soft sets are defined by combining fuzzy soft sets with hesitant fuzzy sets. And some operations on hesitant fuzzy soft sets based on Archimedean t-norm and Archimedean t-conorm are defined. Besides, four aggregation operations, such as the HFSWA, HFSWG, GHFSWA, and GHFSWG ope

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Hameed, M. Shazib, Salman Mukhtar, Haq Nawaz Khan, Shahbaz Ali, M. Haris Mateen, and Muhammad Gulzar. "Pythagorean Fuzzy N-Soft Groups." Indonesian Journal of Electrical Engineering and Computer Science 21, no. 2 (2021): 1030–38. https://doi.org/10.11591/ijeecs.v21i2.pp1030-1038.

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We elaborate in this paper a new structure Pythagorean fuzzy N-soft groups which is the generalization of intuitionistic fuzzy soft group initiated by Karaaslan in 2013. In Pythagorean fuzzy N-soft sets concepts of fuzzy sets, soft sets, N-soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets are generalized. We also talk about some elementary basic concepts and operations on Pythagorean fuzzy N-soft sets with the assistance of illusions. We additionally define three different sorts of complements for Pythagor

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20

Yolcu, Adem. "Bipolar Spherical Fuzzy Soft Topology with Applications to Multi-Criteria Group Decision-Making in Buildings Risk Assessment." Symmetry 14, no. 11 (2022): 2362. http://dx.doi.org/10.3390/sym14112362.

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A generalized soft set model that is more accurate, useful, and realistic is the bipolar spherical fuzzy soft set (BSFSs). It is a more developed variant of current fuzzy soft set models that may be applied to characterize erroneous data in practical applications. Bipolar spherical fuzzy soft sets and bipolar spherical fuzzy soft topology are novel ideas that are intended to be introduced in this work. Bipolar spherical fuzzy soft intersection, bipolar spherical fuzzy soft null set, spherical fuzzy soft absolute set, and other operations on bipolar spherical fuzzy soft sets are some of the fun

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BHUNIA, SUPRIYA, and GANESH GHORAI. "An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups." Kragujevac Journal of Mathematics 48, no. 6 (2024): 893–906. http://dx.doi.org/10.46793/kgjmat2406.893b.

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The Pythagorean fuzzy environment is a modern way of depicting uncertainty. The concept of Pythagorean fuzzy semi-level subgroups of any group is described in this paper. The Pythagorean fuzzy order of an element in a Pythagorean fuzzy subgroup is introduced and established various algebraic attributes. The relation between the Pythagorean fuzzy order of an element of a group and the order of that group is established. The Pythagorean fuzzy normalizer and Pythagorean fuzzy centralizer of Pythagorean fuzzy subgroups are discussed. Further, the concept of Pythagorean fuzzy quotient group and the

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V., Ramadas, and Anitha B. "ON PSEUDO COMPATIBLE P-FUZZY SOFT RELATIONS." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2017): 7–11. https://doi.org/10.5281/zenodo.1133940.

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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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Tripathy, B. K., T. R. Sooraj, R. K. Mohanty, and Abhilash Panigrahi. "Group Decision Making Through Interval Valued Intuitionistic Fuzzy Soft Sets." International Journal of Fuzzy System Applications 7, no. 3 (2018): 99–117. http://dx.doi.org/10.4018/ijfsa.2018070106.

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This article describes how the lack of adequate parametrization in some of the earlier uncertainty based models like fuzzy sets, rough sets motivated Molodtsov to introduce a new model in soft set. A suitable combination of individual models leads to hybrid models, which are more efficient than their individual components. So, the authors find the introduction of many hybrid models of soft sets, like the fuzzy soft set (FSS), intuitionistic fuzzy soft sets (IFSS), interval valued fuzzy soft set (IVFSS) and the interval valued intuitionistic fuzzy soft set (IVIFSS). Following the characteristic

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rajan, K. Sunder, A. Senthil kumar та R. Muthu raj. "Homomorphism and Anti Homomorphism of L-Fuzzy Quotient ℓ-Group". International Journal of Mathematics Trends and Technology 30, № 1 (2016): 39–42. http://dx.doi.org/10.14445/22315373/ijmtt-v30p507.

