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Journal articles on the topic 'Fuzzy Soft Interior Ideal'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

V., Chinnadurai, and Arulmozhi K. "ANTI FUZZY SOFT GAMMA REGULAR SEMIGROUPS." International Journal of Scientific Research and Modern Education 2, no. 1 (2017): 159–70. https://doi.org/10.5281/zenodo.810156.

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In this paper, we have introduce the notion of anti fuzzy soft -semigroups, anti fuzzy soft -ideal, bi-ideal, interior ideal-regular, soft-regular anti fuzzy soft-regular and obtain some interesting properties results and discusse in this paper

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2

Krishna Rao, M. Murali, та B. Venkateswarlu. "TRIPOLAR FUZZY SOFT IDEALS AND TRIPOLAR FUZZY SOFT INTERIOR IDEALS OVER Γ−SEMIRING". Facta Universitatis, Series: Mathematics and Informatics 35, № 1 (2020): 029. http://dx.doi.org/10.22190/fumi2001029k.

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In this paper, we have introduced the notion of tripolar fuzzy soft $\Gamma -$subsemi-ring,tripolar fuzzy soft ideal, tripolar fuzzy soft interior ideals over $\Gamma -$semiring and also studiedsome of their algebraic properties and the relations between them.

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3

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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4

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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5

Dr., R. Ramadoss, and Ramashankari N. "COMPLEX TEMPORAL FUZZY SOFT INTERIOR IDEALS OVER SEMIGROUPS." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2018): 283–87. https://doi.org/10.5281/zenodo.1256852.

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In this paper, we introduce the notion of Complex temporal fuzzy soft semi groups (CTFSG) and its Cartesian product with the help of suitable example, also we define direct product, ideals and prove some results.

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S., Subramanian, and Sathiya S. "ON PRODUCT OF COMPLEX DOUBLE FRAMED FUZZY SOFT STRUCTURES." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2018): 288–92. https://doi.org/10.5281/zenodo.1256856.

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In this paper, we are initiating the study of complex double-framed fuzzy soft semi groups. We define characteristic function of complex double-framed fuzzy soft set direct product and complex double-framed fuzzy soft interior ideals and proved some results.

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7

Arulmozhi, K., V. Chinnadurai, and M. Seenivasan. "Bipolar Fuzzy Soft Hyperideals and Homomorphism of Gamma-Hypersemigroups." International Journal of Engineering & Technology 7, no. 4.10 (2018): 127. http://dx.doi.org/10.14419/ijet.v7i4.10.20822.

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In this paper, we introduce the concept of bipolar fuzzy soft gamma hyperideals in gamma hyper semigroups. We define bipolar fuzzy soft hyper ideals, bi-ideals and interior ideals of gamma hyper semigroups and discuss some properties.

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8

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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9

Habib, Sana, Kashif Habib, Violeta Leoreanu-Fotea, and Faiz Muhammad Khan. "Exploring the Structure of Possibility Multi-Fuzzy Soft Ordered Semigroups Through Interior Ideals." Mathematics 13, no. 2 (2025): 210. https://doi.org/10.3390/math13020210.

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This paper aims to introduce a novel idea of possibility multi-fuzzy soft ordered semigroups for ideals and interior ideals. Various results, formulated as theorems based on these concepts, are presented and further validated with suitable examples. This paper also explores the broad applicability of possibility multi-fuzzy soft ordered semigroups in solving modern decision-making problems. Furthermore, this paper explores various classes of ordered semigroups, such as simple, regular, and intra-regular, using this innovative method. Based on these concepts, some important conclusions are draw

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10

tha, V. Vani, G. Sub biah, and M. Navaneetha krishnan. "Complex Intuitionistic Flexible Fuzzy Soft Interior Ideals Over Semigroups." International Journal of Mathematics Trends and Technology 59, no. 4 (2018): 239–47. http://dx.doi.org/10.14445/22315373/ijmtt-v59p534.

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11

Habib, Sana, Harish Garg, Yufeng Nie, and Faiz Muhammad Khan. "An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application." Mathematics 7, no. 12 (2019): 1183. http://dx.doi.org/10.3390/math7121183.

