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Journal articles on the topic 'Fuzzy Normed Linear Space'

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Published: 3 June 2025

Last updated: 22 June 2025

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1

ZHU, YUANGUO. "ON PARA-NORMED SPACE WITH FUZZY VARIABLES BASED ON EXPECTED VALUED OPERATOR." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 01 (2008): 95–106. http://dx.doi.org/10.1142/s0218488508005066.

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Fuzzy variables are functions from credibility spaces to the set of real numbers. The set of fuzzy variables is a linear space with the classic operations of addition and multiplication by numbers. Its subspace formed by fuzzy variables with finite pth absolute moments is showed to be a complete para-normed space. The concept of para-normed space is novel, and is an extension of normed space. It is seen that most properties of normed spaces hold in para-normed spaces. Also some useful inequalities in para-normed spaces are obtained.

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2

Sinha, Kalyan, and Pinaki Majumdar. "Picture fuzzy normed linear space." Boletim da Sociedade Paranaense de Matemática 42 (May 7, 2024): 1–9. http://dx.doi.org/10.5269/bspm.65363.

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Picture fuzzy set (PFS) is a recent advancement tool to deal with vulnerability. It is an immediate expansion of intuitionistic fuzzy set that can display vulnerability in such circumstances including more responses of these kinds: indeed, decline, no. In this manuscript the idea of Picture fuzzy normed linear space (PFNLS) is discussed for the first time. Naturally PFNLS is an hybrid concept of PFS and normed linear space. Also Convergence in PFNLS are shown. Later on Completeness property on PFNLS are explored. Finally boundedness of Cauchy sequence in PFNLS is analysed.

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3

Dr., M. Mary Jansi Rani, and Abirami S. "INTUITUIONISTIC FUZZY ANTI n-NORMED LINEAR SPACE." International Journal of Advanced Trends in Engineering and Technology 2, no. 2 (2017): 80–84. https://doi.org/10.5281/zenodo.852635.

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The main purpose of this paper to introduce the concept of Intuitionistic fuzzy anti n-normed linear space<strong>. </strong>In this paper we have introduced the definition of intuitionistic fuzzy anti n-normed linear space and gave some example on it.

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4

Bayaz, Daraby, Delzendeh Fataneh, and Rahimi Asghar. "Parseval's equality in fuzzy normed linear spaces." MATHEMATICA 63 (86), no. 1 (2021): 47–57. http://dx.doi.org/10.24193/mathcluj.2021.1.05.

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We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces are wider than for the category of the frames in the classical Hilbert spaces.

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5

Chandra Das, Paritosh. "Fuzzy normed linear sequence space." Proyecciones (Antofagasta) 37, no. 2 (2018): 389–403. http://dx.doi.org/10.4067/s0716-09172018000200389.

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6

Kadari, Ramalingaiah, and B. Surender Reddy. "Cubic Structure on Soft Gamma-m-Normed Linear Space." Indian Journal Of Science And Technology 17, no. 28 (2024): 2933–44. http://dx.doi.org/10.17485/ijst/v17i28.1713.

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Objectives: The purpose of this research is to take the lead in comprehending the fuzzy idea of cubic structure on soft Gamma-m normed linear space. According to the theory of Soft m-Normed Linear Space (SMNLS), we offer the conviction of Cauchy's sequence and convergence in cubic Soft Gamma-m Normed Linear Space (CSGMNLS). We have obtained certain results like the concept of completeness in CSGMNLS. Methods: In this paper we defined the soft gamma ring, soft gamma ideals and soft gamma vector space which are used to introduce the notion of soft gamma-2-normed linear space, Soft Gamma-m-Normed Linear Space (SGMNLS) and its properties. Also, the CSGMNLS can be analyzed by using the SGMNLS. Findings: In this research from CSGMNLS construct a norm function that satisfies the properties of SGMNLS, and additionally given that example with proof in which a sequence is cauchy sequence and convergence in SGMNLS if it is cauchy and convergence sequence in CSGMNLS. Also, provided theorem and its proof for completeness of a sequence in CSGMNLS. Novelty: Already gamma ring and fuzzy n-normed linear space has been defined. We introduced the concept of SGMNLS using this also initiated the CSGMNLS and some results obtained from its properties. We suggested a necessary conditions for completeness of a sequence in CSGMNLS. Keywords: Soft Gamma ring, Soft gamma vector space, Soft gamma normed linear space, Soft m-norm, Soft m-normed linear space, 2-Normed and m-normed right soft gamma linear space