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M.Subha and G. Subbiah. "Group Actions on Intuitionistic Fuzzy Soft G-Modules." International Journal of Fuzzy Mathematical Archive 15, no. 02 (2018): 271–78. http://dx.doi.org/10.22457/ijfma.v15n2a19.

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The main purpose of this paper is to introduce a basic version of intuitionistic fuzzy soft G-modulo theory, which extends the notion of modules by introducing some algebraic structures in soft set. Finally, we investigate some basic properties of maximal intuitionistic fuzzy soft G-modules.

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Riaz, Muhammad, Khalid Naeem, Muhammad Aslam, Deeba Afzal, Fuad Ali Ahmed Almahdi, and Sajjad Shaukat Jamal. "Multi-criteria group decision making with Pythagorean fuzzy soft topology." Journal of Intelligent & Fuzzy Systems 39, no. 5 (2020): 6703–20. http://dx.doi.org/10.3233/jifs-190854.

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Pythagorean fuzzy set (PFS) introduced by Yager (2013) is the extension of intuitionistic fuzzy set (IFS) introduced by Atanassov (1983). PFS is also known as IFS of type-2. Pythagorean fuzzy soft set (PFSS), introduced by Peng et al. (2015) and later studied by Guleria and Bajaj (2019) and Naeem et al. (2019), are very helpful in representing vague information that occurs in real world circumstances. In this article, we introduce the notion of Pythagorean fuzzy soft topology (PFS-topology) defined on Pythagorean fuzzy soft set (PFSS). We define PFS-basis, PFS-subspace, PFS-interior, PFS-closu

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A., Rajakumari, and Sivakumar S. "N-FUZZY SOFT SUBGROUPS OVER IDEAL STRUCTURES." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2018): 165–68. https://doi.org/10.5281/zenodo.1193687.

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In this paper, we introduced the concept of N-fuzzy soft N−fuzzy neutrosopic soft right ideal, N−fuzzy neutrosopic soft (1, 2)−ideal, N−fuzzy neutrosopic soft bi-ideal of a group, N−fuzzy neutrosopic soft subgroupoid and regular groupoid and its properties. An illustrative examples are also given.

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A., Solairaju, and Mahalakshmi S. "A MULTICRITERIA GROUP DECISION MAKING USING BIPOLAR HESITANT FUZZY SOFT A-IDEALS IN BCK/BCI ALGEBRAS." International Journal of Current Research and Modern Education, Special Issue (August 13, 2017): 47–52. https://doi.org/10.5281/zenodo.842232.

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In this paper, we introduce the notion of hesitant set in bipolar fuzzy soft set and studied its relations and properties. Also the notion of bipolar hesitant fuzzy soft subalgebras and soft a-deals is introduced. The relation between the concepts of bipolar hesitant fuzzy set function and soft a-ideals in BCK/BCI algebras are considered. A multicriteria group decision making approach using bipolar hesitant fuzzy soft a-ideal are also proposed.

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Mateen, MUHAMMAD Haris. "Pythagorean Fuzzy N-Soft Groups." Indonesian Journal of Electrical Engineering and Computer Science 21, no. 2 (2021): 1030. http://dx.doi.org/10.11591/ijeecs.v21.i2.pp1030-1038.

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<p>We elaborate in this paper a new structure Pythagorean fuzzy<br />$N$-soft groups which is the generalization of intuitionistic fuzzy<br />soft group initiated by Karaaslan in 2013. In Pythagorean fuzzy<br />N-soft sets concepts of fuzzy sets, soft sets, N-soft sets, fuzzy<br />soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft<br />sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets are<br />generalized. We also talk about some elementary basic concepts and<br />operations on Pythagorean fuzzy N-soft sets with the assistanc

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Sunderrajan, K., M. Suresh, and R. Muthuraj. "Homomorphism and Anti Homomorphism on Multi L-Fuzzy Quotient Group of a Group." International Journal of Mathematics Trends and Technology 23, no. 1 (2015): 33–39. http://dx.doi.org/10.14445/22315373/ijmtt-v23p505.

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Kousar, Sajida, Tahzeeb Saleem, Nasreen Kausar, Dragan Pamucar, and Gezahagne Mulat Addis. "Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3." Computational Intelligence and Neuroscience 2022 (April 28, 2022): 1–11. http://dx.doi.org/10.1155/2022/6847138.

