Yejun Xu

• PhD
• Researcher at Tianjin University

The River Chief System (RCS), an innovative top-down and bottom-up water resource management system in China, is implemented to manage increasingly complex water environment issues. However, there has been a time lag in policy implementation. To accurately and scientifically assess the effect of RCS, a dynamic multiple-attribute decision-making met...

In recent years, water, energy, food, and their nexus have become an increasingly significant and active area of research in economic and management science, especially in terms of safety, a research area where several important problems are emerging [...]

The classical Best-Worst Method (BWM) and its expansion form in the multiple criteria decision-making problem under different backgrounds are widely used to calculate the weights of criteria. The traditional BWM uses the accurate value based on Saaty’s scale to describe a decision maker (DM)’s preferences. However, a DM may be unsure about his pref...

Existing studies on social-network large-scale decision making (SN-LSDM) have overlooked two vital roles of the information credibility of decision makers (DMs): 1) Information credibility directly determines the reliability of clustering results and final decision output; 2) Consideration of minority opinions may hold the truth but may also be ris...

In traditional social network analysis-based large-scale group decision making (LSGDM), decision makers (DMs) often trust others based on social prestige/status without sufficient information to understand others’ credibility. Notably, this ignores the inherent risks of trust, resulting in the LSGDM process being subject to trust risk behaviors (bl...

Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identi...

This article introduces the design and evaluation method of the capability Maturity Model for the Integration of Industry and Education. Based on the interpretation of the industry-education integration documents issued by the country and major provinces and cities, the capability model architecture is designed into four levels: Dimension, Process...

In this chapter, we propose the eigenvector method (EM) for priority from an incomplete fuzzy reciprocal preference relation. EM is well known for multiplicative preference relation, which was proposed by Saaty (1980). Lipovetsky and Conklin (2002) and Wang and Parkan (2005) investigated the eigenvector problem for complete fuzzy reciprocal prefere...

In this chapter, we present logarithmic least squares method (LLSM) for priority for incomplete fuzzy reciprocal preference relations. LLSM method is well known for multiplicative preference relation, which was investigated by Saaty and Vargas (1984). Wang and Fan (2007) used the LLSM to derive the weights from complete fuzzy preference relations....

In this chapter, we propose a method called weighted least square method (WLSM) for priority of an incomplete fuzzy reciprocal preference relation (Xu & Da, 2008). It is similar with Gong (2008)’s least square method.

In this chapter, we propose another method called least deviation method (LDM).

In 2015, Rezaei (2015) proposed the best-worst method (BWM). A nonlinear minmax model is used to derive the weights. The minmax model may result in multiple optimal solutions. Later, Rezaei (2016) proposed a linear model for BWM, which yields a unique solution. On the one hand, this method has been widely used to solve various decision-making probl...

In Chap. 1, we have introduced the relationship between the elements of fuzzy reciprocal preference relations and the weights for additive consistency, and it is described in Eq. (1.33). In this chapter, we further investigate the parameter β and call it normalizing rank aggregation-based method when β = n/2 or β = (n − 1)/2. Additionally, we will...

In Sect. 4.1, we have described the group decision-making problems with incomplete fuzzy reciprocal preference relations, where the relationship between the elements \( {c}_{ij}^{(k)} \) and weights wi(i ∈ N) should satisfy Eq. (4.1). In the following, we propose another method called chi-square method.

In the former chapters, we have introduced several priority methods for incomplete fuzzy reciprocal preference relations. In this chapter, we introduce another preference relation called hesitant fuzzy reciprocal preference relation and present how to derive the priority weights from incomplete hesitant fuzzy reciprocal preference relations.

The Best–Worst Method (BWM) has been recently proposed to derive the weights of criteria using two vectors of the pairwise comparison. For BWM, the best criteria and the worst criteria of alternatives are first determined by the decision-maker (DM). Then, the DM gives his best-to-others vector (BV) and the others-to-worst vector (WV). In this paper...

Natural language could be a common method for individuals to specific social relationships or self-evaluation (i.e., assured or unconfident). Hence, it is important to contemplate customized linguistics in collective decisions that involve linguistic variables, because the same linguistic term set may have totally different individual numerical sca...

