Decision Maker's Preference Information Research Articles

An interval number group decision-making method based on the prospect SMAA-2 model and extended cross-entropy

The preference information of decision-makers (DMs) often cannot be explicitly expressed in complex decision-making environments. Therefore, to address decision-making problems with uncertain preference information, this paper proposes a method based on the prospect SMAA-2 model and extended cross-entropy in interval number environments. We first construct the prospect SMAA-2 model to simulate preference information. This model incorporates central risk-averse and risk-seeking factors, significantly enhancing the ability to identify alternatives. When DMs’ preference information is unknown or partially known, these factors can determine the appropriate level of risk-averse or risk-seeking for alternatives. Next, we devise an extended cross-entropy algorithm based on the continuous ordered weighted harmonic (C-OWH) averaging operator to handle interval numbers. Subsequently, a comprehensive algorithm is designed to derive the weights of DMs, taking into account the relationships among individuals as well as between individuals and the group. Furthermore, we construct the framework for the proposed method. Finally, the applicability of the developed method can be validated by an illustrative example. Comparative analysis is used to verify the rationality and superiority of this method.

Blockchain service platform evaluation with probabilistic linguistic preference information based on Choquet integral and ExpTODIM

The application of Internet of Medical Things (IoMT) can improve the treatment efficiency of medical institutions, but it still has hidden dangers in security and privacy. The introduction of blockchain technology into IoMT is expected to prevent these hidden dangers. This study proposes a multiple criteria decision aiding model to select a suitable blockchain service platform for IoMT to enhance its safety and reliability. The proposed model combines the probabilistic linguistic term set (PLTS), multiple criteria hierarchy process (MCHP), 2-additive Choquet integral and ExpTODIM method to assist decision-makers (DMs) to obtain a reliable and low-risk decision result. The MCHP is employed to analyze decision-making problems by hierarchical criteria. The 2-additive Choquet integral is adopted to reflect interactions between criteria, and parameter values in the 2-additive Choquet integral are indirectly determined based on the preference information of DMs. PLTSs are used to represent the evaluation information of experts and the preference information of DMs. The ExpTODIM (Exponential TODIM) method is adopted to rank alternatives considering the psychological characteristics of DMs. An illustrative example demonstrates the applicability and merits of the proposed model with comparative analysis.

A process capability function approach to multiple response surface optimization based on a posterior procedure

Multiple response surface optimization (MRSO) aims to determine a setting of input variables that simultaneously optimizes multiple responses. The process capability function (PCF) approach is an attractive alternative to MRSO because it considers both the mean and variance of the responses systematically through the process capability index. In MRSO, the responses are often in conflict. Thus, the preference information of a decision maker (DM) on the tradeoffs among the responses should be considered. However, the existing PCF methods are based on an unrealistic assumption that all DM preference information is given in advance. In this article, a posterior preference articulation procedure based on the PCF approach, called P-PCF, is proposed. P-PCF first generates nondominated solutions using the ε-constraint method and then allows the DM to select his/her preferred cluster or final solution using the K-means clustering method. The proposed method is illustrated using a well-known MRSO problem.

Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent.

A robust ordinal regression feedback consensus model with dynamic trust propagation in social network group decision-making

This paper proposes a robust ordinal regression feedback consensus model based on trust relationships for social network group decision-making problems in intuitionistic fuzzy environment. The model consists of two main parts: (a) the construction of the complete trust matrix among decision makers (DMs) and (b) the design of a feedback mechanism formulated on robust ordinal regression. In Part (a), to complete the initial trust matrix between DMs, a dynamic trust propagation mode founded on maximum credibility is proposed to investigate indirect trust relationships between unfamiliar DMs from the perspective of overall optimization. In Part (b), when the group consensus does not reach the consensus threshold, the utility function compatible with the preference information of DMs is constructed through robust ordinal regression, and the most representative utility function is selected by maximizing the difference of the necessary weak preference relationship. In addition, the performance of DMs under four evaluation dimensions, individual consensus degree, individual comprehensive influence, individual opinion retention, and individual proximity centrality, is aggregated into a total utility value. In each iteration, the DM with the lowest total utility value is identified for opinion adjustments. Further, based on trust-similarity analysis, recommendations are designed for opinion adjustments to improve the group consensus. An illustrative example along with the related sensitivity analysis and comparative study is used to examine the effectiveness and advantages of the proposed model.

