梯形直觉模糊数集成算子及在决策中的应用研究

在直觉模糊集理论基础上,用梯形模糊数表示直觉模糊数的隶属度和非隶属度,进而提出了梯形直觉模糊数;然后定义了梯形直觉模糊数的运算法则,给出了相应的证明,并基于这些法则,给出了梯形直觉模糊加权算数平均算子(TIFWAA)、梯形直觉模糊数的加权二次平均算子(TIFWQA)、梯形直觉模糊数的有序加权二次平均算子(TIFOWQA)、梯形直觉模糊数的混合加权二次平均算子(TIFHQA)并研究了这些算子的性质;建立了不确定语言变量与梯形直觉模糊数的转化关系,并证明了转化的合理性;定义了梯形直觉模糊数的得分函数和精确函数,给出了梯形直觉模糊数大小比较方法;最后提供了一种基于梯形直觉模糊信息的决策方法,并通过实例结果证明了该方法的有效性。     

基于改进直觉模糊集成算子的多属性决策方法及其应用研究

基于直觉模糊集理论,提出了改进直觉模糊集成算子方法来研究多属性决策问题。本文定义了直觉模糊数的运算法则和比较了直觉模糊信息的一系列集成算子,然后改进了传统得分函数,并将其与直觉模糊集成算子相结合,从而得到新的直觉模糊信息的集成方式,将其运用于解决属性权重已知的直觉模糊多属性决策问题。最后,通过具体实例说明该方法的有效性和具体应用过程。     

基于k阶二元关系的直觉模糊粗糙集

利用k阶二元关系定义直觉模糊粗糙集,讨论了分别为串行、自反、对称、传递关系时所对应的上、下近似算子的性质。在有限论域U中,研究了任一自反二元关系所诱导的直觉模糊拓扑空间中直觉模糊闭包、内部算子与相对应的上、下近似算子的关系。     

三角直觉模糊决策的变权方法

研究了属性值为三角直觉模糊数的多属性决策问题,提出了一种基于变权综合的决策方法。首先,针对三角直觉模糊数,提出一种新的三角直觉模糊排序方法;其次,定义了三角直觉模糊变权加权算术平均算子和三角直觉模糊变权加权几何平均算子;然后,提出一种基于三角直觉模糊变权集成算子的多属性决策方法;最后,数值算例说明了该方法的有效性。     

Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers

The aim of this work is to present some cases of aggregation operators with intuitionistic trapezoidal fuzzy numbers and study their desirable properties. First, some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Next, based on these operational laws, we develop some geometric aggregation operators for aggregating intuitionistic trapezoidal fuzzy numbers. In particular, we present the intuitionistic trapezoidal fuzzy weighted geometric (ITFWG) operator, the intuitionistic trapezoidal fuzzy ordered weighted geometric (ITFOWG) operator, the induced intuitionistic trapezoidal fuzzy ordered weighted geometric (I-ITFOWG) operator and the intuitionistic trapezoidal fuzzy hybrid geometric (ITFHG) operator. It is worth noting that the aggregated value by using these operators is also an intuitionistic trapezoidal fuzzy value. Then, an approach to multiple attribute group decision making (MAGDM) problems with intuitionistic trapezoidal fuzzy information is developed based on the ITFWG and the ITFHG operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

直觉梯形模糊语言Frank算子及其在决策中的应用

本文在直觉梯形模糊语言集的基础上,引入了Frank算子,提出一组新的算子——直觉梯形模糊语言Frank集结算子,并将其应用到多属性决策中。首先,本文提出了直觉梯形模糊语言集Frank算子的表达式,并给出相应的运算规则。然后提出了直觉梯形模糊语言Frank加权算术平均(ITrFLFWA)算子、直觉梯形模糊语言Frank加权几何平均(ITrFLFWG)算子、直觉梯形模糊语言Frank广义加权平均(ITrFLGFWA)算子等,并证明了其具有幂等性、有界性、单调性等性质。最后,通过实例验证了直觉梯形模糊语言Frank算子可以有效解决直觉梯形模糊语言环境下的多属性决策问题。     

Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator

Normal intuitionistic fuzzy numbers (NIFNs), which use normal fuzzy numbers to express their membership and non-membership functions, can reflect the evaluation information exactly in different dimensions. In this paper, we are committed to apply NIFNs to multi-criteria decision-making (MCDM) problems, and meanwhile some new aggregation operators are proposed, including normal intuitionistic fuzzy weighted arithmetic averaging operator, normal intuitionistic fuzzy weighted geometric averaging operator, normal intuitionistic fuzzy-induced ordered weighted averaging operator, normal intuitionistic fuzzy-induced ordered weighted geometric averaging operator and normal intuitionistic fuzzy-induced generalized ordered weighted averaging operator (NIFIGOWA). Based on the NIFIGOWA operator, an approach is introduced to solve MCDM problems where the criteria values are NIFNs and the criteria weight information is fixed. Finally, the proposed method is compared to the existing methods by virtue of a numerical example to verify its feasibility and rationality.     

Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making

The intuitionistic uncertain fuzzy linguistic variable can easily expressthe fuzzy information, and the power average (PA) operator is a usefultool which provides more versatility in the information aggregation procedure.At the same time, Einstein operations are a kind of various t-normsand t-conorms families which can be used to perform the corresponding intersectionsand unions of intuitionistic fuzzy sets (IFSs). In this paper, wewill combine the PA operator and Einstein operations to intuitionistic uncertainlinguistic environment, and propose some new PA operators. Firstly,the definition and some basic operations of intuitionistic uncertain linguisticnumber (IULN), power aggregation (PA) operator and Einstein operationsare introduced. Then, we propose intuitionistic uncertain linguistic fuzzypowered Einstein averaging (IULFPEA) operator, intuitionistic uncertain linguisticfuzzy powered Einstein weighted (IULFPEWA) operator, intuitionisticuncertain linguistic fuzzy Einstein geometric (IULFPEG) operator and intuitionisticuncertain linguistic fuzzy Einstein weighted geometric (IULFPEWG)operator, and discuss some properties of them in detail. Furthermore, we developthe decision making methods for multi-attribute group decision making(MAGDM) problems with intuitionistic uncertain linguistic information andgive the detail decision steps. At last, an illustrate example is given to showthe process of decision making and the effectiveness of the proposed method.     

区间直觉模糊集多属性决策方法

定义了区间直觉模糊集的加权算子和加权几何集成算子,介绍了现有的区间直觉模糊集的得分函数和精确函数.定义了一个新的精确函数,此函数弥补了已有函数的不足和缺陷,应用新定义的精确函数,提出了对区间直觉模糊集多属性决策问题进行决策的方法.最后以应用实例对该方法进行说明和验证.     

基于直觉模糊集的世界一流学科建设成效评价

针对目前我国世界一流学科建设成效评价存在主客观偏好,建立了直觉模糊综合评判法的数学模型。基于直觉模糊集,提出了两种直觉模糊合成算子,即直觉模糊加权平均算子(IFWA)和直觉模糊主因素突出算子(IFPFP),将其应用于世界一流学科建设成效的评价。应用实例表明,该方法有效地解决了目前学科评价领域中部分评价指标量化困难、代表性差等突出问题,可给出更加科学、准确的评价结果。     

Multi-criteria decision-making methods based on intuitionistic fuzzy sets

In this paper we present new methods for solving multi-criteria decision-making problem in an intuitionistic fuzzy environment. First, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker’s requirement. Then, we introduce and discuss the concept of intuitionistic fuzzy point operators. By using the intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an intuitionistic fuzzy set. Furthermore, a series of new score functions are defined for multi-criteria decision-making problem based on the intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.     

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval‐valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval‐valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval‐valued intuitionistic fuzzy generalized weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016     

An approach to decision making based on intuitionistic fuzzy rough sets over two universes

Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.     

Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) is a special intuitionistic fuzzy set on a real number set. TrIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The focus of this paper is on multi-attribute group decision making (MAGDM) problems in which the attribute values are expressed with TrIFNs, which are solved by developing a new decision method based on power average operators of TrIFNs. The new operation laws for TrIFNs are given. From a viewpoint of Hausdorff metric, the Hamming and Euclidean distances between TrIFNs are defined. Hereby the power average operator of real numbers is extended to four kinds of power average operators of TrIFNs, involving the power average operator of TrIFNs, the weighted power average operator of TrIFNs, the power ordered weighted average operator of TrIFNs, and the power hybrid average operator of TrIFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TrIFNs. Applying the hybrid average operator of TrIFNs, the individual overall evaluation values of alternatives are then integrated into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.     

Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making

In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment.     

基于直觉模糊集的突发事件应急预案评估

提出了一种基于直觉模糊集理论的突发事件应急预案评价的新方法.首先,定义了直觉模糊集和两个直觉模糊集之间的距离;然后,建立了应急预案评价指标体系,给出了直觉模糊正理想点和负理想点的概念,提出了基于直觉模糊集和TOPS IS法的应急预案评估方法.最后通过实例说明了该方法的有效性.     

粗糙直觉模糊集的近似表示

在粗糙直觉模糊集的基础上,从新的角度提出了不确定目标概念的近似表示和处理的方法(通过近似模糊集和近似精确集刻画).首先将已有的直觉模糊集相似概念和均值直觉模糊集概念引入到该模型,定义了Pawlak近似空间U/R下的阶梯直觉模糊集、0.5-精确集的概念,然后得到了均值直觉模糊集(0.5-精确集)是所有直觉模糊集中与目标直觉模糊集最接近的直觉模糊集(近似精确集),接着分析了均值直觉模糊集、0.5-精确集分别与目标直觉模糊集的相似度随着知识粒度变化的变化规律.     

Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations

The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community. However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the extension principle. The representation theorem and extension principles as well as algebraic operations form an important part of Atanassov’s IF set theory.     

基于改进熵权法的区间直觉模糊TOPSIS方法

本文对区间直觉模糊信息的TOPSIS多属性决策方法进行了研究。在属性权重信息完全未知的情况下,通过研究熵权法以及区间直觉模糊集本身的一些性质特点,将熵权法拓展到区间直觉模糊环境中来确定属性权重,进而提供了一种可直接利用评估信息的新的TOPSIS决策方法。该方法不仅拓展了传统熵权法的应用范围,而且不需要决策者事先给出权重信息,结果更加客观和可靠。应用实例表明该方法的可行性和有效性,具有推广应用价值。     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.