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1.
Determining the attribute weights, in the multiple attribute group decision-making analysis with interval-valued intuitionistic fuzzy information, plays a crucial role because of its direct effect on the optimal alternative. In this paper, we develop a new attribute weight based on the support and entropy measure of attribute values. Then, the interval-valued intuitionistic fuzzy combined weighted averaging (IVIFCWA) operator is proposed and its some primary properties are discussed. The IVIFCWA operator’s attribute values take the form of interval-valued intuitionistic fuzzy numbers and the principal component of the interval-valued intuitionistic fuzzy number is fully taken into account. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method.  相似文献   

2.
基于区间值直觉模糊相容关系,给出了双论域上的区间值直觉模糊粗糙集模型并讨论了其相关性质,为粗糙集的应用提供了新的理论基础与操作手段。最后,通过一个例子阐述了本文提出的区间值直觉模糊粗糙集模型在临床诊断系统中的具体应用。  相似文献   

3.
The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.  相似文献   

4.
To model the uncertainty in the secondary possibility distributions, this paper develops a new method for handling interval-valued fuzzy variables with variable lower and upper possibility distributions. For a parametric interval-valued fuzzy variable, we define its lower selection variable, upper selection variable and lambda selection variable. The three selection variables are characterized by variable possibility distributions, and their numerical characteristics like expected values and n-th moments are important indices in practical optimization and decision-making problems. Under this consideration, we establish some useful analytical expressions of the expected values and n-th moments for the lambda selections of parametric interval-valued trapezoidal, normal and Erlang fuzzy variables. Furthermore, we focus on the arithmetic about the sums of common parametric interval-valued fuzzy variables. Finally, we apply the proposed optimization indices to a quantitative finance problem, where the second moment is used to measure the risk of a portfolio.  相似文献   

5.
The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number, and the information about attribute weights is partially known, which is an important research field in decision science and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.  相似文献   

6.
Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388–393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.  相似文献   

7.
In this paper, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then we use the obtained attribute weights and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator to fuse the interval-valued intuitionistic fuzzy information in the collective interval-valued intuitionistic fuzzy decision matrix to get the overall interval-valued intuitionistic fuzzy values of alternatives, and then rank the alternatives according to the correlation coefficients between IVIFNs and select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.  相似文献   

8.
TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.  相似文献   

9.
《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   

10.
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.  相似文献   

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