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| 1 | Intuitionistic fuzzy C-means clustering algorithms显示文摘Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets. | Zeshui Xu Junjie Wu | 2010 | Journal of Systems Engineering and Electronics2010，21，4： | 17 |
| 2 | ORDERED WEIGHTED DISTANCE MEASURE显示文摘The aim of this paper is to develop an ordered weighted distance(OWD) measure,which is the generalization of some widely used distance measures,including the normalized Hamming distance, the normalized Euclidean distance,the normalized geometric distance,the max distance,the median distance and the min distance,etc.Moreover,the ordered weighted averaging operator,the generalized ordered weighted aggregation operator,the ordered weighted geometric operator,the averaging operator,the geometric mean operator,the ordered weighted square root operator,the square root operator,the max operator,the median operator and the min operator are also the special cases of the OWD measure.Some methods depending on the input arguments are given to determine the weights associated with the OWD measure.The prominent characteristic of the OWD measure is that it can relieve(or intensify) the influence of unduly large or unduly small deviations on the aggregation results by assigning them low(or high) weights.This desirable characteristic makes the OWD measure very suitable to be used in many actual fields,including group decision making,medical diagnosis, data mining,and pattern recognition,etc.Finally,based on the OWD measure,we develop a group decision making approach,and illustrate it with a numerical example. | Zeshui XU Jian CHEN | 2008 | Journal of Systems Science and Systems Engineering2008，17，4： | 16 |
| 3 | A MULTI-CRITERIA DECISION MAKING PROCEDURE BASED ON INTERVAL-VALUED INTUITIONISTIC FUZZY BONFERRONI MEANS显示文摘Inspired by the idea of Bonferroni mean,in this paper we develop an aggregation technique called the interval-valued intuitionistic fuzzy Bonferroni mean for aggregating interval-valued intuitionistic fuzzy information.We study its properties and discuss its special cases.For the situations where the input arguments have different importance,we then define a weighted interval-valued intuitionistic fuzzy Bonferroni mean,based on which we give a procedure for multi-criteria decision making under interval-valued intuitionistic fuzzy environments. | Zeshui XU | 2011 | Journal of Systems Science and Systems Engineering2011，20，2： | 11 |
| 4 | DUAL HESITANT FUZZY INFORMATION AGGREGATION WITH EINSTEIN T-CONORM AND T-NORM显示文摘双犹豫的模糊集合(DHFS ) 是由二部分组成的模糊集合(FS ) 的新归纳(即,会员迟疑功能和非会员迟疑工作) ,它面对显示认识的度的几不同可能的价值是否必然或无常。它包含模糊集合(FS ) , intuitionistic 模糊集合(IFS ) ,和犹豫的模糊集合(HFS ) 以便它能在决策的过程更灵活地处理不明确的信息。在这份报纸,我们基于爱因斯坦 t-conorm 和t标准在双犹豫的模糊集合上建议一些新操作,学习他们的性质和关系然后给一些双犹豫的模糊聚集操作员,它能被看作一些存在的归纳在下面模糊, intuitionistic 模糊、犹豫的模糊环境。最后,在双犹豫的模糊环境下面的一个决策算法基于建议聚集操作员被给,一个数字例子被用来表明方法的有效性。 | Hua Zhao Zeshui Xu Shousheng Liu | 2017 | Journal of Systems Science and Systems Engineering2017，26，2： | 10 |
| 5 | SOME NEW SIMILARITY MEASURES FOR INTUITIONISTIC FUZZY VALUES AND THEIR APPLICATION IN GROUP DECISION MAKING显示文摘We first propose a series of similarity measures for intuitionistic fuzzy values (IFVs) based on the intuitionistic fuzzy operators (Atanassov 1995). The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment. | Meimei XIA Zeshui XU | 2010 | Journal of Systems Science and Systems Engineering2010，19，4： | 9 |
| 6 | Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making显示文摘The class of multiple attribute decision making(MADM) problems is studied,where the attribute values are intuitionistic fuzzy numbers,and the information about attribute weights is completely unknown.A score function is first used to calculate the score of each attribute value and a score matrix is constructed,and then it is transformed into a normalized score matrix.Based on the normalized score matrix,an entropy-based procedure is proposed to derive attribute weights.Furthermore,the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives,by which the ranking of all the given alternatives is obtained.This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided. | Xu Zeshui~(1,2) & Hu Hui~3 1.School of Economics and Management,Southeast Univ.,Nanjing 210096,P.R.China 2.Inst.of Sciences,PLA Univ.of Sciences and Technology,Nanjing 210007,P.R.China 3.Inst.of Communications Engineering,PLA Univ.of Sciences and Technology, Nanjing 210007,P.R.China | 2009 | Journal of Systems Engineering and Electronics2009，20，5： | 6 |
| 7 | The Generalized Mixed Least Square Methodsfor the Estimation of Weights in AHP | XU Zeshui(Institute of Communications Engineering, Nanjing,210016, China) | 1998 | Systems Science and Systems Engineering1998，8，4： | 4 |
| 8 | A New Method for Calculating Priorities in AHP | XU Zeshui LU Jianjiang(Institute of Communications Engineering, Nanjing 210016, Jjangsu, China) | 1999 | Systems Science and Systems Engineering1999，9，2： | 4 |