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7

Raghad Ibrahim Sabre. "Some Properties Of Cartesian Product Of Two Fuzzy Normed Spaces." Journal of the College of Basic Education 21, no. 88 (2023): 109–16. http://dx.doi.org/10.35950/cbej.v21i88.9956.

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In this paper , the concept of the Cartesian Product of two fuzzy normed spaces is presented. Some basic properties and theorems on this concept are proved. The main goal of this paper is to prove that the Cartesian product of two complete fuzzy normed spaces is a complete fuzzy normed space. Key words:Fuzzy normed space , Cartesian product , Cauchy sequence , complete fuzzy normed space. 1- Introduction  The fuzzy set concepts was introduced in mathematics by K.Menger in 1942 and reintroduced in the system theory by L.A.Zadeh in 1965. In 1984, Katsaras [ 1 ] , first introduced the notation of fuzzy norm on linear space, in the same year Wu and Fang [ 4 ] also introduced a notion of fuzzy normed space . Later on many other mathematicians like Felbin [ 2 ] , Cheng and Mordeson [ 10] , Bag and Samanta [12], J.Xiao and X.Zhu [8,9] , Krishna and Sarma [11] , Balopoulos and Papadopoulos [ 13] etc, have given different definitions of fuzzy normed spaces . J.Kider introduced the definition of fuzzy normed space[ 7 ] , we use this definition to prove that the Cartesian product of two fuzzy normed spaces is also fuzzy normed space.  The structure of the paper is as follow : In section 2 we present some fundamental concepts . In section 3, the definition of fuzzy normed space appeared [7] is used to prove that the cartesain product of two fuzzy normed spaces is also fuzzy normed space, then we prove that the cartesain product of two complete fuzzy normed spaces is complete fuzzy normed space.  2. Preliminaries In this section, we briefly recall some definitions and preliminary results which are used in this paper.

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8

Sinha, Parijat, and Yogesh Chandra. "FUZZY CONTINUOUS AND FUZZY BOUNDED LINEAR OPERATORS OVER ANTI-FUZZY FIELDS." jnanabha 53, no. 02 (2023): 168–76. http://dx.doi.org/10.58250/jnanabha.2023.53220.

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In this paper, we have studied the concept of anti-norm and anti-inner product function on anti-fuzzy linear space over anti-fuzzy field, we have also given fuzzy continuous linear operator from an anti-normed anti-fuzzy linear space to another anti-normed anti-fuzzy linear space and also introduced three types (strong, weak and sequential) of fuzzy bounded linear operators.

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9

Recai Turkmen, Muhammed, та Husamettin Bar Akbay. "λ -STATISTICAL CONVERGENCE IN FUZZY N NORMED LINEAR SPACES". Journal of Mathematical Analysis 15, № 4 (2024): 1–14. https://doi.org/10.54379/jma-2024-4-1.

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In this paper, we introduce λ− statistical convergence and the condition of being λ− statistical Cauchy of real number sequences in fuzzy n normed linear spaces. At the same time, in fuzzy n normed space, we have introduced the concept of (V, λ) summability and (C, 1) summability. Then, we studied the relation between these concepts and λ− statistical convergence.

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10

Xu, Yanyan, Lu Sun, Hao Li, and Guanggui Chen. "The Fuzzy Width Theory in the Finite-Dimensional Space and Sobolev Space." Mathematics 11, no. 10 (2023): 2331. http://dx.doi.org/10.3390/math11102331.

