区间灰数直觉模糊集及其G-TOPSIS模糊多属性决策方法

提出以区间灰数为隶属度、非隶属度和犹豫度的区间灰数直觉模糊集概念,定义了两个区间灰数直觉模糊集之间的距离.对于以灰直觉模糊数为属性值的模糊多属性决策,依据经典TOPSIS准则,提出了基于区间灰数直觉模糊集的模糊多属性决策方法G-TOPSIS.其包含两种方法:一是将区间灰数白化后,按直觉模糊集的TOPSIS方法进行;一是基于区间灰数直觉模糊距离的TOPSIS方法.示例分析表明了两种方法的有效性与一致性.     

直觉模糊熵与加权决策算法

直觉模糊熵是直觉模糊集理论中的一个重要概念,反映了直觉模糊集的模糊程度和不确定程度.首先给出一种新的直觉模糊熵,并运用到多属性直觉模糊决策问题中.决策时根据直觉模糊熵计算属性权重,再综合决策者的偏好对各属性权重进行修正,然后使用直觉模糊集结算子和得分函数对方案进行排序,从而获得最优方案.     

直觉模糊数可能度的概率定义及其决策

发现直觉模糊数可能度的传统定义考虑的因素不全面,计算结果不太符合常理,提出基于均匀分布的直觉模糊数可能度定义,得到相对简单且精确的可能度计算公式;证明可能度的传统定义不稳定;探索多属性直觉模糊集利用可能度进行决策的方法.最后,运用多属性直觉模糊集决策实例,既验证基于均匀分布的可能度定义的优越性,又验证可能度传统定义的不稳定性和不能敏锐区别方案间的差别,难以得到最优决策,甚至可能导致错误决策.     

基于模糊数直觉模糊集的多属性决策方法

对属性权重信息完全未知且属性值为模糊数直觉模糊数的多属性决策问题进行了研究,定义了模糊数直觉模糊数的得分函数,进而提出了一种基于线性规划模型的模糊数直觉模糊多属性决策方法.最后通过实例对该决策途径的详细过程及有效性进行了说明.     

权重为直觉模糊数的直觉模糊多属性群决策方法

针对属性权重以直觉模糊数形式给出的直觉模糊多属性群决策问题,提出了一种新的集成算子,首先证明了该算子具有诸如单调性等良好的性质,然后将该算子应用到权重为直觉模糊数的直觉模糊多属性群决策方法中,给出了决策方法的一般步骤,最后用实例说明了该方法的有效性和实用性.     

一种基于Choquet积分的多属性直觉模糊决策方法

研究了决策者对方案的主观偏好值以及属性值均为直觉模糊数的且属性间存在关联的多属性决策问题.利用Choquet模糊积分作为集结算子,构建了基于属性关联的M OD和SOD模型.通过求解模型获得属性的权重,进而给出了一种新的直觉模糊多属性决策方法.最后通过一个算例说明了该决策方法的有效性和可行性.     

直觉模糊数风险偏好一致排序方法和决策

证明直觉模糊数的Hong排序法、刘华文排序法和陈东峰排序法都要求决策者的风险态度随直觉模糊数变化而变化,不满足风险偏好一致性,违背决策者的风险态度相对稳定的实际情况.提出基于风险偏好系数的直觉模糊数排序方法,它能保证决策者风险偏好一致;并且,面对相同的决策问题,不同风险偏好的决策者可能有不同的决策结果.最后,把基于风险偏好系数的直觉模糊数排序法应用于直觉模糊集多属性决策.     

基于TOPSIS的区间直觉模糊多属性决策法

对基于区间直觉模糊信息的多属性决策问题进行了研究。给出了区间直觉模糊数之间的距离公式,并定义了区间直觉模糊正、负理想点,进而提出了一种基于TOPSIS的区间直觉模糊多属性决策方法。最后进行了实例分析。     

基于直觉模糊多属性决策的公路工程评标方法

公路工程评标定标问题的实质是多属性决策问题,专家对参评标书给出了各指标的区间直觉模糊属性值和属性权重的部分信息后,先定义了区间直觉模糊数的得分函数及标准得分差,进而提出了一种基于线性规划模型的区间直觉模糊多属性决策方法,最后通过实例对该决策途径的详细过程及有效性进行了说明.     