Distrust behavior is a human behavior that has a significant impact on water pollution management, but it is neglected in existing approaches. To solve this problem, we design a large-scale group decision making in social network (LSGDM-SN) approach based on distrust behavior and apply it to water pollution management. The purpose of this paper is...

This paper proposes a novel expertise-based consensus reaching process (CRP) for probability-hesitant fuzzy preference relations (PHFPRs). First, to identify each expert's comprehensive expertise level, an expertise identification function is constructed based on consistency, hesitancy, and discrimination indicators of PHFPRs. Then, we introduce an...

Preference relation is an effective tool in multi-criteria decision making (MCDM). The fuzzy best-worst method (FBWM), which is an extension of the BWM, is proposed to determine weights for criteria. In the FBWM, the Fuzzy Best-to-others Vector (FBV) and Fuzzy others-to-Worst Vector (FWV) are given. The FBV and FWV can intrinsically formulate one i...

A solution concept (or stability definition) determines whether a state is stable for a decision-maker (DM) in a Graph Model for Conflict Resolution. An equilibrium according to that stability definition is a state stable for all DMs. Thus, stability definitions correspond to anticipated patterns of collective behavior in conflicts. This study focu...

This paper mainly solves the individual consistency and group consensus in the decision-making with hesitant fuzzy preference relations (HFPRs). The worst consistency index (WCI) is used to measure the individual consistency level. The envelop of an HFPR called envelop of HFPR (EHFRP) is proposed in the consensus reaching process (CRP). Two algorit...

In the process of human survival and sustainable development, water security, energy security and food security have become the three most prominent issues, but they are interrelated and directly affect each other, that is, to form a Water–Energy–Food (WEF) nexus. Scientific understanding and correct response to the relationship between WEF is impo...

Within the structure of the graph model for conflict resolution (GMCR), a new matrix representation approach is introduced to analyze the strategic conflicts with grey-based preferences for decision-makers (DMs). Specifically, the DM’s grey-based preferences, unilateral movements (UMs), and grey unilateral improvement (GUI) are redefined by the mat...

The main resources needed for human survival are water, energy and food, and the research on the relationship among the three resources has become the research topic. Due to the shortage of natural resources, research on the efficiency of water–energy–food (WEF) nexus has become a hot issue among scholars and governments all over the world. The sim...

Hesitant fuzzy preference relation (HFPR) is a valid tool to describe the hesitation, ambiguity and uncertainty of decision makers. As a crucial criterion to ensure the rationality of preferences and final decision results, the consistency of preference relations is a valuable research topic. In this study, the additive consistency of HFPRs is inve...

Decision-making situations have been dramatically impacted by the development of the economy and technology. Large-scale group decision making (LSGDM) in social networks has become one of the hot topics in the decision-making field. In this paper, we develop a novel framework to reach consensus in social networks for LSGDM with incomplete probabili...

Self-confidence actually affects group decision making (GDM) because it can somehow reflect decision maker (DM)’s expertise and cognitive level. This paper proposed a new form of preference relation named interval-valued fuzzy preference relation with self-confidence (IFPR-SC). IFPR-SC requires DMs to express self-confidence levels when offering in...

To analyze a strategic conflict involving composite decision makers (CDMs), this paper uses the methodology of the Graph Model for Conflict Resolution (GMCR). A CDM is a group of individuals with differing decision characteristics conservative or aggressive any one of whom can make a decision on behalf of the group. In our model, a conservative CDM...

In group decision making (GDM), to facilitate an acceptable consensus among the experts from different fields, time and resources are paid for persuading experts to modify their opinions. Thus, consensus costs are important for the GDM process. Notwithstanding, the unit costs in the common linear cost functions are always fixed, yet experts will ge...

Every decision may involve risks. Real-world risk issues are usually supervised by third parties. Decision-making may be affected by the absence of sufficient or reasonable trust or to the opposite, an unconditional, excessive, or blind trust, which is called trust risks. The conflict-eliminating process (CEP) aims to facilitate satisfactory consen...

Preference relation is one of the most effective tools for decision makers (experts) to express their evaluation information in decision making. Recently, a new type of preference relation called linguistic preference relations with self-confidence (LPRs-SC) has been proposed. In an LPR-SC, experts can express multiple self-confidence levels when p...