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This paper aims to fuzzify the width problem of classical approximation theory. New concepts of fuzzy Kolmogorov n-width and fuzzy linear n-width are introduced on the basis of α-fuzzy distance which is induced by the fuzzy norm. Furthermore, the relationship between the classical widths in linear normed space and the fuzzy widths in fuzzy linear normed space is discussed. Finally, the exact asymptotic orders of the fuzzy Kolmogorov n-width and fuzzy linear n-width corresponding to a given fuzzy norm in finite-dimensional space and Sobolev space are estimated.

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11

Ramalingaiah Kadari. "Cubic Intuitionistic Fuzzy Gamma-m-Normed Linear Space." Communications on Applied Nonlinear Analysis 31, no. 8s (2024): 441–58. http://dx.doi.org/10.52783/cana.v31.1537.

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Objectives: The purpose of this research is to take the lead in foggiest idea of convergence in cubic intuitionistic fuzzy Gamma-m normed linear space(CCIFGMNLS). According to the theory of fuzzy m-Normed Linear Space(FMNLS),we offer the conception of Cauchy's sequence and convergence in cubic intuitionistic fuzzy Gamma-m Normed Linear Space (CIFGMNLS). We have reviewed the certain results, and this paper proposes the hypothesis of completeness in CIFGMNLS. Methods: In this research paper we defined the intuitionistic fuzzy Gamma gamma ring, intuitionistic fuzzy gamma ideals, left and right intuitionistic fuzzy gamma vector space which are using to approach the theory of intuitionistic fuzzy gamma-2-normed linear space, intuitionistic fuzzy Gamma-m-Normed Linear Space and its axioms. And the CCIFGMNLS can be approached using the IFGMNLS. Findings: In this research paper from CCIFGMNLS construct a norm function that satisfies the properties of IFGMNLS, and provided that example with proof of a sequence is cauchy sequence and convergence in IFGMNLS if and only it is cauchy sequence and convergence sequence in CCIFGMNLS. Also derived a theorem and its proof for completeness of a sequence in CCIFGMNLS. Novelty: Already gamma ring and fuzzy n-normed linear space has been defined. we originated the notion of IFGMNLS using this also put forwarded the CCIFGMNLS and some results obtained from its properties . we provided a necessary axioms to completeness of a sequence in CCIFGMNLS.

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12

Chandra Das, Paritosh. "Fuzzy normed linear space valued sequence space." Proyecciones (Antofagasta) 36, no. 2 (2017): 245–55. http://dx.doi.org/10.4067/s0716-09172017000200245.

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13

Alegre, Carmen, and Salvador Romaguera. "The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/151472.

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This paper deals with fuzzy normed spaces in the sense of Cheng and Mordeson. We characterize fuzzy norms in terms of ascending and separating families of seminorms and prove an extension theorem for continuous linear functionals on a fuzzy normed space. Our result generalizes the classical Hahn-Banach extension theorem for normed spaces.

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14

Ömer, Kişi, and Tuzcuoğlu Ibrahim. "Fibonacci Lacunary Statistical Convergence In Intuitionistic Fuzzy Normed Linear Spaces." Journal of Progressive Research in Mathematics 16, no. 3 (2020): 3001–7. https://doi.org/10.5281/zenodo.3973308.

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We investigate the concept of Fibonacci lacunary statistical convergence in intuitionistic fuzzy normed linear spaces. We also introduce here a new concept, that is, Fibonacci lacunary statistical completeness and show that every intuitionistic fuzzy normed linear space is Fibonacci lacunary statistically complete.

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15

Vijayabalaji, Srinivasan, Natesan Thillaigovindan, and Young-Bae Jun. "INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE." Bulletin of the Korean Mathematical Society 44, no. 2 (2007): 291–308. http://dx.doi.org/10.4134/bkms.2007.44.2.291.

