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.     

群上的模糊软同余

为了进一步研究模糊软集理论,通过将软集与模糊同余结合,给出了模糊软同余的定义,并在一定程度上推广了模糊软集。研究了群上的模糊软同余的相关性质。建立了群上的模糊软同余与正规模糊软群之间的联系,给出了软模糊同态定理。     

一类格值自动机的极小化

给出了格值自动机的同余和同态,从代数角度出发详细研究了同余和同态关系的代数性质,揭示了格值自动机的代数性质和取值格半群的紧密联系,利用同余和同态关系最终研究了格值自动机的极小化问题,在正则同余下给出了可在有限步实现具有模糊初始状态和特殊模糊终状态的自动机极小化的算法。     

Congruences et Automorphismes des Automates Finis

Summary We study a class of congruences of strongly connected finite automata, called the group congruences, which may be defined in this way: every element fixing any class of the congruence induces a permutation on this class. These congruences form an ideal of the lattice of all congruences of the automaton and we study the group associated with the maximal group congruence (maximal induced group) with respect to the Suschkevitch group of the transition monoid of . The transitivity equivalence of the subgroups of the automorphism group of are found to be the group congruences associated with regular groups, which form also in ideal of the lattice of congruences of . We then characterize the automorphism group of with respect to the maximal induced group. As an application, we show that, given a group G and an automaton , there exists an automaton whose automorphism group is isomorphic to G and such that the quotient by the automorphism congruence is .     

剩余格的T-模糊滤子与T-模糊同余关系

将t-模应用于模糊滤子和模糊同余上,引入剩余格的T-模糊滤子与T-模糊同余,并分别研究T-模糊滤子与T-模糊同余的性质与一些等价刻画;得到全体T-模糊滤子的集合与T-模糊同余的集合是同构;研究了由T-模糊滤子所诱导的商剩余格以及同态定理。这些理论在其他的逻辑代数系统仍然成立。     

The schnittaxiom and unions of fuzzy subgroups

A necessary and sufficient condition for the union of an arbitrary family of fuzzy subgroups of a group to be a fuzzy group has been proposed. The criterion which gives a cut of the unit interval is called the Schnittaxiom. It has been applied successfully to investigate fuzzy subgroupness of arbitrary unions of homomorphic images and preimages.     

Bisimulations for a calculus of broadcasting systems

We develop a theory of bisimulation equivalence for the broadcast calculus CBS. Both the strong and weak versions of bisimulation congruence we study are justified in terms of a characterisation as the largest CBS congruences contained in an appropriate version of barbed bisimulation. We then present sound and complete proof systems for both the strong and weak congruences over finite terms. The first system we give contains an infinitary proof rule to accommodate input prefixes. We improve on this by presenting a unitary proof system where judgements are relative to properties of the data domain.     

On fuzzy spaces and fuzzy group theory

The concept of fuzzy space is introduced. This concept corresponds to the concept of the universal set in the ordinary case. The algebra of fuzzy spaces and fuzzy subspaces is studied. Using the concept of fuzzy space and fuzzy binary operation, a new approach to study fuzzy group theory is given. This approach can be considered as a generalization and reformulation of the Rosenfeld theory of fuzzy subgroups. Therefore, it is an active tool to develop the theory of fuzzy groups.     

基于前景M-V准则的正态三角模糊随机多属性决策方法

针对具有正态三角模糊随机变量且属性权重未知的多属性决策问题, 提出基于前景均值-方差(M-V) 准则的正态三角模糊随机多属性决策方法. 该方法首先构建正态三角模糊随机决策矩阵, 进而通过运算得到属性值的期望与方差, 并将其转化为M-V 决策矩阵; 然后, 通过定义前景效应构建前景M-V 决策矩阵, 利用改进灰色系统理论模型求解属性权重值, 获取综合前景M-V 决策矩阵; 最后, 定义前景序关系, 两两比较前景M-V 价值获取方案排序. 在此基础上, 通过案例验证了所提出方法的可行性及有效性.

     

Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs.

This paper studies reliable linear quadratic (LQ) fuzzy regulator problem for nonlinear discrete-time systems with actuator faults. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. A sufficient condition expressed in linear matrix inequality (LMI) terms for the existence of reliable guaranteed cost (GC) fuzzy controllers is obtained. The fuzzy controller directly obtained from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system, while provide a guaranteed cost on the quadratic cost function of the system in the normal and actuator fault cases. Furthermore, an optimal reliable GC fuzzy controller in the sense of minimizing a bound on the worst or nominal case guaranteed cost is also given by means of an LMI optimization procedure. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Fuzzy relations and fuzzy groups

Given a group S, we consider fuzzy relations on S, that is, maps from S × S into [0,1]. Of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on S × S. We prove that if σ is a fuzzy subset of S and μ_σ is the strongest fuzzy relation on S that is a fuzzy relation on σ, then μ_σ is a fuzzy subgroup if and only if σ is a fuzzy subgroup. A number of other results are obtained about the interrelationships between fuzzy relations on S (including the weakest fuzzy relation) and fuzzy subgroups on S × S.     

