双极值模糊软子群和双极值模糊正规软子群

研究了双极值模糊软子群的等价刻画。在双极值模糊软子群的基础上定义了双极值模糊正规软子群,得到了它的一些性质及等价刻画,进一步还研究了在双极值模糊软同态下,双极值模糊正规软子群的像与原像一些性质。     

Preferential normal fuzzy subgroups

In this paper we consider the notion of normality on preferential fuzzy subgroups of a finite group G and define the associated concept of a normal pinned-flag. We discuss the preferential equality of quotients and products of normal preferential fuzzy subgroups. Further normalizers of fuzzy subgroups under preferential equality are briefly dealt with. Examples are given to illustrate the structure of preferential normal fuzzy subgroups and normal pinned-flags.     

Some constructions of the join of fuzzy subgroups and certain lattices of fuzzy subgroups with sup property

In this paper, some new lattices of fuzzy substructures are constructed. For a given fuzzy set μ in a group G, a fuzzy subgroup S(μ) generated by μ is defined which helps to establish that the set L_s of all fuzzy subgroups with sup property constitutes a lattice. Consequently, many other sublattices of the lattice L of all fuzzy subgroups of G like , etc. are also obtained. The notion of infimum is used to construct a fuzzy subgroup i(μ) generated by a given fuzzy set μ, in contrast to the usual practice of using supremum. In the process a new fuzzy subgroup i(μ)^∗ is defined which we shall call a shadow fuzzy subgroup of μ. It is established that if μ has inf property, then i(μ)^∗ also has this property.     

Distributivity in lattices of fuzzy subgroups

The main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive. We obtain a characterization of these groups which is similar to a well-known result of group theory.     

Fuzzy orders relative to fuzzy subgroups

In this paper, we introduce the notion of fuzzy orders of the elements of a group and show that most of the basic properties of orders of elements in the group theory are valid in the theory of fuzzy groups where ordinary orders of elements are replaced by fuzzy orders of elements. Reports of further development of the subject will follow in subsequent essays.     

双极值模糊（反）软子群

在双极值模糊软集理论的基础上,给出了双极值模糊（反）软子群的概念,讨论了它们的一些相关性质及等价刻画。提出了双极值模糊软映射下双极值模糊软集的像与原像的概念,并研究了双极值模糊软同态下双极值模糊（反）软子群的同态像与原像的初等性质。     

On the definition of the intuitionistic fuzzy subgroups

In this paper, a new kind of intuitionistic fuzzy subgroup theory, which is different from that of Ma, Zhan and Davvaz (2008) [22], [23], is presented. First, based on the concept of cut sets on intuitionistic fuzzy sets, we establish the neighborhood relations between a fuzzy point $x_a$ and an intuitionistic fuzzy set $A$. Then we give the definitions of the grades of $x_a$ belonging to $A$, $x_a$ quasi-coincident with $A$, $x_a$ belonging to and quasi-coincident with $A$ and $x_a$ belonging to or quasi-coincident with $A$, respectively. Second, by applying the 3-valued Lukasiewicz implication, we give the definition of $(\alpha ,\beta )$-intuitionistic fuzzy subgroups of a group $G$ for $\alpha ,\beta \in \{\in ,q,\in \wedge q,\in \vee q\}$, and we show that, in 16 kinds of $(\alpha ,\beta )$-intuitionistic fuzzy subgroups, the significant ones are the $(\in ,\in )$-intuitionistic fuzzy subgroup, the $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup and the $(\in \wedge q,\in )$-intuitionistic fuzzy subgroup. We also show that $A$ is a $(\in ,\in )$-intuitionistic fuzzy subgroup of $G$ if and only if, for any $a\in (0,1]$, the cut set $A_a$ of $A$ is a 3-valued fuzzy subgroup of $G$, and $A$ is a $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup (or $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup) of $G$ if and only if, for any $a\in (0,0.5]$(or for any $a\in (0.5,1]$), the cut set $A_a$ of $A$ is a 3-valued fuzzy subgroup of $G$. At last, we generalize the $(\in ,\in )$-intuitionistic fuzzy subgroup, $(\in ,\in \vee q)$-intuitionistic fuzzy subgroup and $(\in \wedge q,\in )$-intuitionistic fuzzy subgroup to intuitionistic fuzzy subgroups with thresholds, i.e., $(s,t]$-intuitionistic fuzzy subgroups. We show that $A$ is a $(s,t]$-intuitionistic fuzzy subgroup of $G$ if and only if, for any $a\in (s,t]$, the cut set $A_a$ of $A$ is a 3-valued fuzzy subgroup of $G$. We also characterize the $(s,t]$-intuitionistic fuzzy subgroup by the neighborhood relations between a fuzzy point $x_a$ and an intuitionistic fuzzy set $A$.     