With the continuous development of economic globalization and the increasing strengthening of human exchanges, the Water-Energy-Food (WEF) nexus evaluation has become a new research area. The purpose of this paper is to develop an inverse approach of graph model for conflict resolution (GMCR) to the conflict problems of WEF nexus evaluation in real...

Consensus reaching is a key issue in group decision-making, because conflicts of interest among groups are common. Democratic consensus refers to achieve a soft consensus among collective as well as ensure the effective participation and satisfaction of individuals. Multi-person multi-criteria large scale decision making (MpMcLSDM) usually involves...

Consistency has a crucial influence on the rationality of preference information and even the final decision result. This paper presents two new definitions of additive consistency for hesitant fuzzy preference relations (HFPRs): completely additive consistency (CAC) and weakly additive consistency (WAC). To verify the CAC or WAC of HFPRs, some lin...

With the development of social network platforms, large-scale group decision-making in social network (LSGDM-SN) has been formed. As decision makers (DMs) come from different fields and have complex individual backgrounds, which leads to their distrust in the moderator. Moreover, in LSGDM-SN, since DMs can hardly grasp all the information about the...

This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0-1 mixed programming models and simple algebraic ope...

Preference relation has been one of the most useful tools for experts to express their comparison information over alternatives in group decision‐making (GDM) problems. Recently, a new type of preference relations called linguistic preference relations with self‐confidence (LPRs‐SC) has been proposed, which makes multiple self‐confidence levels int...

Drivers of urban flood disaster risk may be related to many factors from nature and society. However, it is unclear how these factors affect each other and how they ultimately affect the risk. From the perspective of risk uncertainty, flood inundation risk is considered to be the probability of inundation consequences under the influence of various...

Due to the development of network technology, large-scale group decision making (LSGDM) has become increasingly concerned. In this paper, a k-core decomposition-based opinion leaders identifying method and clustering-based consensus model are developed for LSGDM problems. Firstly, a clustering method based on similarity degree is provided for divid...

Allocating initial water rights in a river basin is not only a significant problem but also an essential research topic. It plays a crucial role in promoting the construction of a system of water rights and water-saving society as well as alleviating the contradiction between water supply and demand. Thus, the effective initial allocation of water...

Recently, large-scale group decision making (LSGDM) in social network comes into being. In the practical consensus of LSGDM, the unit adjustment cost of experts is difficult to obtain and may be uncertain. Therefore, the purpose of this paper is to propose a consensus model based on robust optimization. This paper focuses on LSGDM, considering the...

Conflict of environmental sustainable development as a common phenomenon can be seen everywhere in life. To capture consensus problems of decision makers (DMs) in conflict, a consensus and non-consensus fuzzy preference relation (FPR) matrix is proposed to the framework of the Graph Model for Conflict Resolution (GMCR). Concentrating on the case of...

Hesitant fuzzy preference relations (HFPRs) are formally proposed to model the conflict situation in which each decision maker (DM) consists of multiple individuals and each individual has its own fuzzy preferences over the feasible states within the framework of the graph model for conflict resolution (GMCR). Based on HFPRs, new definitions for he...

With the rapid increase and development of global population and economic, the water-energy-food (WEF) nexus evaluation which is related to the sustainable development of human has become a hotspot. Whereas, the study of the WEF nexus evaluation from the perspectives of social network group decision making (SNGDM) is still a challenge. Hence, this...

This research focuses on group decision making (GDM) under hesitant fuzzy condition. All experts (decision makers) are allowed to use hesitant fuzzy preference relations (HFPRs) to express their opinions. Subsequently, a dynamically expert contribution-based consensus model is developed for GDM with HFPRs. In the proposed method, a combination of a...

Within the framework of the graph model, a matrix formulation is developed to model and analyze conflicts in which decision makers (DMs) may have reciprocal preferences. Specifically, matrix expressions are employed to represent DMs' reciprocal preference relations, unilateral movements (UMs) and fuzzy unilateral improvements (FUIs), as well as joi...

