Fuzzy Normed Research Articles

Fuzzy Bounded and Continuous Linear Operators on Standard Fuzzy Normed Spacesa

Fuzzy Bounded and Continuous Linear Operators on Standard Fuzzy Normed Spacesa

Fixed Point of Generalized Eventual Cyclic Gross in Fuzzy Norm Spaces for Contractive Mappings

We define generalized eventual cyclic gross contractive mapping in fuzzy norm spaces, which is a generalization of the eventual cyclic gross contractions. Also we prove the existence of a fixed point for this type of contractive mapping on fuzzy norm spaces.

Fuzzy pseudo-norms and fuzzy F-spaces

In the present paper we firstly introduce the notion of fuzzy pseudo-norm, then we extend, improve and complete the results obtained by T. Bag and S.K. Samanta for fuzzy norms, in the fuzzy pseudo-norms context. Lastly, we introduce and discuss the notions of fuzzy F-norm and fuzzy F-space. By means of several auxiliary results, we obtain a characterization of metrizable topological linear spaces in terms of fuzzy F-norm.

Lacunary Statistical Convergence of Multiple Sequences in Intuitionistic Fuzzy Normed Spaces

In this paper we introduce the notion ideal statistical convergence and ideal lacunary statistical convergence of multiple sequences with respect to the intuitionistic fuzzy norm (μ, v), investigate their relationships, and make some observations about these classes.

Fuzzy Euclidean Normed Spaces for Data Mining Applications

The aim of this paper is to introduce some special fuzzy norms on Kn and to obtain, in this way, fuzzy Euclidean normed spaces. In order to introduce this concept we have proved that the cartesian product of a finite family of fuzzy normed linear spaces is a fuzzy normed linear space. Thus any fuzzy norm on K generates a fuzzy norm on Kn. Finally, we prove that each fuzzy Euclidean normed space is complete. Fuzzy Euclidean normed spaces can be proven to be a suitable tool for data mining. The method is based on embedding the data in fuzzy Euclidean normed spaces and to carry out data analysis in these spaces.

Fuzzy norm method for evaluating random vibration of airborne platform from limited PSD data

For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density (PSD) data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method (FNM) is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.

On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

Certain summability methods in intuitionistic fuzzy normed spaces

In this paper, we introduce the notion of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence with respect to the intuitionistic fuzzy norm $\left( \mu,v\right)...

Fuzzy Inner Product and Fuzzy Norm \of Hyperspaces

We introduce and study fuzzy (co-)inner product and fuzzy (co- )norm of hyperspaces. In this regard by considering the notion of hyperspaces, as a generalization of vector spaces, rst we will introduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions of fuzzy (co-)norm and fuzzy (co-)orthogonality in hyperspaces. In particular, we will prove that to every fuzzy hyperspace there is an associated unique fuzzy inner product in a natural way.

Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces

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.

SOME PROPERTIES OF FUZZY NORM OF LINEAR OPERATORS

In the present paper, we study some properties of fuzzy norm of linear operators. At rst the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

DET-NORM ON FUZZY MATRICES

In this paper we introduce fuzzy det-norm ordering with fuzzy matrices using the structure of Mn(F), the set of (n×n) fuzzy det-norm ordering with fuzzy matrices is introduced. From this row and column, determinant of the fuzzy norm has been obtained by imposing an equivalence relation on Mn(F). We know that the comparability relation on fuzzy matrices is a partial ordering. We prove that det-norm ordering is a partitions ordering on the set of all idempotent matrices in Mn(F). We begin with the det-norm ordering on fuzzy matrices as analogue of the ordering on real matrices. Several properties of these orderings are derived. Discuss their relationship between these ordering with det-norm ordering and Also we introduce the concept of Fuzzy norm and partitions of Mn(F), Properties of fuzzy det-norm ordering.

Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces

Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces

Approximation of a General Cubic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces

In this paper, we investigate the generalized Hyers–Ulam stability of a general cubic functional equation in Felbin’s type fuzzy normed linear spaces and some applications of our results in the stability of general cubic functional equation from a linear space to a Banach space will be exhibited.

On I-Limit Superior and I-Limit Inferior of Sequences in Intuitionistic Fuzzy Normed Spaces

In this article we introduce the notions of I-limit superior and I-limit inferior for sequences in intuitionistic fuzzy normed linear spaces and prove intuitionistic fuzzy analogue of some results of I-limit superior and I-limit inferior for real sequences. The concept of I-limit points and I-cluster points in intuitionistic fuzzy normed linear spaces are introduced and some of their properties have been established.

Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications

Wavelet analysis is a powerful tool with modern applications as diverse as: image process- ing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in applications to signal processing and sampling theory among other areas. First we give a general definition of fuzzy normed linear spaces and we obtain decomposition theorems for fuzzy norms into a family of semi-norms, within more general settings. The results are both for Bag-Samanta fuzzy norms and for Katsaras fuzzy norms. As a consequence, we obtain locally convex topologies induced by this types of fuzzy norms. The results established in this paper, constitute a foundation for the development of fuzzy operator

The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited

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.

Approximate Quadratic-Additive Mappings in Fuzzy Normed Spaces

We examine the generalized Hyers-Ulam stability of the following functional equation:2fx+y+z+w+f-x-y+z+w+f-x+y-z+w+f-x+y+z-w+fx-y-z+w+fx-y+z-w+fx+y-z-w-5fx-3f-x-5fy-3f-y-5fz-3f-z-5fw-3f-w=0,in the fuzzy normed spaces with the fixed point method.

Certain summability methods in intuitionistic fuzzy normed spaces

In this paper, we introduce the notion of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence with respect to the intuitionistic fuzzy norm $\left( \mu,v\right) $, investigate their relationship, and make some observations about these classes.

A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces

We introducefuzzy norm-preservingmaps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, we provide the following generalized version of the Mazur-Ulam theorem in the fuzzy context: letX,Ybe fuzzy normed spaces and letf:X→Ybe a fuzzy norm-preserving surjection satisfyingf(0)=0. Thenfis additive.