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The lattice-valued intuitionistic fuzzy set was introduced by Gerstenkorn and Tepavcevi as a generalization of both the fuzzy set and the L -fuzzy set by incorporating membership functions, nonmembership functions from a nonempty set X to any lattice L , and lattice homomorphism from L to the interval 0,1 . In this article, lattice-valued intuitionistic fuzzy subgroup type-3 (LIFSG-3) is introduced. Lattice-valued intuitionistic fuzzy type-3 normal subgroups, cosets, and quotient groups are defined, and their group theocratic properties are compared with the concepts in classical group theory.

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Feng, Qinrong, and Xiao Guo. "A Novel Approach to Fuzzy Soft Set-Based Group Decision-Making." Complexity 2018 (July 12, 2018): 1–12. http://dx.doi.org/10.1155/2018/2501489.

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There are many uncertain problems in practical life which need decision-making with soft sets and fuzzy soft sets. The purpose of this paper is to develop an approach to effectively solve the group decision-making problem based on fuzzy soft sets. Firstly, we present an adjustable approach to solve the decision-making problems based on fuzzy soft sets. Then, we introduce knowledge measure and divergence degree based on α-similarity relation to determine the experts’ weights. Further, we develop an effective group decision-making approach with unknown experts’ weights. Finally, sensitivity anal

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Surendra Nath Bhagat, Premansu Sekhar Rath, Anirban Mitra. "Fuzzy Soft Sets in Collaborative Decision-Making: Bridging Uncertainty and Consensus." Cuestiones de Fisioterapia 54, no. 3 (2025): 329–45. https://doi.org/10.48047/zxkyaq40.

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A useful technique for dealing with ambiguity and impreciseness in judgment situations is soft set theory. To assess how well soft sets, fuzzy soft sets, and fuzzy soft sets handle ambiguity and variability, this study investigates their use in a group decision-making framework. Fuzzy soft sets expand the adaptable framework of soft sets by adding degrees of membership, allowing for a more thorough examination of challenging decision-making issues.

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Tchier, Fairouz, Ghous Ali, Muhammad Gulzar, Dragan Pamučar, and Ganesh Ghorai. "A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information." Entropy 23, no. 9 (2021): 1176. http://dx.doi.org/10.3390/e23091176.

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As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft

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Zulqarnain, Rana Muhammad, Imran Siddique, Fahd Jarad, Y. S. Hamed, Khadijah M. Abualnaja, and Aiyared Iampan. "Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets with Their Application in Multiattribute Group Decision-Making." Journal of Function Spaces 2022 (March 31, 2022): 1–21. http://dx.doi.org/10.1155/2022/1358675.

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The Pythagorean fuzzy soft set (PFSS) is the most proficient and manipulative leeway of the Pythagorean fuzzy set (PFS), which contracts with parameterized values of the alternatives. It is a generalized form of the intuitionistic fuzzy soft set (IFSS), which provides healthier and more accurate evaluations through decision-making (DM). The main determination of this research is to prolong the idea of Einstein’s aggregation operators for PFSS. We introduce the Einstein operational laws for Pythagorean fuzzy soft numbers (PFSNs). Based on Einstein operational laws, we construct two novel aggreg

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Rajareega, S., J. Vimala, and D. Preethi. "Complex Intuitionistic Fuzzy Soft Lattice Ordered Group and Its Weighted Distance Measures." Mathematics 8, no. 5 (2020): 705. http://dx.doi.org/10.3390/math8050705.

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In recent years, the complex fuzzy set theory has intensified the attention of many researchers. This paper focuses on developing the algebraic structures pertaining to lattice ordered groups and lattice ordered subgroups for complex intuitionistic fuzzy soft set theory. Furthermore, some of their properties and operations are discussed. In addition, the weighted distance measures between two complex intuitionistic fuzzy soft lattice ordered groups such as weighted hamming, weighted normalized hamming, weighted euclidean and weighted normalized euclidean distance measures were introduced and a

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S., Subramanaian, and Nalini D. "CHARACTERIZATION OF COMPLEX BI FUZZY SOFT SET ON REGULAR SEMI GROUP." International Journal of Advanced Trends in Engineering and Technology 3, no. 1 (2018): 159–63. https://doi.org/10.5281/zenodo.1285145.