梯形模糊数直觉模糊Bonferroni平均算子及其应用

本文研究决策信息为梯形模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出一种基于梯形模糊数直觉模糊加权Bonferroni平均(TFNIFWBM)算子的决策方法.首先,介绍了TFNIFN的概念和运算法则,基于这些运算法则和Bonferroni平均(Bonferroni mean,BM)算子,定义了梯形模糊数直觉模糊Bonferroni平均算子和TFNIFWBM算子.然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的多属性群决策模型,结合排序方法进行决策.最后,将该方法应用在MAGDM中,算例结果表明了该方法的有效性与可行性.     

Fuzzy addition in the L-fuzzy real line

Under the hypothesis L is a chain, we construct a binary operation ⊕ on the L-fuzzy real line $\text{R}$(L) which reduces to the usual addition on $\text{R}$ if ⊕ is restricted to the embedded image of $\text{R}$ in $\text{R}$(L), which yields a partially ordered, abelian cancellation semigroup with identity, and which is jointly fuzzy continuous on $\text{R}$(L). We show ⊕ is unique, i.e. it is the only extension of addition to $\text{R}$(L) which is consistent. We study the relationship between ⊕ and other fuzzy continuous extensions of the usual addition. We also show that fuzzy translation is a weak fuzzy homeomorphism and, under certain conditions, a fuzzy homeomorphism.     

A type of fuzzy ring

In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical study their basic properties analogous to those of ordinary rings.      

Editorial

Linear programming problems with fuzzy parameters are formulated by fuzzy functions. The ambiguity considered here is not randomness, but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership. Parameters on constraint and objective functions are given by fuzzy numbers. In this paper, our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters. This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential.     

群,环上的Fuzzy关系

一些学者已对群和环上的Ｆｕｚｚｙ关系进行了研究，本文进一步研究了群、环上的Ｆｕｚｚｙ关系，得出了若干重要的结论。     

Toward extended fuzzy logic—A first step

Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally important capability—a capability to reason imprecisely with imperfect information. This capability comes into play when precise reasoning is infeasible, excessively costly or unneeded. In extended fuzzy logic, p-validity of results is desirable but not required. What is admissible is a mode of reasoning which is fuzzily valid, or f-valid for short. Actually, much of everyday human reasoning is f-valid reasoning.f-Valid reasoning falls within the province of what may be called unprecisiated fuzzy logic, FLu. FLu is the logic which underlies what is referred to as f-geometry. In f-geometry, geometric figures are drawn by hand with a spray pen—a miniaturized spray can. In Euclidean geometry, a crisp concept, C, corresponds to a fuzzy concept, f-C, in f-geometry. f-C is referred to as an f-transform of C, with C serving as the prototype of f-C. f-C may be interpreted as the result of execution of the instructions: Draw C by hand with a spray pen. Thus, in f-geometry we have f-points, f-lines, f-triangles, f-circles, etc. In addition, we have f-transforms of higher-level concepts: f-parallel, f-similar, f-axiom, f-definition, f-theorem, etc. In f-geometry, p-valid reasoning does not apply. Basically, f-geometry may be viewed as an f-transform of Euclidean geometry.What is important to note is that f-valid reasoning based on a realistic model may be more useful than p-valid reasoning based on an unrealistic model.     

A new approach to fuzzy programming

A fuzzy program is defined in the usual way as a sequence of statements (instruction) which are considered as functions (possibly fuzzy functions) and fuzzy predicates defined on the given input domain. The essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs, and a new method of evaluating fuzzy predicates. The result of the fuzzy program execution is an appropriate fuzzy subset in the output domain.     

n维模糊度量空间及其完备性

定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。     

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.     

Bi-matrix Games with Fuzzy Goals and Fuzzy

A bi-matrix game with fuzzy goal is shown to be equivalent to a (crisp) non-linear programming problem in which the objective as well as all constraint functions are linear except two constraint functions, which are quadratic. This equivalence is further extended to bi-matrix games with fuzzy pay-offs, as well as to bi-matrix games with fuzzy goals and fuzzy payoffs, whose equilibrium strategies are conceptualized by employing a suitable ranking (defuzzification) function.