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The objective of this paper is put forward the novel concept of possibility fuzzy soft ideals and the possibility of fuzzy soft interior ideals. The various results in the form of the theorems with these notions are presented and further validated by suitable examples. In modern life decision-making problems, there is a wide applicability of the possibility fuzzy soft ordered semigroup which has also been constructed in the paper to solve the decision-making process. Elementary and fundamental concepts including regular, intra-regular and simple ordered semigroups in terms of possibility fuzzy

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12

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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13

Anwar, Muhammad Zishan, Shahida Bashir, Muhammad Aslam, and Muhammad Shabir. "Approximations of Intuitionistic Fuzzy Ideals over Dual Spaces by Soft Binary Relations." Journal of Function Spaces 2022 (June 2, 2022): 1–17. http://dx.doi.org/10.1155/2022/3996256.

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The major advantage of this proposed work is to investigate roughness of intuitionistic fuzzy subsemigroups (RIFSs) by using soft relations. In this way, two sets of intuitionistic fuzzy (IF) soft subsemigroups, named lower approximation and upper approximation regarding aftersets and foresets, have been introduced. In RIFSs, incomplete and insufficient information is handled in decision-making problems like symptom diagnosis in medical science. In addition, this new technique is more effective as compared to the previous literature because we use intuitionistic fuzzy set (IFS) instead of fuzz

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14

Abdurrahman, Saman. "INTERIOR IDEAL FUZZY SEMIRING." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 15, no. 2 (2022): 116. http://dx.doi.org/10.20527/epsilon.v15i2.4894.

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Semiring is one of the ring extensions, which eliminates the inverse axiom in the first operation. One of the topics on the semiring is the ideal interior. This study introduces the concept of the ideal interior semiring and the ideal interior fuzzy semiring. Further, it examined the properties of the ideal fuzzy semiring interior and the nature of the existence of the ideal interior semiring if the ideal fuzzy interior is given.

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15

Sezgin, Aslıhan, and Zeynep Hare BAŞ. "Soft-int Almost Interior Ideals for Semigroups." Information Sciences with Applications 4 (October 1, 2024): 25–36. http://dx.doi.org/10.61356/j.iswa.2024.4374.

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Just as the concept of interior ideal of semigroups is a generalization of ideal in semigroups, the notion of soft intersection (soft-int) interior ideal is a generalization of soft-int ideal. In this paper, we propose the concepts of soft-int (weakly) almost interior ideal of a semigroup as a generalization of the nonnull soft-int interior ideals. We explore their algebraic properties in detail. We also show that an idempotent soft-int almost interior ideal is a soft-int almost subsemigroup. We additionally derive several intriguing relations related to semiprimeness, minimality, and (strongl

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16

Borah, Manash, and Bipan Hazarika. "Soft ideal topological space and mixed fuzzy soft ideal topological space." Boletim da Sociedade Paranaense de Matemática 37, no. 1 (2017): 141–51. http://dx.doi.org/10.5269/bspm.v37i1.29647.

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In this paper we introduce fuzzy soft ideal and mixed fuzzy soft ideal topological spaces and some properties of this space. Also we introduce fuzzy soft $I$-open set, fuzzy soft $\alpha$-$I$-open set, fuzzy soft pre-$I$-open set, fuzzy soft semi-$I$-open set and fuzzy soft $\beta$-$I$-open set and discuss some of their properties.

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17

SEZGİN, Aslıhan, and Aleyna İLGİN. "SOFT INTERSECTION ALMOST WEAK-INTERIOR IDEALS OF SEMIGROUPS: A THEORETICAL STUDY." Journal of Natural Sciences and Mathematics of UT-JNSM 9, no. 17-18 (2024): 372–85. http://dx.doi.org/10.62792/ut.jnsm.v9.i17-18.p2834.

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This study aims to introduce the concept of soft intersection almost weak-interior ideals of a semigroup, which extends the notion of nonnull soft intersection weak-interior ideals of a semigroup. We explore the properties of the ideal in depth. We show that soft intersection almost ideal and soft intersection almost weak-interior ideal coincide with each other when the soft set is idempotent and we also illustrate that an idempotent soft almost weak-interior ideal is a soft intersection almost subsemigroup. We also establish significant connections between almost weak-interior ideals and soft

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18

Vijay Peter, Selvaraj, and Thiagarajan Manikantan. "Generated interior ideals of semigroups in terms of fuzzy subset." International Journal of Algebra and Statistics 6, no. 1-2 (2017): 131. http://dx.doi.org/10.20454/ijas.2017.1268.

