共查询到18条相似文献,搜索用时 140 毫秒
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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。 相似文献
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将毕达哥拉斯模糊数与直觉正态模糊数相结合,提出了毕达哥拉斯正态模糊数,研究了其运算和运算性质,定义了毕达哥拉斯正态模糊数的得分函数和精确函数,实现其大小排序.然后,针对毕达哥拉斯正态模糊信息的集成问题,提出毕达哥拉斯正态模糊有序加权平均(PNFOWA)算子、广义有序加权平均(GPNFOWA)算子和毕达哥拉斯正态模糊有序加权几何平均(PNFOWGA)算子及广义有序加权几何平均(GPNFOWGA)算子,并研究了其性质.最后,提出基于广义毕达哥拉斯正态模糊集成算子的多属性决策方法,并通过实例说明该方法的有效性. 相似文献
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本文研究广义q-阶正交模糊混合几何平均算子及其在多属性决策中的应用.基于q-阶正交模糊集的隶属度空间大于直觉模糊集与毕达哥拉斯模糊集的特点,在q-阶正交模糊环境下,将算子自身的权重与位置权重相结合,定义了广义q-阶正交模糊混合几何平均算子.提出基于广义q-阶正交模糊混合几何平均算子的多属性决策方法,并通过选取最优拍摄地... 相似文献
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直觉模糊Choquet积分集成算子能有效解决属性关联的直觉模糊决策问题,直觉模糊数交叉影响运算能反映出不同直觉模糊数的隶属度和非隶属度之间的交叉影响.通过将直觉模糊Choquet积分平均算子与直觉模糊数交叉影响运算相结合,定义了直觉模糊交叉影响Choquet积分集成算子,包括直觉模糊交叉影响Choquet积分平均算子(IFICIA)和直觉模糊交叉影响Choquet积分几何算子(IFICIG),推导出它们的计算公式,讨论了它们的性质.通过研究直觉模糊交叉影响Choquet积分集成算子的特殊形式,发现直觉模糊交叉加权平均算子(IFIWA)和有序加权平均算子(IFIOWA)、直觉模糊交叉加权几何算子(IFIWG)和有序加权几何算子(IFIOWG)等均为它们的特例。最后,提出了基于直觉模糊交叉影响Choquet积分集成算子的决策方法,通过决策实例说明其可行性和稳定性。 相似文献
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《数学的实践与认识》2020,(2)
在不确定隶属度语言变量和Einstein算子的基础上,提出了一种新的算子—不确定隶属度语言Einstein算子,并将其应用到多属性群决策中.首先定义了不确定隶属度语言Einstein算子的概念、相应的运算规则、大小比较方法.之后提出了几种新的不确定隶属度语言Einstein算子,比如:不确定隶属度语言Einstein加权算术平均算子(UMLEWA)、不确定隶属度语言Einstein加权几何平均算子(UMLEWG)、不确定隶属度语言Einstein有序加权算术平均算子(UMLEOWA)、不确定隶属度语言Einstein有序加权几何平均算子(UMLEOWG)、广义不确定隶属度语言Einstein加权算术平均算子(GUMLEWA)、广义不确定隶属度语言Einstein加权几何平均算子(GUMLEWG),以及算子的相应性质(幂等性,有界性,单调性),并证明了性质的正确性.其次在不确定隶属度语言Einstein加权算术平均算子(UMLEWA)和不确定隶属度语言Einstein加权几何平均算子(UMLEWG)基础上,提出了两种不同的方法来处理多属性群决策问题,并给出了具体的群决策步骤.最后,通过实例验证了所提方法的有效性和可行性. 相似文献
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梯形模糊数直觉模糊Bonferroni平均算子及其应用 总被引:1,自引:0,他引:1
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. 相似文献
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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。 相似文献
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Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator
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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 相似文献
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Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making
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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. 相似文献
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With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic uncertain linguistic variables, some new group decision making analysis methods are developed. Firstly, some operational laws, expected value and accuracy function of interval-valued intuitionistic uncertain linguistic variables are introduced. Then, an interval-valued intuitionistic uncertain linguistic weighted geometric average (IVIULWGA) operator and an interval-valued intuitionistic uncertain linguistic ordered weighted geometric (IVIULOWG) operator have been developed. Furthermore, some desirable properties of the IVIULWGA operator and the IVIULOWG operator, such as commutativity, idempotency and monotonicity, have been studied, and an interval-valued intuitionistic uncertain linguistic hybrid geometric (IVIULHG) operator which generalizes both the IVIULWGA operator and the IVIULOWG operator, was developed. Based on these operators, an approach to multiple attribute group decision making with interval-valued intuitionistic uncertain linguistic information has been proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness. 相似文献
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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. 相似文献
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《Applied Mathematical Modelling》2014,38(7-8):2190-2205
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. 相似文献
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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. 相似文献
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Multi-person multi-attribute decision making models under intuitionistic fuzzy environment 总被引:1,自引:0,他引:1
Zeshui Xu 《Fuzzy Optimization and Decision Making》2007,6(3):221-236
Intuitionistic fuzzy numbers, each of which is characterized by the degree of membership and the degree of non-membership
of an element, are a very useful means to depict the decision information in the process of decision making. In this article,
we investigate the group decision making problems in which all the information provided by the decision makers is expressed
as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionistic fuzzy number, and
the information about attribute weights is partially known, which may be constructed by various forms. We first use the intuitionistic
fuzzy hybrid geometric (IFHG) operator to aggregate all individual intuitionistic fuzzy decision matrices provided by the
decision makers into the collective intuitionistic fuzzy decision matrix, then we utilize the score function to calculate
the score of each attribute value and construct the score matrix of the collective intuitionistic fuzzy decision matrix. Based
on the score matrix and the given attribute weight information, we establish some optimization models to determine the weights
of attributes. Furthermore, we utilize the obtained attribute weights and the intuitionistic fuzzy weighted geometric (IFWG)
operator to fuse the intuitionistic fuzzy information in the collective intuitionistic fuzzy decision matrix to get the overall
intuitionistic fuzzy values of alternatives by which the ranking of all the given alternatives can be found. Finally, we give
an illustrative example. 相似文献
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With respect to the multiple attribute group decision making problems in which the attribute values take the form of generalized interval-valued trapezoidal fuzzy numbers (GITFN), this paper proposed a decision making method based on weighted geometric aggregation operators. First, some operational rules, the distance and comparison between two GITFNs are introduced. Second, the generalized interval-valued trapezoidal fuzzy numbers weighted geometric aggregation (GITFNWGA) operator, the generalized interval-valued trapezoidal fuzzy numbers ordered weighted geometric aggregation (GITFNOWGA) operator, and the generalized interval-valued trapezoidal fuzzy numbers hybrid geometric aggregation (GITFNHGA) operator are proposed, and their various properties are investigated. At the same time, the group decision methods based on these operators are also presented. Finally, an illustrate example is given to show the decision-making steps and the effectiveness of this method. 相似文献