Water-energy-food (W-E-F) nexus is an essential element for human survival, as well as the basis for the sustainable development of regional economy and ecological environment. Water resource is an important input element of energy production and food production, which makes the W-E-F nexus become closer and more complicated. Taking water resource...

Reciprocal fuzzy preference relation (FPR) is a hot topic in the research field of group decision making (GDM). Within the framework of GDM, a two-stage consensus reaching model is proposed to modify the decision makers’ (DMs’) FPRs. In the first stage which is called consistency improving stage, a consistency index and an iterative algorithm are e...

Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised: 1) to find the multiplicative inconsistent elements and 2) to detect the ordinal...

Pairwise comparison is a useful tool to express decision makers’ (DMs’) preferences in the group decision-making (GDM) problems. However, the preferences provided by pairwise comparisons could be self-contradictory, i.e., ordinal inconsistencies exist. Therefore, before reaching consensus, the first thing is to assure the DM’s judgments that are no...

Due to the development of intelligent decision-making, social network group decision-making (SNGDM) has become increasingly valued. Generally, real SNGDM cases involve not only the mathematical formulation of the social network analysis but also the experts’ psychological behaviors. Self-confidence, an expert's psychological implication of self-sta...

Consensus reaching models are widely used to derive a representative solution in group decision‐making problems. Current models present limitations regarding the achievement of the agreement and keeping enough consistency for achieving valid solutions. Therefore, this paper proposed a new consensus model based on the deviation degree of two fuzzy p...

An incomplete fuzzy preference framework for the Graph Model for Conflict Resolution (GMCR) is proposed to handle both complete and incomplete fuzzy preference information. Usually, decision makers’ (DMs’) fuzzy preferences are assumed to be complete fuzzy preference relations (FPRs). However, in real-life situations, due to lack of information or...

Self-confidence as one of the human psychological behaviors has important influence on emergency management decision making, which has been ignored in existing methods. To fill this gap, we dedicate to design a group decision making approach considering self-confidence behaviors and apply it to the environmental pollution emergency management. In t...

In practical group decision-making (GDM) problems, it is nature for experts to express their preference relations in uncertain linguistic pattern, due to the ambiguity of the external environments and the internal nature of human judgments. In this paper, a consensus process is introduced to deal with GDM problems with incomplete uncertain linguist...

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions, Information Fusion (2018), doi: https://doi. Highlight  We review additive consistency measurements of various reciprocal preference relations.  We review decision making methods based...

Preference relations have been widely used in group decision‐making (GDM) problems. Recently, a new kind of preference relations called fuzzy preference relations with self‐confidence (FPRs‐SC) has been introduced, which allow experts to express multiple self‐confidence levels when providing their preferences. This paper focuses on the analysis of...

Within the paradigm of the Graph Model for Conflict Resolution (GMCR), fuzzy reciprocal preference relations (FPRs) can be usually employed to handle decision makers’ (DMs’) certain and uncertain preferences. Due to lack of time, limited expertise, or dynamic factors, the DMs’ fuzzy preferences over the alternatives or states may be incomplete. Thu...

Recently, large scale group decision making (LSGDM) problems are becoming a hotspot. This paper focuses on the hesitant fuzzy LSGDM problems, where decision makers (DMs) use hesitant fuzzy reciprocal preference relations (HFPRs) to express their assessment information. HFPRs can represent the fuzziness and hesitancy of DM assessment information wel...

Consistency is related with reasonableness. This paper proposes a graphical method to visualize and rectify different inconsistencies for fuzzy reciprocal preference relations (FPRs), and the consistency includes the ordinal and cardinal consistencies. Ordinal inconsistency implies cardinal inconsistency, but not vice versa, and cardinal consistenc...

In practical group decision making (GDM) problems, decision maker (DM) may have to tackle with incomplete information and uncertain linguistic preference relation (ULPR). Consequently, the DMs may provide incomplete ULPRs. In this paper, the property of additive transitivity of fuzzy preference relations is extended to linguistic domain firstly. Th...

Fuzzy linguistic preference relations (FLPRs), which decision makers (DMs) use to express their pairwise comparison information, are suitable for modeling the qualitative aspects of problems. Ordinal consistency is the minimum condition that DM's preference values arenot self-contradictory. In this paper, we first define and study the ordinal consi...