A characterization of fuzzy subgroups of some Abelian groups

We introduce the notion of fuzzy p^*-subgroups and characterize fuzzy subgroups of torsion groups and cyclic groups by their minimal fuzzy p-subgroups and minimal fuzzy p^*-subgroups.     

The equivalence between fuzzy Mealy and fuzzy Moore machines

We study the relationships between fuzzy Mealy and fuzzy Moore machines in the frame of truth values in a lattice-ordered monoid. In particular, we show that lattice-valued sequential-like machines and lattice-valued finite Moore machines are equivalent in the sense they exhibit the same input–output characteristics.     

Approximate unions of lines and minkowski sums

We study the complexity of, and algorithms to construct, approximations of the union of lines and of the Minkowski sum of two simple polygons. We also studythick unions of lines and Minkowski sums, which are inflated with a small disc. Letb=D/ɛ be the ratio of the diameter of the region of interest and the maximum distance (or error) of the approximation. An approximate union of lines or Minkowski sum has complexity Θ (b ²) in the worst case. The thick union ofn lines has complexity Ω(n+b ²) andO(n +b√bn), and thick Minkowski sums have complexity Ω(n ²+b²) andO((n+b)n√blogn+n ² logn) in the worst case. We present algorithms that run inO(n+n ^2/3+δ b ^4/3 andO(min(bn,n ^4/3+δ b ^2/3)) time (any δ>0) for approximate and thick arrangements. For approximate Minkowski sums, the running time isO(min(b ² n,n ² +b ² + (nb)^4/3+δ); thick Minkowski sums takeO(n ^8/3+δ b ^2/3) time to compute.     

Fuzzy subgroups and similarities

 Given a set S, we show that there is a strict relation between the notion of similarity on S and the one of fuzzy subgroup of transformations in S . Such a relation enables us to extablish a connection between fuzzy subgroups and distances.     

Canonization for disjoint unions of theories

If there exist efficient procedures (canonizers) for reducing terms of two first-order theories to canonical form, can one use them to construct such a procedure for terms of the disjoint union of the two theories? We prove this is possible whenever the original theories are convex. As an application, we prove that algorithms for solving equations in the two theories (solvers) can not be combined in a similar fashion. These results are relevant to the widely used Shostak’s method for combining decision procedures for theories. They provide the first rigorous answers to the questions about the possibility of directly combining canonizers and solvers.     

Image interpolation using unions of spheres

union of spheres volumetric model of an image. The technique requires little preprocessing and is not labour-intensive. It allows the user a reasonable degree of control of the matching process. Our method easily facilitates intuitive manual specification of features where desired. The results of our tests are very positive. The problems encountered in using our algorithm are largely predictable and suggest definite directions for future work.     

The complex fuzzy system forecasting model based on fuzzy SVM with triangular fuzzy number input and output

This paper presents a new version of fuzzy support vector machine to forecast the nonlinear fuzzy system with multi-dimensional input variables. The input and output variables of the proposed model are described as triangular fuzzy numbers. Then by integrating the triangular fuzzy theory and v-support vector regression machine, the triangular fuzzy v-support vector machine (TFv-SVM) is proposed. To seek the optimal parameters of TFv-SVM, particle swarm optimization is also applied to optimize parameters of TFv-SVM. A forecasting method based on TFv-SVRM and PSO are put forward. The results of the application in sale system forecasts confirm the feasibility and the validity of the forecasting method. Compared with the traditional model, TFv-SVM method requires fewer samples and has better forecasting precision.     

Compressed bitmap indexes: beyond unions and intersections

Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND, OR and NOT) that are ideally suited for bitmaps. However, it is less obvious how to apply bitmaps to more advanced queries. For example, we might seek products in a store that meet some, but maybe not all, criteria. Such threshold queries generalize intersections and unions; they are often used in information‐retrieval and data‐mining applications. We introduce new algorithms that are sometimes three orders of magnitude faster than a naïve approach. Our work shows that bitmap indexes are more broadly applicable than is commonly believed. Copyright © 2014 John Wiley & Sons, Ltd.     

模糊识别方法及其应用

模式识别的应用日益广泛,在现实世界中,存在着许多定义不太严格或者说具有模糊性的概念。这就要求相应的识别方法进行识别,本文首先对模式识别进行介绍,在此基础上讲解模糊识别的方法及其应用。