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Mo and Wang, in 1995, defined and studied the notion of fuzzy interior ideal generated by a fuzzy subset in a semigroup with unity. In this paper, we study the concept of fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our study does not require the existence of unit element. We provide an expression for generated fuzzy interior ideal in terms of interior ideals generated by the level subsets of the given fuzzy subset. Further, we study the homomorphic image and homomorphic pre-image of generated fuzzy interior ideal in a semigroup.

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19

Gaketem, Thiti. "Almost Bi-interior Ideal in Semigroups and Their Fuzzifications." European Journal of Pure and Applied Mathematics 15, no. 1 (2022): 281–89. http://dx.doi.org/10.29020/nybg.ejpam.v15i1.4279.

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In this paper, we define the concepts of alomst bi-interior ideal and fuzzy almost bi-interior ideal in semigroups. Moreover, we prove that relation between almost bi interior ideal and fuzzy almost bi-interior ideal.

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20

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

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

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21

İlgin, Aleyna, Aslıhan Sezgin, and Thiti Gaketem. "Generalized Soft Union Bi-Ideals and Interior Ideals of Semigroups: Soft Union Bi-Interior Ideals of Semigroups." International Journal of Analysis and Applications 23 (June 26, 2025): 149. https://doi.org/10.28924/2291-8639-23-2025-149.

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Generalizing the ideals of an algebraic structure has shown to be both beneficial and interesting for mathematicians. In this context, the idea of the bi-interior ideal was introduced as a generalization of the bi-ideal and interior ideal of a semigroup. By introducing "soft union (S-uni) bi-interior ideals of semigroups", we apply this idea to semigroups and soft set theory in this study. Finding the relationships between S-uni bi-interior ideals and other specific kinds of S-uni ideals of a semigroup is the main aim of this study. Our results show that an S-uni bi-interior ideal is an S-uni

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22

Gaketem, Thiti, and Tanaphong Prommai. "On Interval Valued Fuzzy Bi-interior Ideals in Semigroups." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 121–30. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4616.

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In this paper, we study the concept of an interval valued fuzzy bi-interior ideal. We investigate the properties of an interval valued fuzzy bi-interior ideal in semigroups. We characterize a regular semigroup in terms of an interval valued fuzzy bi-interior ideal.

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23

Muhiuddin, G., Habib Harizavi, and Young Bae Jun. "Bipolar-valued fuzzy soft hyper BCK ideals in hyper BCK algebras." Discrete Mathematics, Algorithms and Applications 12, no. 02 (2020): 2050018. http://dx.doi.org/10.1142/s1793830920500184.

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Using the notion of bipolar-valued fuzzy soft set, the concepts of bipolar-valued fuzzy soft (weak, [Formula: see text]-weak, strong) hyper BCK ideal are introduced, and related properties and relations are investigated. Characterizations of bipolar-valued fuzzy soft (weak) hyper BCK ideal are considered. Conditions for a bipolar-valued fuzzy soft weak hyper BCK ideal to be a bipolar-valued fuzzy soft [Formula: see text]-weak hyper BCK ideal are provided. Conditions for a bipolar-valued fuzzy soft set to be a bipolar-valued fuzzy soft strong hyper BCK ideal are displayed.

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24

T. Anitha. "Characterization of Pythagorean Fuzzy Bi-Interior Ideal and Bi-Quasi-Ideal in Γ-Semirings". Communications on Applied Nonlinear Analysis 32, № 4s (2024): 150–67. https://doi.org/10.52783/cana.v32.2746.

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In this paper, we introduce the Pythagorean fuzzy bi-interior-ideals and Pythagorean fuzzy bi-quasi-ideals in Γ - semiring. More over we prove the every Pythagorean fuzzy left and right ideals are Pythagorean fuzzy bi-interior -ideal in Γ - semiring. Also we study the notion of Pythagorean fuzzy bi-quasi-ideal in Γ - semiring and characterize Pythagorean fuzzy bi-quasi-ideal in Γ - semiring.