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16

Felbin, Clementina. "Finite dimensional fuzzy normed linear space." Fuzzy Sets and Systems 48, no. 2 (1992): 239–48. http://dx.doi.org/10.1016/0165-0114(92)90338-5.

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17

Et al., Kider. "Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces." Baghdad Science Journal 16, no. 1 (2019): 0104. http://dx.doi.org/10.21123/bsj.2019.16.1.0104.

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In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.

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18

Moradi, Hamid Reza. "Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces." International Journal of Fuzzy System Applications 4, no. 2 (2015): 47–55. http://dx.doi.org/10.4018/ijfsa.2015040104.

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In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy a-Cauchy sequence of fuzzy points and fuzzy completeness.

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19

Altaweel, Nifeen H., Mohammad H. M. Rashid, Olayan Albalawi, Maryam G. Alshehri, Nidal H. E. Eljaneid, and Razan Albalawi. "On the Ideal Convergent Sequences in Fuzzy Normed Space." Symmetry 15, no. 4 (2023): 936. http://dx.doi.org/10.3390/sym15040936.

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This article discusses a variety of important notions, including ideal convergence and ideal Cauchyness of topological sequences produced by fuzzy normed spaces. Furthermore, the connections between the concepts of the ideal limit and ideal cluster points of a sequence in a fuzzy normed linear space are investigated. In a fuzzy normed space, we investigated additional effects, such as describing compactness in terms of ideal cluster points and other relevant but previously unresearched ideal convergence and adjoint ideal convergence aspects of sequences and nets. The countable compactness of a fuzzy normed space and its link to it were also defined. The terms ideal and its adjoint divergent sequences are then introduced, and specific aspects of them are explored in a fuzzy normed space. Our study supports the importance of condition (AP) in examining summability via ideals. It is suggested to use a fuzzy point symmetry-based genetic clustering method to automatically count the number of clusters in a data set and determine how well the data are fuzzy partitioned. As long as the clusters have the attribute of symmetry, they can be any size, form, or convexity. One of the crucial ways that symmetry is used in fuzzy systems is in the solution of the linear Fuzzy Fredholm Integral Equation (FFIE), which has symmetric triangular (Fuzzy Interval) output and any fuzzy function input.

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20

Thangaraj Beaula and M. Merlin Priyanga. "Conjugate space of fuzzy soft normed linear space." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 13, no. 5 (2017): 651–63. http://dx.doi.org/10.30948/afmi.2017.13.5.651.

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21

Prakasam, Prakasam, and Krishnamoorthy Kavitha. "An Exploration of Hesitant Fuzzy Normed Linear Space." International Journal of Neutrosophic Science 25, no. 3 (2025): 373–84. http://dx.doi.org/10.54216/ijns.250333.

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In this paper, the notion of hesitant fuzzy norm based on the Bag-Samanta’s Type Fuzzy Norm on linear space has been introduced. Further the concepts of ascending family of semi-norms, convergence and fuzzy continuous linear operators are studied in hesitant fuzzy normed linear space.

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22

Ramalingaiah, Kadari, and Surender Reddy B. "Cubic Structure on Soft Gamma-m-Normed Linear Space." Indian Journal of Science and Technology 17, no. 28 (2024): 2933–44. https://doi.org/10.17485/IJST/v17i28.1713.