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In this article, we define a new structure of complex bi fuzzy soft left ideals (resp., right) of a semi group S, Union and Intersection of ideals is again ideals. Also, we prove the set of all idempotent elements of S from a right zero semi group of S, then C(x) = C(y) for all idempotents elements of x and y of S. If C<sub>1</sub> and C<sub>2 </sub>be a complex bi fuzzy soft left and right ideals of a semi group S, respectively, then C<sub>1</sub> * C<sub>2</sub>  C<sub>1</sub><sup> </sup>C<sub>2</sub><strong>.</strong> For every Complex bi fuzzy soft right ideal C<strong><sub>1</sub></s

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Chen, Huiping, and Yan Liu. "Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Soft Information for Medical Diagnosis Model." Mathematics 12, no. 12 (2024): 1823. http://dx.doi.org/10.3390/math12121823.

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The medical diagnosis of many critical diseases is difficult as it usually requires the combined effort of several doctors. At this time, the process of medical diagnosis is actually a group decision-making (GDM) problem. In group medical diagnosis, considering doctors’ weight information and fusing the interaction relation of symptoms remain open issues. To address this problem, a group decision-making method for intuitionistic fuzzy soft environments is proposed for medical diagnosis because the intuitionistic fuzzy soft set (IFSS) integrates the advantages of the soft set and intuitionistic

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Das, Ajoy Kanti, and Carlos Granados. "FP-intuitionistic multi fuzzy N-soft set and its induced FP-Hesitant N soft set in decision-making." Decision Making: Applications in Management and Engineering 5, no. 1 (2022): 67–89. http://dx.doi.org/10.31181/dmame181221045d.

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Intuitionistic fuzzy sets (IFSs) can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers (DMs). In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. As a result, in this research work, we offer an approach for solving group decision-making problems (GDMPs) with fuzzy parameterized intuitionistic multi fuzzy N-soft set (briefly, FPIMFNSS) of dimension q by introducing its induced fuzzy parameterized hesitant N-soft set (FPHNSS) as an extension of the multi-fuzzy N-s

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Kazancı, Osman, Sarka Hoskova-Mayerova, and Bijan Davvaz. "Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups." Mathematics 10, no. 13 (2022): 2178. http://dx.doi.org/10.3390/math10132178.

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The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. I

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Hayat, Khizar, Raja Aqib Shamim, Hussain AlSalman, Abdu Gumaei, Xiao-Peng Yang, and Muhammad Azeem Akbar. "Group Generalized q-Rung Orthopair Fuzzy Soft Sets: New Aggregation Operators and Their Applications." Mathematical Problems in Engineering 2021 (December 31, 2021): 1–16. http://dx.doi.org/10.1155/2021/5672097.

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In recent years, q-rung orthopair fuzzy sets have been appeared to deal with an increase in the value of q > 1 , which allows obtaining membership and nonmembership grades from a larger area. Practically, it covers those membership and nonmembership grades, which are not in the range of intuitionistic fuzzy sets. The hybrid form of q-rung orthopair fuzzy sets with soft sets have emerged as a useful framework in fuzzy mathematics and decision-makings. In this paper, we presented group generalized q-rung orthopair fuzzy soft sets (GGq-ROFSSs) by using the combination of q-rung orthopair fuzzy

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M. Kaliraja and S. Rumenaka. "M-N Fuzzy Normal Soft Groups." International Journal of Fuzzy Mathematical Archive 13, no. 02 (2017): 159–65. http://dx.doi.org/10.22457/ijfma.v13n2a6.

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In this paper, we have discussed the concept of M-N fuzzy normal soft group, we then define the M-N level subsets of a fuzzy normal soft subgroup and its some elementary properties are also discussed. The presented method in this manuscript is more sensible and also reliable in solving the problems. This method can solve the decision making problems

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Meryline S., Arul Roselet, and Felbin C. Kennedy. "Solution to a Soft Fuzzy Group Decision-Making Problem Involving a Soft Fuzzy Number Valued Information System." Fuzzy Information and Engineering 11, no. 3 (2019): 320–56. http://dx.doi.org/10.1080/16168658.2020.1870339.