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25

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

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

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G.Subbiah and S. Anitha. "Certain Double Action on Bipolar Fuzzy Soft G-Modules." International Journal of Fuzzy Mathematical Archive 15, no. 02 (2018): 263–70. http://dx.doi.org/10.22457/ijfma.v15n2a18.

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In this paper, we apply the notion of bipolar-valued fuzzy soft set to module theory. We introduce the concept of bipolar fuzzy soft G-modules, fuzzy soft d-ideals of modules and investigate several properties. We give relations between a bipolar fuzzy soft G-modules and bipolar fuzzy soft d-ideal. We provide a condition for bipolar fuzzy soft G-modules to be a bipolar fuzzy soft d-ideal. We also give characterizations of bipolar fuzzy soft ideal. We consider the concept of strongest bipolar fuzzy relations on bipolar fuzzy soft d-ideals of a module and discuss some related properties.

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27

Sezgin, Aslıhan, and Fatıma Zehra Kocakaya. "Soft Intersection Quasi-interior Ideals of Semigroups." Journal of Basic & Applied Sciences 21 (April 3, 2025): 101–18. https://doi.org/10.29169/1927-5129.2025.21.11.

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It has been shown that generalizing the ideals of an algebraic structure is both interesting and beneficial for mathematicians. In this context, the concept of quasi-interior (Ԛꟾ) ideal was introduced as a generalization of quasi-ideal and interior ideal of a semigroup. In this paper, we apply this concept to soft set theory and semigroups, introducing a new form of soft intersection (S-int) ideal called the "soft intersection (S-int) quasi-interior (Ԛꟾ) ideal." The main objective of this study is to investigate the relationships between S-int Ԛꟾ ideals and other specific types of S-int ideals

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28

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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29

Jun, Young Bae, Sun Shin Ahn, and G. Muhiuddin. "Hesitant Fuzzy Soft Subalgebras and Ideals inBCK/BCI-Algebras." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/763929.

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As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories inBCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Condit

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30

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

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

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31

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

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

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et al., Muhiuddin. "Fuzzy soft set theory applied to commutative ideals of BCK-algebras." International Journal of ADVANCED AND APPLIED SCIENCES 8, no. 6 (2021): 48–56. http://dx.doi.org/10.21833/ijaas.2021.06.006.

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In the present paper, we apply the fuzzy soft set theory to commutative ideals of BCK-algebras. In fact, the notion of fuzzy soft commutative ideals over BCK-algebras is introduced, and related properties are investigated. Relations between fuzzy soft ideals and fuzzy soft commutative ideals are discussed, and conditions for a fuzzy soft ideal to be a fuzzy soft commutative ideal are provided. The “AND” operation, “extended intersection” and “union” of fuzzy soft (commutative) ideals are studied. Furthermore, characterizations of fuzzy soft (commutative) ideals are considered.

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Asaad, Samah H., and Akram S. Mohammed. "New Properties of Anti Fuzzy Ideals of Regular Semigroups." Ibn AL-Haitham Journal For Pure and Applied Sciences 32, no. 3 (2019): 109–16. http://dx.doi.org/10.30526/32.3.2287.

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In this article, we study some properties of anti-fuzzy sub-semigroup, anti fuzzy left (right, two sided) ideal, anti fuzzy ideal, anti fuzzy generalized bi-ideal, anti fuzzy interior ideals and anti fuzzy two sided ideal of regular semigroup. Also, we characterized regular LA-semigroup in terms of their anti fuzzy ideal.

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34

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

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

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

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

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A., Pannerselvam, and Umamaheswari B. "CERTAIN STRUCTURES OF DOUBLE FUZZY SOFT IDEALS." International Journal of Advanced Trends in Engineering and Technology 3, no. 1 (2018): 164–67. https://doi.org/10.5281/zenodo.1288728.

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In this article, we introduce the notion of double fuzzy soft sub ideal and double fuzzy soft ideal with examples. We have proved some interesting results which are very close to the results which are very closer to the results fuzzy soft ideal in BCK-Algebras.

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Khan, Hidayat Ullah, Nor Haniza Sarmin, Asghar Khan, and Faiz Muhammad Khan. "Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals." Journal of Intelligent Systems 25, no. 2 (2016): 297–318. http://dx.doi.org/10.1515/jisys-2015-0035.