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Abstract <strong>Objectives:</strong> The purpose of this research is to take the lead in comprehending the fuzzy idea of cubic structure on soft Gamma-m normed linear space. According to the theory of Soft m-Normed Linear Space (SMNLS), we offer the conviction of Cauchy's sequence and convergence in cubic Soft Gamma-m Normed Linear Space (CSGMNLS). We have obtained certain results like the concept of completeness in CSGMNLS.<strong> Methods:</strong> In this paper we defined the soft gamma ring, soft gamma ideals and soft gamma vector space which are used to introduce the notion of soft gamma-2-normed linear space, Soft Gamma-m-Normed Linear Space (SGMNLS) and its properties. Also, the CSGMNLS can be analyzed by using the SGMNLS. <strong>Findings:</strong> In this research from CSGMNLS construct a norm function that satisfies the properties of SGMNLS, and additionally given that example with proof in which a sequence is cauchy sequence and convergence in SGMNLS if it is cauchy and convergence sequence in CSGMNLS. Also, provided theorem and its proof for completeness of a sequence in CSGMNLS. <strong>Novelty:</strong> Already gamma ring and fuzzy n-normed linear space has been defined. We introduced the concept of SGMNLS using this also initiated the CSGMNLS and some results obtained from its properties. We suggested a necessary conditions for completeness of a sequence in CSGMNLS. <strong>Keywords:</strong> Soft Gamma ring, Soft gamma vector space, Soft gamma normed linear space, Soft m-norm, Soft m-normed linear space, 2-Normed and m-normed right soft gamma linear space

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23

Xu, Tian Zhou. "On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces." ISRN Mathematical Analysis 2013 (September 16, 2013): 1–7. http://dx.doi.org/10.1155/2013/814067.

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The motivation of this paper is to present a new notion of non-Archimedean fuzzy -normed space over a field with valuation. We obtain a Mazur-Ulam theorem for fuzzy -isometry mappings in the strictly convex non-Archimedean fuzzy -normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the corresponding triangle. And then, using this result, we get a Mazur-Ulam theorem for the interior preserving fuzzy -isometry mappings in non-Archimedean fuzzy -normed spaces over a linear ordered non-Archimedean field.

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24

张, 入化. "0-Norm of Fuzzy Normed Linear Space." Advances in Applied Mathematics 12, no. 06 (2023): 2945–50. http://dx.doi.org/10.12677/aam.2023.126296.

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25

Das, Paritosh Chandra. "Fuzzy normed linear sequence space bvFp (X)." Proyecciones (Antofagasta) 37, no. 2 (2018): 389–403. https://doi.org/10.22199/issn.0717-6279-2924.

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In this article we introduce the notion of class of sequences bvFp (X),1 ≤ p < ∞ with the concept of fuzzy norm. We study some of its properties such as completeness, solidness, symmeticity and convergence free. Also, we establish some inclusion results.

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26

Narayanan, AL, and S. Vijayabalaji. "Fuzzyn-normed linear space." International Journal of Mathematics and Mathematical Sciences 2005, no. 24 (2005): 3963–77. http://dx.doi.org/10.1155/ijmms.2005.3963.

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The primary purpose of this paper is to introduce the notion of fuzzyn-normed linear space as a generalization ofn-normed space. Ascending family ofα-n-norms corresponding to fuzzyn-norm is introduced. Best approximation sets inα-n-norms are defined. We also provide some results on best approximation sets inα-n-normed space.

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27

C., Faria. "On Fuzzy Conjugate Spaces of Fuzzy 2-Normed Spaces." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), no. 1 (October 16, 2021): 127–42. http://dx.doi.org/10.55562/jrucs.v33i1.305.

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In this paper we give the definition of fuzzy 2-bounded linear functional and the notions of his fuzzy norm is introduced. Also, we introduce fuzzy conjugate space of a fuzzy 2-normed linear space and give some facts that are related with it.

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Mami Sharma and Debajit Hazarika. "On linear operators in Felbin's fuzzy normed linear space." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 13, no. 6 (2017): 749–58. http://dx.doi.org/10.30948/afmi.2017.13.6.749.

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Omana, Rebecca Walo, and Jean-Louis Akakatshi Ossako. "BIFURCATION FROM INFINITY IN A FUZZY NORMED SPACE." Advances in Fuzzy Sets and Systems 29, no. 2 (2024): 99–122. https://doi.org/10.17654/0973421x24005.