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Shahzadi, Gulfam, and Muhammad Akram. "Group decision-making for the selection of an antivirus mask under fermatean fuzzy soft information." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1401–16. http://dx.doi.org/10.3233/jifs-201760.

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With the rapid increase of COVID-19, mostly people are facing antivirus mask shortages. It is necessary to select a good antivirus mask and make it useful for everyone. For maximize the efficacy of the antivirus masks, we propose a decision support algorithm based on the concept of Fermatean fuzzy soft set (FFSfS). The basic purpose of this article is to introduce the notion of FFSfS to deal with problems involving uncertainty and complexity corresponding to various parameters. Here, the valuable properties of FFSfS are merged with the Yager operator to propose four new operators, namely, Ferm

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

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

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Yaylalı Umul, Gözde. "Decision-Making Method That Prioritizes User Ranking by Using Intuitionistic Fuzzy Soft Set." Karadeniz Fen Bilimleri Dergisi 15, no. 2 (2025): 764–86. https://doi.org/10.31466/kfbd.1618462.

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Decision-making holds significant importance in real life applications. To manage uncertainties in practical applications, soft sets, fuzzy sets and fuzzy soft sets are commonly used nowadays. Also, the effectiveness of intuitionistic fuzzy soft sets has been highlighted in numerous studies. In daily life, considering users priorities in decisions always affects the decision, for this reason, user priority ranking is important in a decision-making algorithm. This study aims to address decision-making problems by using fuzzy soft set (FSS) and intuitionistic fuzzy soft set (IFSS) frameworks. A

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Ali, Ghous, G. Muhiuddin, Arooj Adeel, and Muhammad Zain Ul Abidin. "Ranking Effectiveness of COVID-19 Tests Using Fuzzy Bipolar Soft Expert Sets." Mathematical Problems in Engineering 2021 (July 24, 2021): 1–19. http://dx.doi.org/10.1155/2021/5874216.

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The theory of fuzzy bipolar soft sets is an efficient extension of soft sets for depicting the bipolarity of uncertain fuzzy soft information; however, it is limited to a single expert. The present research article introduces the theory of an innovative hybrid model called the fuzzy bipolar soft expert sets, as a natural extension of two existing models (including fuzzy soft expert sets and fuzzy bipolar soft sets). The proposed model is highly suitable for describing the bipolarity of fuzzy soft information having multiple expert opinions. Some fundamental properties of the developed hybrid m

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Palanikumar, M., Aiyared Iampan, Said Broumi, Lejo J. Manavalan, and K. Sundareswari. "Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach." International Journal of Neutrosophic Science 22, no. 1 (2023): 104–13. http://dx.doi.org/10.54216/ijns.220108.

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In contrast to the Pythagorean interval valued fuzzy soft set and the neutrosophic interval valued fuzzy soft set, the Pythagorean neutrosophic interval valued fuzzy soft set is a generalization of these sets. We discuss aggregating PyNIVFS decision matrixes by using aggregated operations. The VIKOR method, which is an extension of neutrosophic fuzzy soft sets, is a powerful method for evaluating multi-criteria group decision making. The score function in this approach is based on the aggregation of the VIKOR method to a PyNIVFSpositive and negative solution. Optimal alternatives are introduce

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Abbasi, Aqsa Zafar, Ayesha Rafiq, Umar Ishtiaq, SanaUllah Saqib, and Salvatore Sessa. "Some Algebraic Characteristics of Bipolar-Valued Fuzzy Subgroups over a Certain Averaging Operator and Its Application in Multi-Criteria Decision Making." International Journal of Analysis and Applications 23 (March 3, 2025): 54. https://doi.org/10.28924/2291-8639-23-2025-54.

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In this manuscript, we introduce the concepts of ψ-bipolar-valued fuzzy set (ψ-BVFS), ψ-bipolar-valued fuzzy normal subgroup (ψ-BVFNSG), cut sets Mψ(υ,χ)(Cυ,χMψ)) of ψ-BVFS and ψ-BVFSG, and bipolar-valued fuzzy cosets (BVF cosets). Further, we explore some algebraic properties of newly defined ψ-BVFSG. In addition, we present some new results of homomorphism and quotient group of ψ-BVFSG. At the end, we provide an application of ψ-BVFS in decision making by using topsis method.

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