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Journal of Systems Science and Systems Engineering 2023年第4期32卷 483-513页

作者： Ling Pan Zeshui Xu Business School Sichuan UniversityChengdu 610064China

Social trust network(STN)and minimum cost consensus(MCC)models have been widely used to address consensus issues in multi-attribute group decision-making(MAGDM)problems with limited resources.However,most researchers have overlooked the decision maker‘(DMs)’confidence levels(CLs)and adjustment willingness implicit in their evaluations.To address these problems,this paper explores a confidence-based MCC model that considers DMs’adjustment willingness in the STN.The proposed model includes several modifications to the traditional trust propagation and consensus optimization models.Firstly,the improved method for measuring CLs of DMs and the confidence-based normalization approach are defined,respectively.Secondly,the bounded trust propagation operator is proposed,which considers the credibility of mediators to complete the STN.Thirdly,the identification rules based on the consensus index and CL are defined,and the MCC model with personalized cost functions and acceptable adjustment thresholds is built to automatically generate adjustment values for non-consensus DMs.Finally,a model to identify the non-cooperative behavior at the element level is established and the hybrid MCC model with persuasion strategies is provided.Finally,a case study is processed to verify the applicability of the proposed model,and comparison and sensitivity analysis are conducted to highlight its benefits.

关键词： Confidence level social trust network bounded trust propagation minimum cost consensus models multi-attribute group decision making

An Emergency Shelter Location Model Based on the Sense of Security and the Reliability Level

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Journal of Systems Science and Systems Engineering 2023年第1期32卷 100-127页

作者： Yiying Wang Zeshui Xu Business School Sichuan UniversityChengdu610064China

Based on the value function of the prospect theory,this paper constructs a security function,which is used to describe the victims’feelings about the distance in emergency evacuation.Since different paths between the demand points and the emergency shelters are generally of different importance degrees,they are divided into main paths and auxiliary paths.The security function values and the reliability levels of main paths and auxiliary paths are given different weights.The weighted sum of the security function values and the weighted sum of the reliability level function values of all demand points are maximized to determine the location and the number of the emergency shelters,the transfer paths,the reinforced edges and the incremental reliability level of the selected edge.In order to solve the model,a two-stage simulated annealing-particle swarm optimization algorithm is proposed.In this algorithm,the particle swarm optimization(PSO)algorithm is embedded into the simulated annealing(SA)algorithm.The cumulative probability operator and the cost probability operator are formed to determine the evolution of the particles.Considering the budget constraint,the algorithm eliminates the shelter combinations that do not meet the constraint,which greatly saves the calculation time and improves the efficiency.The proposed algorithm is applied to a case,which verifies its feasibility and stability.The model and the algorithm of this paper provide a basis for emergency management departments to make the earthquake emergency planning.

关键词： Emergency shelter location security function reliability level two-stage SA-PSO algorithm cumulative probability operator cost probability operator

Multiplicative Integral Theory of Generalized Orthopair Fuzzy Sets and Its Applications

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Journal of Systems Science and Systems Engineering 2022年第4期31卷 457-479页

作者： Jie Gao Zeshui Xu Chao Zhong Yunshu Mao School of Business Administration Southwestern University of Finance and EconomicsChengdu610207China Business School Sichuan UniversityChengdu610064China

There are two main issues of fuzzy multi-attribute decision-making:determine the weight of each attribute and choose an appropriate aggregation method to integrate the evaluation information of different attributes.In order to solve the multi-attribute decision-making problem in generalized orthopair fuzzy environment with unknown attribute weights more effectively,we give a decision-making method based on generalized orthopair fuzzy definite integrals.To be specific,we first introduce the complement operations of q-rung orthopair fuzzy numbers,and then investigate the multiplicative q-rung orthopair fuzzy calculus.Through the complement operations,we establish the mutual conversion formula between additive and multiplicative q-rung orthopair fuzzy calculus theory.Then,we give a multiplicative integral-based q-rung orthopair fuzzy multi-attribute decision-making method,and discuss the relationship between the q-rung orthopair fuzzy definite integrals and the q-rung orthopair fuzzy weighted geometric operator.Compared with traditional decision-making methods,this method does not rely on subjective weight information,which is especially important when dealing with large sample data.Finally,the application of election is studied to verify the feasibility and effectiveness of the proposed method.With the introduction of generalized orthopair fuzzy sets,the expression form of election evaluation information has been expanded.We also provide some examples to compare the obtained results with the results generated by the addition operation and reveal the correlation between them.