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The aim of the paper is the study of bifurcation phenomena in fuzzy normed linear space. We first define topological degrees (Leray-Schauder and Brouwer) and the index of an isolated zero in fuzzy linear normed space with topology induced by Felbin’s norm. Using this index, we prove the existence of the bifurcation of solutions from the 0-line and from infinity for functional equation defined by a compact mapping, we also give some global results.

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30

Asif, Awais, Hassen Aydi, Muhammad Arshad, and Zeeshan Ali. "A Novel Picture Fuzzy n-Banach Space with Some New Contractive Conditions and Their Fixed Point Results." Journal of Function Spaces 2020 (September 25, 2020): 1–12. http://dx.doi.org/10.1155/2020/6305856.

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A picture fuzzy n-normed linear space (NPF), a mixture of a picture fuzzy set and an n-normed linear space, is a proficient concept to cope with uncertain and unpredictable real-life problems. The purpose of this manuscript is to present some novel contractive conditions based on NPF. By using these contractive conditions, we explore some fixed point theorems in a picture fuzzy n-Banach space (BPF). The discussed modified results are more general than those in the existing literature which are based on an intuitionistic fuzzy n-Banach space (BIF) and a fuzzy n-Banach space. To express the reliability and effectiveness of the main results, we present several examples to support our main theorems.

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Raghad I. Sabri. "Fuzzy Open Mapping and Fuzzy Closed Graph Theorems in Fuzzy Length Space." Al-Qadisiyah Journal Of Pure Science 25, no. 4 (2020): 32–39. http://dx.doi.org/10.29350/qjps.2020.25.4.1189.

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The theory of fuzzy set includes many aspects that regard important and significant in different fields of science and engineering in addition to there applications. Fuzzy metric and fuzzy normed spaces are essential structures in the fuzzy set theory. The concept of fuzzy length space has been given analogously and the properties of this space are studied few years ago. In this work, the definition of a fuzzy open linear operator is presented for the first time and the fuzzy Barise theorem is established to prove the fuzzy open mapping theorem in a fuzzy length space. Finally, the definition of a fuzzy closed linear operator on fuzzy length space is introduced to prove the fuzzy closed graph theorem.

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Thangaraj Beaula and Lilly Esthar Rani. "Fuzzy boundedness and contractiveness on intuitionistic 2-fuzzy 2-normed linear space." Malaya Journal of Matematik 1, no. 03 (2013): 64–72. http://dx.doi.org/10.26637/mjm103/010.

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The concepts of fuzzy boundedness, fuzzy continuity and intuitionistic fuzzy 2- contractive mapping on intutionistic 2-fuzzy 2-normed linear space are introduced. Using these concepts some theorems are proved.

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33

Debnath, Pradip. "Statistical Cesàro Summability in Intuitionistic Fuzzy n-Normed Linear Spaces Leading towards Tauberian Theorems." Axioms 13, no. 8 (2024): 557. http://dx.doi.org/10.3390/axioms13080557.

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The concept of summability is crucial in deriving formal solutions to partial differential equations. This paper explores the connection between the methods of statistical convergence of sequences and statistical Cesàro summability in intuitionistic fuzzy n-normed linear space (IFnNLS). While the existing literature covers Cesàro summability and its statistical variant in fuzzy, intuitionistic fuzzy, and classical normed spaces, this study stands out not only for its methodology but also for its comprehensive approach, encompassing a broader range of spaces and detailing the pathway from the statistical Cesàro summability method to statistical convergence. These results will lead us to Tauberian theorems in IFnNLS.

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34

Sadeqi, I., and F. Solaty Kia. "Fuzzy normed linear space and its topological structure." Chaos, Solitons & Fractals 40, no. 5 (2009): 2576–89. http://dx.doi.org/10.1016/j.chaos.2007.10.051.

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35

Clementina, F. "The Completion of a Fuzzy Normed Linear Space." Journal of Mathematical Analysis and Applications 174, no. 2 (1993): 428–40. http://dx.doi.org/10.1006/jmaa.1993.1128.