基于熵权直觉模糊拓展MULTIMOORA的机场消防站选址评价模型

针对准则权重信息完全未知的直觉模糊多准则群决策问题,考虑经典直觉模糊熵公式及MULTIMOORA模型的不足,提出新的直觉模糊熵公式以充分刻画直觉模糊数的直觉信息和模糊信息,定义占优凸组合运算,拓展解决多准则决策问题的MULTIMOORA模型以适用于解决多准则群决策问题.在以直觉模糊数为信息输入的系统框架内,构建机场消防站选址评价指标体系,进而提出基于熵权直觉模糊拓展MULTIMOORA的机场消防站选址评价模型.案例分析表明了所提出方法的可行性,为机场消防站选址评价提供了一种新思路.     

T-直觉模糊子群相关性质研究

主要讨论了直觉模糊粗糙集与群结构之间的联系.通过借助群上的T-直觉模糊正规子群,得到群上的T-直觉模糊相似关系,从而建立群上的直觉模糊粗糙集.研究了群上的直觉模糊粗糙集的乘积结构以及群同态下直觉模糊粗糙集上下近似的性质.     

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.     

Congruence relations on some hyperstructures

In this work we study the structure of the set of congruences on several hyperstructures with one and two (hyper-)operations. On the one hand, we show sufficient conditions guaranteeing that the set of congruences of an nd-groupoid forms a complete lattice (which, in turn, is a sublattice of the lattice of equivalence relations on the nd-groupoid). On the other hand, we focus on the study of the congruences on a multilattice; specifically, we prove that the set of congruences on an m-distributive multilattice forms a complete lattice and, moreover, show that the classical relationship between homomorphisms and congruences can be adequately adapted to work with multilattices under suitable restrictions.     

Compromise ratio method for fuzzy multi-attribute group decision making

The aim of this paper is to develop a compromise ratio (CR) methodology for fuzzy multi-attribute group decision making (FMAGDM), which is an important part of decision support system. Owing to fuzziness being inherent in decision data and group decision making processes, the crisp values are inadequate to model real-life situations. In this paper, the weights of all attributes and the ratings of each alternative with respect to each attribute are described by linguistic terms which can be expressed in trapezoid fuzzy numbers. A fuzzy distance measure is developed to calculate difference between trapezoid fuzzy numbers. The compromise ratio method for FMAGDM is developed by introducing the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away from the negative-ideal solution as possible simultaneously. The computation principle and procedure of the compromise ratio method are described in detail in this paper. Moreover the TOPSIS method which was developed for multi-attribute decision making (MADM) with crisp decision data is analyzed and extended to multi-attribute group decision making (MAGDM) under fuzzy environments. A comparative analysis of the compromise ratio method and the extended fuzzy TOPSIS method is illustrated with a numerical example, showing their similarity and some differences.     

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.     

On the diameter and bisector size of Cayley graphs

We present bounds on two combinatorial properties of Cayley graphs in terms relating to the structure of their underlying group, Included in this work is a presentation of lower bounds on the diameter of Cayley graphs of groups with nilpotent subgroups and upper bounds on the size of node bisectors of Cayley graphs of groups with solvable subgroups.Cayley graphs, being endowed with algebraic structure, have been increasingly recognized as a source of interconnection networks underlying parallel computers. Their structure has been shown to endow parallel architectures with advantages, for example, in terms of algorithmic efficiency. Our results demonstrate limits on the communication power of certain classes of well-structured interconnection networks.A portion of this research was supported by National Science Foundation Grant CCR-88-12567 while both authors were attending the University of Massachusetts.     

SUBJECTIVE MENTAL WORKLOAD ASSESSMENT BASED ON GENERALIZED FUZZY NUMBERS

In this article, a new method for subjective mental workload assessment is presented based on generalized fuzzy numbers. First, the linguistic values are modeled as generalized fuzzy numbers, which is more efficient in dealing with uncertain information and representing experts' opinions than normal fuzzy numbers due to the fact that the degree of confidence of decision makers' opinions is taken into consideration. In addition, compared with existing methods, the result of the proposed method is more reasonable because it can correctly determine the degree of similarity between the assessment and the linguistic terms. A numerical example is used to show that the proposed method can provide a useful way to handle subjective mental workload assessments in a linguistic manner.