| 9 | Hesitant fuzzy information aggregation in decision making显示文摘 | Meimei Xia Zeshui Xu | 2010 | International Journal of Approximate Reasoning2010，，3： | 3 |
| 10 | AGGREGATION AND DECISION MAKING USING INTUITIONISTIC MULTIPLICATIVE TRIANGULAR FUZZY INFORMATION显示文摘The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set.In practical applications,we find that the results derived by using the traditional intuitionistic triangular fuzzy aggregation operators based on intuitionistic triangular fuzzy sets are sometimes inconsistent with intuition.To overcome this issue,based on the[1/9,9]scale,we define the concepts of intuitionistic multiplicative triangular fuzzy set and intuitionistic multiplicative triangular fuzzy number,and then we discuss their operational laws and some desirable properties.Based on the operational laws,we develop a series of aggregation operators for intuitionistic multiplicative triangular fuzzy information,and then apply them to propose an approach to multi-attribute decision making under intuitionistic fuzzy environments.Finally,we use a practical example involving the evaluation of investment alternatives of an investment company to demonstrate our aggregation operators and decision making approach. | Shan YU Zeshui XU | 2014 | Journal of Systems Science and Systems Engineering2014，23，1： | 3 |
| 11 | UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING显示文摘In multiple attribute group decision making(MAGDM) problems based on linguistic information,the granularities of linguistic label sets are usually different due to the differences of thinking modes and habits among decision makers.In order to deal with this inconvenience,the transformation relationships among multigranular linguistic labels(TRMLLs),which are applied to unify linguistic labels with different granularities into a certain linguistic label set with fixed granularity,are presented in this paper.Furthermore,the reference tables are made according to TRMLLs so that the interrelated calculation will be less complicated,and the method of how to use them is explained in detail.At length,the TRMLLs are illustrated through an application example. | Xiaohan YU Zeshui XU Xiumei ZHANG | 2010 | Journal of Systems Science and Systems Engineering2010，19，3： | 3 |
| 12 | Modeling and applying credible interval intuitionistic fuzzy reciprocal preference relations in group decision making显示文摘Intuitionistic fuzzy preference relations are powerful techniques used to express uncertain preference information.However, simultaneously providing the exact priority and nonpriority intensities could be difficult in real applications. A credible interval intuitionistic fuzzy number(CIIFN) is introduced and a credible interval intuitionistic fuzzy reciprocal preference relation(CIIFRPR) is developed to solve this issue. Unlike intuitionistic fuzzy preference relations, the new preference relations use the CIIFNs to express the preference information such that the decision makers simply provide the priority intensity with intervalvalued numbers and calculate the non-preference intensity with the transformed method, which avoids a complex evaluation of non-priority information. Furthermore, some basic operations and comparison laws are investigated, based on which three credible interval intuitionistic fuzzy aggregation operators are proposed.Two models are presented to manage the group decision-making.Finally, a practical case is used to demonstrate the feasibility and reasonability of the proposed preference relations and aggregation operators. | Wei Zhou Zeshui Xu | 2017 | Journal of Systems Engineering and Electronics2017，28，2： | 2 |
| 13 | An interactive procedure for linguistic multiple attribute decision making with incomplete weight information显示文摘 | Zeshui Xu | 2007 | Fuzzy Optimization and Decision Making2007，，1： | 2 |
| 14 | A method based on preference degrees for handling hybrid multiple attribute decision making problems显示文摘 | Xiaohan Yu Zeshui Xu Qi Chen | 2010 | Expert Systems With Applications2010，，4： | 2 |
| 15 | An overview of operators for aggregating information显示文摘 | ZESHUI XU QINGLI DA | 2003 | International Journal of Intelligent Systems2003，18，： | 1 |
| 16 | Projection method for uncertain multiattribute decision making with preference information on alternatives显示文摘 | Xu Zeshui Da Qingli | 2004 | International Journal of Information Technology and Decision Making2004，3，3： | 1 |
| 17 | On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives显示文摘 | Xu Zeshui | 2005 | Fuzzy Optimization and Decision Making2005，4，2： | 1 |
| 18 | On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives显示文摘 | XU Zeshui | 2005 | Fuzzy Optimization and Decision Making2005，4，13： | 1 |
| 19 | On multi-period multi-attribute decision making显示文摘 | Xu Zeshui | 2008 | Knowledge-Based Systems2008，21，2： | 1 |
| 20 | MAGDM linear programming models with distinct uncertain preference structures显示文摘 | Xu Zeshui Chen Jian | 2008 | IEEE Transactions on Systems Man and Cybernetics-Part B2008，38，5： | 1 |
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