A New Form of Fuzzy Compact Spaces and Related Topics via Fuzzy Idealization

Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon.     

The Semantical Completeness of the Extensions Ln^＊ to the System L^＊ ＊

The terminology of “fuzzy logic” has been formed and employed with different meanings by a large number of researchers soon after Zadeh published his initiate paper (see [1]), but perhaps the most serious work on fuzzy logic is the Pavelka‘s series papers (see [2]) which provided a systematical theory of fuzzy logic mathematically and profoundly, and hence has been accepted by scholars as a standard theory in developing their researches on fuzzy logic.     

A SURVEY OF SOME ASPECTS ON THE RESEARCH WORK OF FUZZY TOPOLOGY IN CHINA

The fundamental concept of a fuzzy set,introduced by Zadeh in 1965 [34] provides a natural foundation for treating mathematically the fuzzy phenomena which exist prevasively in our real world and for building new branches of fuzzy mathematics.In the area of fuzzy topology much research has been carried out since 1968 [1].     

Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

ON THE ORDER PROPERTIES OF DIGITAL CURVES IN THE PAN-EUCLIDEAN GEOMETRY

How to increase the speed in drawing and recognizing curves has always been a major concern. From the Breshenham Algorithm and DDA Algorithm in the sixties to the double-step and quadruple-step line generation iu the eighties, curves were all dragon point by point. The algorithm in this paper fully utilizes machine commands to accelerate the generation of lines and curves. We introduce and prove for the first time characterization theorems of the segment code order of digital lines and curyes. These theorems give new methods in the recognition and the measure of smoothness of lines and curves.     

THE OPERATIONAL VIEWPOINT AND SOME OF ITS CONSEQUENCES: A SHORT REVIEW

This paper presents first results on fuzzy set theory (with the emphasis on probability theoretical aspects) from an operational viewpoint, a new approach that claims to be a way out of some of the difficulties and to present a consistent framework for the set-theoretical aspects of fuzzy set theory (e.g.the complementation paradoxes vanish, and fuzzy sets become a topos under this interpretation). As a preliminary conclusion of this approach we conjecture that the concept of fuzzy set has two essentially different semantical dimensions, which have not sufficiently been separated in the traditional theory, they may be considered either as an evaluation over a universe (i.e. as a connotation) or as a collection of evaluated object (i.e.as a denotation).     

THE 'HYBRID' TECHNIQUE FOR RISK ANALYSIS OF SOME DISEASES

51. IntroductionSince the theory of fuszy set was introduced by Lotfi A. Zadeh in 1965, fuzzy techniquehas developed rapidly and has been successfully aPplied into many fields.In receat yeaJrs3 a new and promising way of using the fuzzy technique is combinedwith other deterministic and statistica1 methods. The so-called 'hybrid' technique has beenaPplied to insurance business and achieved positive results (see [1, 2], etc.).Based on the data obtained from a survey recelltly made in a commun…     

半模糊凸模糊映射

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.     

Heteroscedasticity check in nonlinear semiparametric models based on nonparametric variance function

The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.     

TESTING DIFFERENT CONJUGATE GRADIENT METHODS FOR LARGE—SCALE UNCONSTRAINED OPTIMIZATION

In this PaPer we test different conjugate gradient (CG) methods for solving large-scale unconstrained optimization problems.The methods are divided in two groups:the first group includes five basic CG methods and the second five hybrid CG methods.A collection of medium-scale and large-scale test problems are drawn from a standard code of test problems.CUTE.The conjugate gradient methods are ranked according to the numerical results.Some remarks are given.     

Fuzzy codes and distance properties

A fuzzy code is defined as a fuzzy subset of n-tuples over a set F. An analysis of the Hamming distance between two fuzzy codewords and the error-correcting capability of a regular code in terms of its corresponding fuzzy code is presented.     

A bipolar model of assertability and belief

Valuation pairs are introduced as a bipolar model of the assertability of propositions. These correspond to a pair of dual valuation functions, respectively, representing the strong property of definite assertability and the dual weaker property of acceptable assertability. In the case where there is uncertainty about the correct valuation pair for a language then a probability distribution is defined on possible valuation pairs. This results in two measures, μ⁺ giving the probability that a sentence is definitely assertable, and μ⁻ giving the probability that a sentence is acceptable to assert. It is shown that μ⁺ and μ⁻ can be determined directly from a two dimensional mass function m defined on pairs of sets of propositional variables. Certain natural properties of μ⁺ and μ⁻ are easily expressed in terms of m, and in particular we introduce certain consonance or nestedness assumptions. These capture qualitative information in the form of assertability orderings for both the propositional variables and the negated propositional variables. On the basis of these consonance assumptions we show that label semantics, intuitionistic fuzzy logic and max-min fuzzy logic can all be viewed as special cases of this bipolar model. We also show that bipolar belief measures can be interpreted within an interval-set model.     