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AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the rel

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Akram S. Mohammed та Samah H. Asaad. "A study on SS- π- regular fuzzy ideals of semi groups". Tikrit Journal of Pure Science 24, № 4 (2019): 77–81. http://dx.doi.org/10.25130/tjps.v24i4.404.

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In this paper, the notion of SS -π- regular fuzzy ideals of semi groups as a generalization of regular fuzzy ideal has been introduced and some of their important related properties have been investigated. Characterizations of fuzzy interior ideal , anti fuzzy ideal , anti fuzzy bi-ideal and anti fuzzy generalized –bi -ideal in terms of SS - π- regular fuzzy ideal have also been obtained .

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Mohammed, Akram S., та Samah H. Asaad. "A study on SS- π- regular fuzzy ideals of semi groups". Tikrit Journal of Pure Science 24, № 4 (2019): 77. http://dx.doi.org/10.25130/j.v24i4.850.

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In this paper, the notion of SS -π- regular fuzzy ideals of semi groups as a generalization of regular fuzzy ideal has been introduced and some of their important related properties have been investigated. Characterizations of fuzzy interior ideal , anti fuzzy ideal , anti fuzzy bi-ideal and anti fuzzy generalized –bi -ideal in terms of SS - π- regular fuzzy ideal have also been obtained .   http://dx.doi.org/10.25130/tjps.24.2019.077

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Ahn, Sun Shin, Seok-Zun Song, Young Bae Jun, and Hee Sik Kim. "Makgeolli Structures and Its Application in BCK/BCI-Algebras." Mathematics 7, no. 9 (2019): 784. http://dx.doi.org/10.3390/math7090784.

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A fuzzy set is an extension of an existing set using fuzzy logic. Soft set theory is a generalization of fuzzy set theory. Fuzzy and soft set theory are good mathematical tools for dealing with uncertainty in a parametric manner. The aim of this article is to introduce the concept of makgeolli structures using fuzzy and soft set theory and to apply it to BCK/BCI-algebras. The notion of makgeolli algebra and makgeolli ideal in BCK/BCI-algebras is defined, and several properties are investigated. It deals with the relationship between makgeolli algebra and makgeolli ideal, and several examples a

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Marapureddy, Murali Krishna Rao Rajendra Kumar Kona∗ And Noorbhasha Rafi. "Fuzzy soft tri-ideals over Gamma-semirings." Annals of Communications in Mathematics 6, no. 4 (2023): 225–37. https://doi.org/10.5281/zenodo.10445482.

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In this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A &sube; E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.

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Satish, T., Madhusudhana Rao, P. Sivaprasad та M. Vasantha. "Fuzzy Soft Ternary Γ-Semirings-II". International Journal of Engineering and Advanced Technology 9, № 1s5 (2019): 235–39. http://dx.doi.org/10.35940/ijeat.a1057.1291s519.

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In this paper we are introducing the notions of “fuzzy soft quasi T  -ideal(FSQTΓI), Fuzzy soft bi-T  - ideal(FSBTΓI)” are introduced. It is proved that (1) A “fuzzy soft set (q,P1,  ) over a ternary Γ-semiring(TΓ-SR)”T is a FSQTΓI over T iff  a  P1, q(a)   is a “quasi-ideal of T”. (2) Every “Fuzzy soft left (right, lateral) T  - ideal[FSLTΓI(FSMTΓI, FSRTΓI)] over a TΓ-SR T is a FSQTΓI over T”: (3)Every “FSQTΓI is a fuzzy soft T  -SR over T”: (4) Let “(r,A,  ), (l,B,  ) and (m,C,  ) be FSLTΓI, FSMTΓI, FSRTΓI over T”, respectively. Then “(r,A,  )  (l,B,  )  (m,C,  ) is a FSQTΓI

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Atmaca, Serkan, and İdris Zorlutuna. "On Topological Structures of Fuzzy Parametrized Soft Sets." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/164176.

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We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.

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Alsulami, S. H., Ismail Ibedou, and S. E. Abbas. "Fuzzy roughness via ideals." Journal of Intelligent & Fuzzy Systems 39, no. 5 (2020): 6869–80. http://dx.doi.org/10.3233/jifs-192072.

