Some fixed point theorems in fuzzy normed linear spaces

In this paper, the concepts of sectional fuzzy continuous mappings, l-fuzzy compact sets, asymptotic fuzzy normal structure and strong uniformly convex fuzzy normed linear spaces have been introduced. Schauder-type and other fixed point theorems have been established in fuzzy normed linear spaces.     

On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces

Recently, the concept of statistical convergence of double sequences has been studied in intuitionistic fuzzy normed spaces by Mursaleen and Mohiuddine [Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, Solitons Fractals, 41 (2009) pp. 2414–2421]. We know that ideal convergence is more general than statistical convergence for single or double sequences. This has motivated us to study the ideal convergence of double sequences in a more general setting. That is, in this paper, we study the concept of ideal convergence and ideal Cauchy for double sequences in intuitionistic fuzzy normed spaces.     

Stability of Cauchy–Jensen type functional equation in generalized fuzzy normed spaces

In this paper, we establish some stability results concerning the Cauchy–Jensen functional equation in generalized fuzzy normed spaces. The results of the present paper improve and extend some recent results.     

Bipolar fuzzy graphs

In this paper, we introduce the notion of bipolar fuzzy graphs, describe various methods of their construction, discuss the concept of isomorphisms of these graphs, and investigate some of their important properties. We then introduce the notion of strong bipolar fuzzy graphs and study some of their properties. We also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs.     

Fuzzy hyperlattices

In this paper, we introduce the notion of fuzzy hyperlattices and establish connections between fuzzy hyperlattices and hyperlattices. Then we discuss the relations between the weak homomorphism of fuzzy hyperlattices and the weak homomorphism of corresponding hyperlattices. Moreover, we define and analyze the hypercongruence on hyperlattices and the fuzzy (strong) hypercongruence on fuzzy hyperlattices. And we study the interrelation between the (fuzzy) hypercongruence on (fuzzy) hyperlattices and the homomorphism of (fuzzy) hyperlattices. Also, a relation between the fuzzy hypercongruence on fuzzy hyperlattices and the hypercongruence on corresponding hyperlattices is obtained. Finally, we apply the hypercongruence and the fuzzy strong hypercongruence to construct quotient structures of hyperlattices and fuzzy hyperlattices, respectively.     

Fuzzy stability of a rational functional equation and its relevance to system design

This study demonstrates the solution and various stabilities of a rational functional equation involving two variables by means of fixed point tactic in the vicinity of Felbin's type fuzzy normed spaces. Only few functional equations are dealt to design systems or to model problems in real time examples. The functional equation considered in this paper focuses on designing various systems involving ridigity modulus and pressure.     

Intuitionistic fuzzy semiregularization spaces

We introduce the intuitionistic fuzzy semiregularization space induced by an intuitionistic fuzzy topological space. We also investigate some properties of intuitionistic fuzzy semiregularization spaces.     

赋范格H蕴涵代数和模糊格H蕴涵代数

在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。     

Constructions in the category of fuzzy T-proximity spaces

This paper is devoted to study the initial fuzzy T-proximity structures of the fuzzy T-proximity spaces defined by Hashem and Morsi in 2002, where T stands for any continuous triangular norm. In this paper, we show that all initial and final lifts in the category T-FPS of these fuzzy T-proximity spaces exist and hence the initial and final fuzzy T-proximity structures exist. We introduce a characterization for the initial fuzzy T-proximity structures, so as a special initial fuzzy T-proximity spaces, the subspaces and product spaces of these fuzzy T-proximity spaces can also be characterized. We also show that the fuzzy topology associated to the initial fuzzy T-proximity structure of a family of fuzzy T-proximity spaces, coincides with the initial fuzzy topology of the family of fuzzy topologies associated to these fuzzy T-proximity spaces.     

Fixed point theorems on fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy convergent sequence, l-fuzzy weakly convergent sequence and l-fuzzy weakly compact set are given in a fuzzy normed linear space. The concepts of fuzzy normal structure, fuzzy non-expansive mapping, uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.     

STRUCTURAL CHARACTERISTICS OF FUZZY MEASURE ON S-COMPACT SPACES

In systems research, the fuzzy measures we encounter most often are finite and established on S-compact spaces, which contain finite and infinitely countable measurable spaces. The structural characteristics of set function, such as null-additivity, autocontinuity, and uniform autocontinuity, are very important for the researches in fuzzy integral. For a fuzzy measure, the null-additivity is a quite weak requirement added on it, but the autocontinuity and the uniform autocontinuity are very powerful properties. In this paper, we prove that the null-additivity is equivalent to the uniform autocontinuity for the finite fuzzy measures on S-compact spaces.     

On mixed fuzzy topological spaces and countability

In this paper, we introduce a new type of mixed fuzzy topological space. We define countability on mixed fuzzy topological spaces. We investigate its different quasi type properties.     