关键词： Fuzzy sets decision making aggregation operators

A MULTI-CRITERIA DECISION MAKING PROCEDURE BASED ON INTERVAL-VALUED INTUITIONISTIC FUZZY BONFERRONI MEANS

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Journal of Systems Science and Systems Engineering 2011年第2期20卷 217-228页

作者： Zeshui Xu School of Economics and Management Southeast University Nanjing Jiangsu 211189 China Institute of Communications Engineering PLA University of Science and Technology Nanjing Jiangsu 210007 China Institute of Sciences PLA University of Science and Technology Nanjing Jiangsu 210007 China

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.

关键词： Bonferroni mean interval-valued intuitionistic fuzzy number multi-criteria decision making interval-valued intuitionistic fuzzy Bonferroni mean weighted interval-valued intuitionistic fuzzy Bonferroni mean

Intuitionistic fuzzy C-means clustering algorithms

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Journal of Systems Engineering and Electronics 2010年第4期21卷 580-590页

作者： Zeshui Xu Junjie Wu School of Economics and Management Southeast UniversityNanjing 210096P.R.China Institute of Sciences PLA University of Sciences and TechnologyNanjing 210007P.R.China Department of Information Systems School of Economics and ManagementBeihang UniversityBeijing 100191P.R.China

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.

关键词： intuitionistic fuzzy set(IFS) intuitionistic fuzzy Cmeans algorithm clustering interval-valued intuitionistic fuzzy set(IVIFS).

Modeling and applying credible interval intuitionistic fuzzy reciprocal preference relations in group decision making

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Journal of Systems Engineering and Electronics 2017年第2期28卷 301-314页

作者： Wei Zhou Zeshui Xu Business School Sichuan University International Business School Yunnan University of Finance and Economics

Intuitionistic fuzzy preference relations are powerful techniques used to express uncertain preference information. However, simultaneously providing the exact priority and non-priority 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 interval-valued 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. ? 2017 Beijing Institute of Aerospace Information.

关键词： Fuzzy rules Fuzzy sets Mathematical operators

AGGREGATION AND DECISION MAKING USING INTUITIONISTIC MULTIPLICATIVE TRIANGULAR FUZZY INFORMATION

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Journal of Systems Science and Systems Engineering 2014年第1期23卷 20-38页

作者： Shan YU Zeshui Xu College of Sciences PLA University of Science and Technology Business School Sichuan University

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.

关键词： Intuitionistic multiplicative triangular fuzzy set intuitionistic multiplicative triangularfuzzy number aggregation operator multi-attribute decision making

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Journal of Systems Science and Systems Engineering 2010年第4期19卷 430-452页

作者： Meimei XIA Zeshui Xu School of Economics and Management Southeast University Nanjing Jiangsu 211189 China Institute of Sciences PLA University of Science and Technology Nanjing Jiangsu 210007 China

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.

关键词： Intuitionistic fuzzy value interval-valued intuitionistic fuzzy value similarity measure aggregation operator

UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING

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Journal of Systems Science and Systems Engineering 2010年第3期19卷 257-276页

作者： Xiaohan YU Zeshui Xu Xiumei ZHANG Institute of Communication Engineering PLA University of Science & Technology Institute of Sciences PLA University of Science & Technology

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.

关键词： Multiple attribute group decision making （MAGDM） transformation relationships multigranular linguistic label set

DUAL HESITANT FUZZY INFORMATION AGGREGATION WITH EINSTEIN T-CONORM AND T-NORM

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Journal of Systems Science and Systems Engineering 2017年第2期26卷 240-264页

作者： Hua Zhao Zeshui Xu Shousheng Liu College of Sciences PLA University of Science and Technology Nanjing Jiangsu 210007 China Business School Sichuan University Chengdu Siehuan 610064 China

Dual hesitant fuzzy set （DHFS） is a new generalization of fuzzy set （FS） consisting of two parts （i.e., the membership hesitancy function and the non-membership hesitancy fimction）, which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set （FS）, intuitionistic fuzzy set （IFS）, and hesitant fuzzy set （HFS） so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-eonorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.

关键词： Dual hesitant fuzzy set Einstein t-conorm and t-norm operation aggregation operator