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In this paper, we join the notion of fuzzy ideal to the notion of fuzzy approximation space to define the notion of fuzzy ideal approximation spaces. We introduce the fuzzy ideal approximation interior operator int Φ λ and the fuzzy ideal approximation closure operator cl Φ λ , and moreover, we define the fuzzy ideal approximation preinterior operator p int Φ λ and the fuzzy ideal approximation preclosure operator p cl Φ λ with respect to that fuzzy ideal defined on the fuzzy approximation space (X, R) associated with some fuzzy set λ ∈ IX. Also, we define fuzzy separation axioms, fuzzy connec

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Azzam, A. A., Radwan Abu-Gdairi, M. Aldawood, and Abdulaziz M. Alotaibi. "On Intuitionistic Fuzzy Soft Pretopology." International Journal of Analysis and Applications 22 (October 22, 2024): 193. http://dx.doi.org/10.28924/2291-8639-22-2024-193.

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This paper defines the following terms: intuitionistic fuzzy soft (IFS) pretopological space, IFS interior function, IFS pre-open set, IFS pre-closed set, trace of a IFS pretopology, IFS separation axioms, IFS subspace, IFS compactness, IFS connectedness, and some of their properties. In addition, the degree of soft non-vacuity, the soft α-cut, and the IFS preneighbourhood system at a soft point are defined. IFS preneighbourhoods produce IFS pretopologies.

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

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

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Al-Abayechi, Ameer, Haneen Al-Janabi, and Heyam Kh Hassan Alkhayyat. "New results in fuzzy soft bitopological spaces via (1,2)-fuzzy soft preopen sets." Journal of Interdisciplinary Mathematics 28, no. 3-B (2025): 1161–72. https://doi.org/10.47974/jim-2205.

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Makherjee and Park [1] introduced and studied a notion for a fuzzy soft bitopological space. This article introduce notions for fuzzy soft pre-open (closed) set of fuzzy soft bitopological space and studied their basic properties. we use these notions to characterize fundamental concepts of fuzzy soft bitopological spaces such as fuzzy soft pre-closures and fuzzy soft pre-interior of a fuzzy soft bitopological space and prove some of their axioms. Through the use of a notion for soft quasi coincidence, as well as we characterized the concept for a fuzzy soft quasi pre-separation axioms of bito

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Abbasi, Mohammad Y., Aakif F. Talee, Sabahat A. Khan та Kostaq Hila. "A Hesitant Fuzzy Set Approach to Ideal Theory in Γ-Semigroups". Advances in Fuzzy Systems 2018 (2 вересня 2018): 1–6. http://dx.doi.org/10.1155/2018/5738024.

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We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in Γ-semigroup and study some properties of them. Finally, a characterization of a simple Γ-semigroup by means of a hesitant fuzzy simple Γ-semigroup is obtained.

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Shi, Dali, M. N. Abu_Shugair, S. E. Abbas, and Ismail Ibedou. "Picture Fuzzy Modal Ideal Multifunctions." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5956. https://doi.org/10.29020/nybg.ejpam.v18i2.5956.

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This paper introduces the notion of a picture fuzzy modal topological structures (PFMTSs) via ideal. These structures are grounded on novel picture fuzzy topological operators for closure and interior types, utilizing the two standard picture fuzzy modal operators $\square $ and $\Diamond $. The paper discusses several fundamental properties of picture fuzzy multifunctions PFMs via ideals. The results indicate that some properties considered satisfactory in the intuitionistic fuzzy modal topological structures, as defined by Atanassov in 2022, are not fulfilled. Also, we introduce many types o

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Chen, Xiao Jun, and Fu Ting Wang. "Soft Furnishing Material in Interior Space." Applied Mechanics and Materials 271-272 (December 2012): 1257–60. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.1257.

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In the case of the improving economic, people no longer pursue luxury and the copies of other homes in house decoration, but have a higher spiritual level requirements. Interior soft decoration has become an unavoidable mean of decoration in modern house decoration and the important direction of interior decoration. The interior soft decoration art is a dynamic art. Its unity can bring vitality to space and build an ideal interior environment that is full of culture taste and comfort. Interior soft decoration will be the future development of housing decoration industry and the popular trend.

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