On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse

This paper proposes a general study of (I,T)-interval-valued fuzzy rough sets on two universes of discourse integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. Some primary properties of interval-valued fuzzy logical operators and the construction approaches of interval-valued fuzzy T-similarity relations are first introduced. Determined by an interval-valued fuzzy triangular norm and an interval-valued fuzzy implicator, a pair of lower and upper generalized interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy relation on two universes of discourse is then defined. Properties of I-lower and T-upper interval-valued fuzzy rough approximation operators are examined based on the properties of interval-valued fuzzy logical operators discussed above. Connections between interval-valued fuzzy relations and interval-valued fuzzy rough approximation operators are also established. Finally, an operator-oriented characterization of interval-valued fuzzy rough sets is proposed, that is, interval-valued fuzzy rough approximation operators are characterized by axioms. Different axiom sets of I-lower and T-upper interval-valued fuzzy set-theoretic operators guarantee the existence of different types of interval-valued fuzzy relations which produce the same operators.     

On distorted probabilities and m-separable fuzzy measures

Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2ⁿ parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature.In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions.     

Fuzzy local ω-systems

The natural language computing today demands for the study of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, the concept of fuzzy local ω-language, Büchi fuzzy local ω-language, and some closure properties of fuzzy local ω-languages are presented. We introduce deterministic fuzzy finite automaton with different acceptance mode on fuzzy ω-languages and establish the relationship between these various classes of fuzzy ω-languages. We have defined deterministic fuzzy local automaton and also establish relationships between deterministic fuzzy local automaton, fuzzy local ω-language and Büchi fuzzy local ω-language. Further we show that every fuzzy regular ω-language is a projection of a Büchi fuzzy local ω-language.     

Pseudolinear fuzzy mappings

Two classes of fuzzy mappings, called pseudolinear and η-pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo-convex and pseudo-invex fuzzy mappings. First, some characterizations of pseudolinear and η-pseudolinear fuzzy mappings are obtained. Then, characterizations of the solution sets of pseudolinear and η-pseudolinear fuzzy programs are derived.     

A linear regression model for imprecise response

A linear regression model with imprecise response and p real explanatory variables is analyzed. The imprecision of the response variable is functionally described by means of certain kinds of fuzzy sets, the LR fuzzy sets. The LR fuzzy random variables are introduced to model usual random experiments when the characteristic observed on each result can be described with fuzzy numbers of a particular class, determined by 3 random values: the center, the left spread and the right spread. In fact, these constitute a natural generalization of the interval data. To deal with the estimation problem the space of the LR fuzzy numbers is proved to be isometric to a closed and convex cone of R³ with respect to a generalization of the most used metric for LR fuzzy numbers. The expression of the estimators in terms of moments is established, their limit distribution and asymptotic properties are analyzed and applied to the determination of confidence regions and hypothesis testing procedures. The results are illustrated by means of some case-studies.     

Some comments on fuzzy variables

Nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed. In this paper we attempt to shed more light on fuzzy variables in analogy with random variables. In particular, we study the problem: if X₁, X₂,…,X_n are mutually unrelated fuzzy variables with common membership function μ and α₁, α₂,…,α_n are real numbers satisfying α_i ? o for every i and Σ_i=1ⁿα_i=1, when does does Z = Σ_{i = 1}ⁿα_iX_i have the same membership function μ?     

An Evolutionary Approach to Spatial Fuzzy c-Means Clustering

Fuzzy c-means clustering algorithm (FCM) can provide a non-parametric and unsupervised approach to the cluster analysis of data. Several efforts of fuzzy clustering have been undertaken by Bezdek and other researchers. Earlier studies in this field have reported problems due to the setting of optimum initial condition, cluster validity measure, and high computational load. More recently, the fuzzy clustering has benefited of a synergistic approach with Genetic Algorithms (GA) that play the role of an useful optimization technique that helps to better tolerate some classical drawbacks, such as sensitivity to initialization, noise and outliers, and susceptibility to local minima. We propose a genetic-level clustering methodology able to cluster objects represented by R ^p spaces. The unsupervised cluster algorithm, called SFCM (Spatial Fuzzy c-Means), is based on a fuzzy clustering c-means method that searches the best fuzzy partition of the universe assuming that the evaluation of each object with respect to some features is unknown, but knowing that it belongs to circular regions of R ² space. Next we present a Java implementation of the algorithm, which provides a complete and efficient visual interaction for the setting of the parameters involved into the system. To demonstrate the applications of SFCM, we discuss a case study where it is shown the generality of our model by treating a simple 3-way data fuzzy clustering as example of a multicriteria optimization problem.     

Evaluation of fully fuzzy matrix equations by fuzzy neural network

In this paper, a new hybrid method based on fuzzy neural network for approximate solution of fully fuzzy matrix equations of the form AX=D$\mathit{AX}=D$, where A and D are two fuzzy number matrices and the unknown matrix X is a fuzzy number matrix, is presented. Then, we propose some definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy matrix equations and fuzzy neural network. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of fuzzy matrix equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the fuzzy neural network is proposed. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.