Fuzzy Normed Research Articles

Intuitionistic fuzzy stability results of additive functional equation by two different approaches

In this current work, we examine the Hyers-Ulam(H-U) stability results for a finite variable additive functional equation (Ref.[6]) in Intuitionistic Fuzzy Normed space(IFN-space) is discussed by means of direct and fixed point methods.

A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces

This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.

A Study of Spaces of Sequences in Fuzzy Normed Spaces

In this paper, spaces of sequences in fuzzy normed spaces are considered. These spaces are a new concept in fuzzy normed spaces. We develop fuzzy norms for spaces of sequences in fuzzy normed spaces. Especially, we study the representation of the dual of a space of sequences in a fuzzy normed space. The approximation property in our context is investigated.

Some Properties of Fuzzy Compact Algebra Fuzzy Normed Spaces and Finite Dimensional Algebra Fuzzy Normed Spaces

Our goal in this article is to recall the notion of algebra fuzzy normed space and its basic properties to introduce the notion of fuzzy compact algebra fuzzy normed space. Then some properties of fuzzy compact algebra fuzzy normed spaces are proved. After that, we study a finite dimensional algebra fuzzy normed space and we proved some properties that algebra fuzzy normed spaces do not admit it.

Application of Fixed Point in Algebra Fuzzy Normed Spaces

In the present paper first we recall the definition of algebra fuzzy metric space and some basic properties of algebra fuzzy metric space are introduced. Our goal is to prove the fixed point theorem in fuzzy complete algebra fuzzy metric space. Finally, the application to this theorem introduced.

On the Completion of Fuzzy Normed Linear Spaces in the Sense of Bag and Samanta

In this paper, the completion of fuzzy normed linear space (in the sense of Bag and Samanta) is studied. First, some properties of convergence fuzzy point sequences are discussed. Specially, we give another characterisation of Q-neighbourhood base of for I-topology introduced by Saheli. Then we show that each fuzzy normed linear space has an (up to isomorphism) unique complete fuzzy normed linear space which contains an uniformly dense in every stratum subspace isomorphic to it.

Fuzzy Inner Product Space: Literature Review and a New Approach

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

Fuzzy Stability Results of Generalized Quartic Functional Equations

In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable.

Linear fuzzifying uniformities

The main purpose of this paper is to study Hutton type fuzzifying uniformities on linear spaces. Firstly, we show that if a base of a fuzzifying uniformity defined over a linear space is translation-invariant, balanced and absorbed, then it generates a linear fuzzifying topology. From this linear fuzzifying topology, we can construct a new linear fuzzifying uniformity (i.e., a fuzzifying uniformity compatible with the linear structure) which is equivalent to the original fuzzifying uniformity. Secondly, the Hausdorff separation and complete boundedness in linear fuzzifying uniformities are investigated. In addition, as an example, the linear fuzzifying uniformity induced by a fuzzy norm is also discussed.

Fuzzy stability results deriving form quadratic functional equation

We establish the generalized Hyers-Ulam stability of the 4 variable quadratic functional equation in Fuzzy Normed Spaces using two different methods.

On Properties of Ideal Convergent Sequences in Jordan Intuitionistic Fuzzy Normed Spaces

On Properties of Ideal Convergent Sequences in Jordan Intuitionistic Fuzzy Normed Spaces

On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces

We introduce logarithmic summability in intuitionistic fuzzy normed spaces($IFNS$) and give some Tauberian conditions for which logarithmic summability yields convergence in $IFNS$. Besides, we define the concept of slow oscillation with respect to logarithmic summability in $IFNS$, investigate its relation with the concept of q-boundedness and give Tauberian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability. A comparison theorem between Ces\`{a}ro summability method and logarithmic summability method in $IFNS$ is also proved in the paper.