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张, 入化. "1-Best Approximation of Fuzzy Normed Linear Space." Advances in Applied Mathematics 12, no. 06 (2023): 2958–64. http://dx.doi.org/10.12677/aam.2023.126298.

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37

Solatikia, Farnaz, Erdem Kiliç, and Gerhard Wilhelm Weber. "Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces." Organizacija 47, no. 2 (2014): 90–97. http://dx.doi.org/10.2478/orga-2014-0010.

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Abstract Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem which is obtained by applying the embedding function to the original fuzzy optimization problem. Results: The proposed method is used to extend the classical Mean-Variance portfolio selection model into Mean Variance-Skewness model in fuzzy environment under the criteria on short and long term returns, liquidity and dividends. Conclusion: A fuzzy optimization problem can be transformed into a multiobjective optimization problem which can be solved by using interactive fuzzy decision making procedure. Investor preferences determine the optimal multiobjective solution according to alternative scenarios.

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Pandit, Shailendra, Ayaz Ahmad, and Ayhan Esi. "A study of triple sequence spaces in fuzzy anti-normed linear spaces." Filomat 37, no. 15 (2023): 4971–80. http://dx.doi.org/10.2298/fil2315971p.

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The proposed article aims to study some topological properties of triple real sequence spaces with respect to fuzzy-anti-normed linear space (FANLS). In this work the algebra of fuzzy I?-limit and fuzzy I? -anti limit, where 0 < ? < 1 and I is an ideal on N3, of triple real sequences along with an interesting example have been studied. Furthermore, the completeness of a special kind of sequence space with respect to fuzzy anti-norm has been examined.

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39

Dinda, Bivas, Santanu Kumar Ghosh, and T. K. Samanta. "Intuitionistic Fuzzy Pseudo-Normed Linear Spaces." New Mathematics and Natural Computation 15, no. 01 (2018): 113–27. http://dx.doi.org/10.1142/s1793005719500078.

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Ji, Peisheng, Weiqing Qi, and Ranhong Wei. "Completeness of fuzzy normed linear space of all weakly fuzzy bounded linear operators." Fuzzy Sets and Systems 251 (September 2014): 92–100. http://dx.doi.org/10.1016/j.fss.2013.11.003.

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Sharma, Mami, and Debajit Hazarika. "Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness." New Mathematics and Natural Computation 16, no. 01 (2020): 177–93. http://dx.doi.org/10.1142/s1793005720500118.

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In this paper, we first investigate the relationship between various notions of fuzzy boundedness of linear operators in fuzzy normed linear spaces. We also discuss the fuzzy boundedness of fuzzy compact operators. Furthermore, the spaces of fuzzy compact operators have been studied.

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Das, Paritosh Chandra. "On fuzzy normed linear space valued statistically convergent sequences." Proyecciones (Antofagasta) 36, no. 3 (2017): 511–27. https://doi.org/10.22199/issn.0717-6279-2394.

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In this article we define the notion of statistically convergent and statistically null sequences with the concept of fuzzy norm and discuss some of their properties such as completeness, monotone, solidness, symmetricity sequence algebra and convergence free.

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Wu, Yaoqiang. "On (fuzzy) pseudo-semi-normed linear spaces." AIMS Mathematics 7, no. 1 (2021): 467–77. http://dx.doi.org/10.3934/math.2022030.

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<abstract><p>In this paper, we introduce the notion of pseudo-semi-normed linear spaces, following the concept of pseudo-norm which was presented by Schaefer and Wolff, and illustrate their relationship. On the other hand, we introduce the concept of fuzzy pseudo-semi-norm, which is weaker than the notion of fuzzy pseudo-norm initiated by N$ \tilde{\rm{a}} $d$ \tilde{\rm{a}} $ban. Moreover, we give some examples which are according to the commonly used $ t $-norms. Finally, we establish norm structures of fuzzy pseudo-semi-normed spaces and provide (fuzzy) topological spaces induced by (fuzzy) pseudo-semi-norms, and prove that the (fuzzy) topological spaces are (fuzzy) Hausdorff.</p></abstract>

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Li, Ruini, and Jianrong Wu. "Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces." AIMS Mathematics 7, no. 3 (2022): 3290–302. http://dx.doi.org/10.3934/math.2022183.