Stability of mixed type functional equation in normed spaces using fuzzy concept

S. M. Ulam once addressed the problem ‘when is it true that a mathematical object satisfying a certain property approximately must be close to an object satisfying the property exactly?’. This problem was solved by D. H. Hyers in 1941 using the functional equation and thereafter numerous research papers and monographs have been published for various types of functional equations in different spaces. The solution proposed by D. H. Hyers (1941) later developed into the famous generalized Hyers-Ulam-Rassias stability of functional equations. In this paper, we intend to attain the general solution to a new mixed type functional equation and interrogate the generalized Hyers–Ulam–Rassias stability in fuzzy normed spaces. Also, we seek to provide its application for generating secret keys in client–server environment.     

Generalized Hermite Approximations and Spectral Method for Partial Differential Equations in Multiple Dimensions

In this paper, we consider a spectral method based on generalized Hermite functions in multiple dimensions. We first introduce three normed spaces and prove their equivalence, which enables us to develop and to analyze generalized Hermite approximations efficiently. We then establish some basic results on generalized Hermite orthogonal approximations in multiple dimensions, which play important roles in the relevant spectral methods. As examples, we consider an elliptic equation with a harmonic potential and a class of nonlinear wave equations. The spectral schemes are proposed, and the convergence is proved. Numerical results demonstrate the spectral accuracy of this approach.     

A general inequality of Chebyshev type for semi(co)normed fuzzy integrals

Generalization of the Chebyshev inequality for semi(co)normed fuzzy integrals on an abstract fuzzy measure space based on a binary operation is given. Also, Minkowski’s and Hölder’s inequalities for semi(co)normed fuzzy integrals are studied in a rather general form. The main results of this paper generalize some previous results. Finally, a conclusion is drawn and an open problem for further investigations is given.     

An axiomatic characterization of a fuzzy generalization of rough sets

In rough set theory, the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties. Several authors have proposed various fuzzy generalizations of rough approximations. In this paper, we introduce the definitions for generalized fuzzy lower and upper approximation operators determined by a residual implication. Then we find the assumptions which permit a given fuzzy set-theoretic operator to represent a upper (or lower) approximation derived from a special fuzzy relation. Different classes of fuzzy rough set algebras are obtained from different types of fuzzy relations. And different sets of axioms of fuzzy set-theoretic operator guarantee the existence of different types of fuzzy relations which produce the same operator. Finally, we study the composition of two approximation spaces. It is proved that the approximation operators in the composition space are just the composition of the approximation operators in the two fuzzy approximation spaces.     

Cycles and cocycles of fuzzy graphs

In this paper we show that if the fuzzy graph (σ,μ) is a cycle, then it is a fuzzy cycle if and only if (σ,μ) is not a fuzzy tree. We also examine the relationship between fuzzy bridges and cycles. We introduce and examine the concepts of chords, twigs, 1-chains with boundary zero, cycle vectors, coboundary, and cocycles for fuzzy graphs. We show that although the set of cycle vectors, fuzzy cycle vectors, cocycles, and fuzzy cocycles do not necessarily form vector spaces over the field Z₂ of integers modulo 2, they nearly do. Thisallows us to introduce the concepts of (fuzzy) cycle rank and (fuzzy) cocycle rank for fuzzy graphs in a meaningful way.     

Fuzzy probabilistic approximation spaces and their information measures

Rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information. By introducing probability into fuzzy approximation space, a theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model. We introduce Shannon's entropy to measure information quantity implied in a Pawlak's approximation space, and then present a novel representation of Shannon's entropy with a relation matrix. Based on the modified formulas, some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space, respectively. As a result, uniform representations of approximation spaces and their information measures are formed with this work.     

Properties of the solution set of a fuzzy relation equation from the viewpoint of attainability

 In a fuzzy relation equation, many properties of the solution set are known, especially when the basic spaces are all finite sets. However, when the basic spaces are infinite, only a few properties are known. In this paper, we introduce a new binary relation that is weaker than the ordinary one defined on fuzzy sets, and we show that an unattainable solution is partly characterized by the proposed binary relation.     

边缘检测在中国东部海域海表温度锋中的应用研究

针对海表温度锋的模糊边缘特点,首先利用詹森香农散度,借助4个方向,5×5大小的结构元素,对2009年、2010年中国东部海域海表温度(SST)卫星遥感数据进行处理,得到锋面的可能发生区,然后引入模糊蕴涵算子,对图像进行模糊变换,最后使用边缘检测方法提取锋面可能发生区内存在的温度锋。检测结果表明:在中国东部海域存在3个主要的锋面,各锋面的空间分布和强度均存在明显的季节变化,大致呈现冬春强,夏秋弱的趋势。