Some Properties of Algebra Fuzzy Absolute ValueSpace and Algebra Fuzzy Normed Space

Our aim in the this research is to introduce the notion of algebra fuzzy absolute value in order to introduce new type of fuzzy normed space called algebra fuzzy normed space after that some examples is introduced to illustrate these notions. Then some properties of algebra fuzzy absolute value space are proved after that basic of algebra fuzzy normed space also proved.

A new intuitionistic fuzzy definiteness norm

In the present paper we introduce a new intuitionistic fuzzy norm over intuitionistic fuzzy pairs and study some of its properties.

Schauder-Type Fixed Point Theorem in Generalized Fuzzy Normed Linear Spaces

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at (1,1). In the fuzzy setting, the concept of the measure of non-compactness is introduced, and some basic properties of the measure of non-compactness are investigated. Darbo’s generalization of the Schauder-type fixed point theorem is developed for the class of ψ-set contractions. This theorem is proven by using the idea of the measure of non-compactness.

Intuitionistic Fuzzy Normed Subrings and Intuitionistic Fuzzy Normed Ideals

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of intuitionistic fuzzy normed rings, we define the concept of intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Some essential operations specially subset, complement, union, intersection and several properties relating to the notion of generalized intuitionistic fuzzy normed rings are identified. Homomorphism and isomorphism of intuitionistic fuzzy normed subrings are characterized. We identify the image and the inverse image of intuitionistic fuzzy normed subrings under ring homomorphism and study their elementary properties. Some properties of intuitionistic fuzzy normed rings and relevant examples are presented.

On the completion of Quasi-fuzzy normed algebra over fuzzy field

The article describes a new concepts in fuzzy mathematics, we introduce fuzzy normed algebra over fuzzy field, Quasi -fuzzy norm, Quasi-p-fuzzy algebra over fuzzy field, Quasi- fuzzy algebra over fuzzy field, and quasi-p-fuzzy algebra over fuzzy field (S, F). We define convergent in fuzzy normed algebra over fuzzy field, Cauchy sequences in Quasi- fuzzy algebra over fuzzy field and open ball in it . Also, we prove every Quasi- normed algebra can be embedded in Quasi - Banach algebra X and an isometry L from X on to a sub algebra Y of X which is dense in X. The Quasi- algebra Ŷ is unique up to isometry, and an isometry L from X on to a sub algebra Y of X which is dense in X. The Quasi- algebra Ŷ is unique up to isometry.

Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness

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.

Fuzzy Hysteresis Smoothing: A New Approach for Image Denoising

Hysteresis smoothing (HS) is one of the recently proposed image denoising schemes, which employs hard threshold levels to model the hysteresis process. Nevertheless, hard thresholding is in contrast with what is observed from the behavior of the hysteresis phenomenon in nature, and this implies that the HS may lead to a suboptimal model. On the other hand, it is proved that fuzzy logic is a promising research field in solving various problems by applying the uncertainty characteristics. Hence, in this article, we develop a novel HS methodology based on the fuzzy norms, which, in addition to incorporating the advantages of the HS, also manages the undesired effects of hard thresholding. In this method, which is called fuzzy HS (FHS), pointwise hard thresholding is replaced by an interval soft manner, which allows the threshold levels to be determined commensurate with the fuzzy norm's free parameter. It is shown that among the classical fuzzy norms, the Yager one can carry out the FHS relatively well. However, this norm causes oversaturation in the hysteresis loop, which leads to an oversmoothing problem in the image denoising process. To alleviate this, a new fuzzy norm with logarithmic nature, named expansion norm, has been proposed, which improves the accuracy of the FHS. The comparative simulations demonstrate the significant superiority of the FHS in terms of both objective and subjective criteria over the classical HS. Besides, the results indicate that the proposed scheme has competitive denoising performance in comparison with some well-known algorithms.

Quadratic (s1,s2)-functional inequality in fuzzy normed space

In this paper, we introduce and prove the Generalized Hyers-Ulam stability of Quadratic (s1,s2)-functional inequality in Fuzzy Normed space using the fixed point method.