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<abstract> <p>In this paper, we first study continuous linear functionals on a fuzzy quasi-normed space, obtain a characterization of continuous linear functionals, and point out that the set of all continuous linear functionals forms a convex cone and can be equipped with a weak fuzzy quasi-norm. Next, we prove a theorem of Hahn-Banach type and two separation theorems for convex subsets of fuzzy quasinormed spaces.</p> </abstract>

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Chandra Das, Paritosh. "On fuzzy normed linear space valued statistically convergent sequences." Proyecciones (Antofagasta) 36, no. 3 (2017): 511–27. http://dx.doi.org/10.4067/s0716-09172017000300511.

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Karpagavalli, S., and V. Visalakshi. "Fixed Point Theorem in Fuzzy Automata Normed Linear Space." Journal of Physics: Conference Series 1377 (November 2019): 012047. http://dx.doi.org/10.1088/1742-6596/1377/1/012047.

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Nadaban, Sorin. "Fuzzy Continuous Mappings in Fuzzy Normed Linear Spaces." International Journal of Computers Communications & Control 10, no. 6 (2015): 74. http://dx.doi.org/10.15837/ijccc.2015.6.2074.

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In this paper we continue the study of fuzzy continuous mappings in fuzzy normed linear spaces initiated by T. Bag and S.K. Samanta, as well as by I. Sadeqi and F.S. Kia, in a more general settings. Firstly, we introduce the notion of uniformly fuzzy continuous mapping and we establish the uniform continuity theorem in fuzzy settings. Furthermore, the concept of fuzzy Lipschitzian mapping is introduced and a fuzzy version for Banach’s contraction principle is obtained. Finally, a special attention is given to various characterizations of fuzzy continuous linear operators. Based on our results, classical principles of functional analysis (such as the uniform boundedness principle, the open mapping theorem and the closed graph theorem) can be extended in a more general fuzzy context.

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Krishna, S. V., and K. K. M. Sarma. "Separation of fuzzy normed linear spaces." Fuzzy Sets and Systems 63, no. 2 (1994): 207–17. http://dx.doi.org/10.1016/0165-0114(94)90351-4.

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F. Al-Mayahi, Noori, and Abbas M. Abbas. "Some Properties of Spectral Theory in Fuzzy Hilbert Spaces." Journal of Al-Qadisiyah for computer science and mathematics 8, no. 2 (2017): 1–7. http://dx.doi.org/10.29304/jqcm.2016.8.2.27.

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In this paper we give some definitions and properties of spectral theory in fuzzy Hilbert spaces also we introduce definitions Invariant under a linear operator on fuzzy normed spaces and reduced linear operator on fuzzy Hilbert spaces and we prove theorms related to eigenvalue and eigenvectors ,eigenspace in fuzzy normed , Invariant and reduced in fuzzy Hilbert spaces and show relationship between them.

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Konwar, Nabanita, and Pradip Debnath. "Intuitionistic fuzzy n-normed algebra and continuous product." Proyecciones (Antofagasta) 37, no. 1 (2018): 63–83. https://doi.org/10.22199/issn.0717-6279-2781.

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In this paper we extend the notion of intuitionistic fuzzy n-normed linear space (IFnNLS) to define an intuitionistic fuzzy n-normed algebra (IFnNA). We give a necessary and sufficient condition for an IFnNA to be with continuous product. Further, the concept of multiplicatively continuous product has been introduced and related results have been established. Illustrative examples have been provided in support of our results.

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