Fuzzy reciprocal preference relations (FPR) are one of the most common preference relations which decision makers (DMs) express their comparison information in decision making, and the consistency of preference relations is an important step for reasonable and reliable decision making. Based on the concept of deviation between two matrices, we deve...

This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relat...

This paper investigates both the ordinal and multiplicative consistencies for reciprocal preference relations simultaneously. First, the relationship among ordinal consistency, acceptable cardinal consistency and perfect cardinal consistency of reciprocal preference relations are analyzed. Then, based on the basic forms of all ordinal inconsistenci...

This paper studies the consistency and consensus models with local adjustment strategy for hesitant fuzzy linguistic preference relations (HFLPRs). A consistency and consensus reaching model with local adjustment strategy is devised. In the consistency improving process, only the most inconsistent preferences are suggested to be modified toward the...

This study analyzes the level of satisfaction of stakeholders in the public participation process (PPP) of water resources management, which is mandatory according to the EU Water Framework Directive (WFD). The methodology uses a fuzzy set/qualitative comparative analysis (fsQCA), which allows the identification of a combination of factors that lea...

There is a growing interest in environmental policies about how to implement public participation engagement in the context of water resources management. This paper presents a robust methodology, based on ordered weighted averaging (OWA) operators, to conflict resolution decision-making problems under uncertain environments due to both information...

This paper proposes a decision support process for incomplete hesitant fuzzy preference relations (HFPRs). First, we present a revised definition of HFPRs, in which the values are not ordered for the hesitant fuzzy element. Second, we propose a method to normalize the HFPRs and estimate the missing elements in incomplete HFPRs based on multiplicati...

In multi-attribute group decision making, it is preferable that a set of experts reach a high degree of consensus amongst their opinions, especially for large-scale group decision making. This paper presents a two-stage method to support the consensus reaching process for large-scale multi-attribute group decision making problems. The first stage c...

This paper proposes a consistency improving procedure for fuzzy preference relations. Fuzzy consistency index (FCI) and fuzzy consistency ratio (FCR) are developed to measure the consistency level for complete (or incomplete) fuzzy reciprocal preference relations (FPRs). The principal eigenvector is used for priorities deriving from a complete (or...

This paper studies the ordinal and additive consistency issues of fuzzy linguistic preference relations (FLPRs). First, a graphic method of Gower plot is proposed to ascertain ordinal and additive inconsistencies for FLPRs. Then, two optimization models are established to adjust the ordinal and additive inconsistencies at the same time. Furthermore...

Hesitant fuzzy linguistic term sets suit the modelling of qualitative setting so that experts provide several possible linguistic values than a single term for an indicator, alternative, variable, etc. This paper proposes a consistency and consensus based decision support model for group decision making with hesitant 2-tuple fuzzy linguistic prefer...

This paper investigates a consensus model for hesitant fuzzy preference relations (HFPRs). First, we present a revised definition of HFPRs, in which the values are not ordered for the hesitant fuzzy element. Second, we propose an additive consistency based estimation measure to normalize the HFPRs, based on which, a consensus model is developed. He...

Decision makers express a strong need for reliable information on future climate changes to develop with the best mitigation and adaptation strategies to address impacts. These decisions are based on future climate projections that are simulated by using different Representative Concentration Pathways (RCPs), General Circulation Models (GCMs), and...

One of the most important problems in quantum thermodynamics is how to distinguish work and heat in autonomous quantum systems. In this paper, work and heat are defined through the following criterion, i.e., work is the energy that cannot change the entropy of the energy resource, and satisfies the Jarzynski equality, while heat does not. Two kinds...

“Connectivity” is the core planning strategy that is used to examine the features of functional and structural connections in urban waterfront redevelopment projects. According to SIA point of view, an index system of assessing urban waterfront redevelopment connectivity including 8 evaluation indexes is proposed from the hierarchy of ecological, s...

The consensus reaching process is a dynamic and iterative process for improving group's consensus level before making a final decision in group decision-making (GDM). As the experts will express their opinions under their own intellectual level from different aspects, it is natural that the experts’ weights should reflect their judgment information...