Pareto efficient correlated multi-response optimisation by considering customer satisfaction

The capability of a manufacturer in satisfying the customer's requirements is an important issue in the current competitive market. Since customers consider several correlated quality characteristics for selecting a product, designing the process variables to meet the required specification limits of the quality characteristics is essential. Furthermore, to attain the most satisfactory solution, a decision maker's preference information should be incorporated into the optimisation procedure. This study suggests a posterior preference articulation approach based on NSGA-II and MOPSO, which is capable to increase customer satisfaction by generating non-dominated solutions within conformance region. The proposed method takes also into account the location and dispersion effects along with the correlation of among quality characteristics as well as the relative importance of them. To demonstrate the applicability of the approach, a computational analysis on two case studies is performed. Results confirm superiority of the suggested method in comparison with the existing posterior approaches.

An Additive Consistency and Consensus Approach for Group Decision Making With Probabilistic Hesitant Fuzzy Linguistic Preference Relations and Its Application in Failure Criticality Analysis.

In this article, probabilistic hesitant fuzzy linguistic preference relations (PHFLPRs) are proposed to present the qualitative pairwise preference information of decision makers (DMs) with hesitation and probability uncertainty assessments. The measurements and improvements of additive consistency and consensus of PHFLPRs are investigated in group decision making (GDM). First, a new concept of probabilistic hesitant fuzzy linguistic term sets is defined. Second, the consistency and consensus measurements are established to survey the additive consistency and consensus levels of PHFLPRs. Subsequently, an optimization model is developed to improve the unacceptably additive consistent PHFLPR. By optimizing the unacceptable consensual PHFLPRs with repeating additive consistency improvement, the acceptably additive consistent and consensual PHFLPRs are obtained, based on which DMs' weights are determined objectively and then, the collective PHFLPR is aggregated from individual PHFLPRs. Alternatives' priority weights are derived from the collective PHFLPR as GDM. Finally, an example about failure criticality analysis is given, and a comparison analysis is presented.

A Clustering Method with Historical Data to Support Large-Scale Consensus-Reaching Process in Group Decision-Making

With the rapid development of information technology and social network, the large-scale group decision-making (LSGDM) has become more and more popular due to the fact that large numbers of stakeholders are involved in different decision problems. To support the large-scale consensus-reaching process (LCRP), this paper proposes a LCRP framework based on a clustering method with the historical preference data of all decision makers (DMs). There are three parts in the proposed framework: the clustering process, the consensus process and the selection process. In the clustering process, we make use of an extended k-means clustering technique to divide the DMs into several clusters based on their historical preferences data. Next, the consensus process consists of the consensus measure and the feedback adjustment. The consensus measure aims to calculate the consensus level among DMs based on the obtained clusters. If the consensus level fails to reach the pre-defined consensus threshold, it is necessary to make the feedback adjustment to modify DMs' preferences. At last, the selection process is carried out to obtain a collective ranking of all alternatives. An illustrative example and detailed simulation experiments are demonstrated to show the validity of the proposed framework against the traditional LCRP models which just consider the preference information of DMs at only one stage for clustering.

A Combined Weighting Model Based on Maximizing Deviation for Multiple Attribute Decision-Making

Multiattribute decision-making is an important part of decision-making theory and modern scientific decision-making. It is widely used in engineering design, economic management, and so on. It is an important part of modern decision science to sort decision objects when considering multiple attributes. Due to time pressure and lack of understanding of decision-making problems, it is difficult for decision makers to accurately express judgment information. Decision-makers’ judgment information is more suitable to be expressed by intuitionistic fuzzy sets rather than deterministic numbers or linguistic variables. In the multiattribute decision-making problem, the size of attribute weight reflects the relative importance of each attribute. The research on attribute weight determination method is one of the core problems of multiattribute decision-making. Whether it is the subjective weighting method, the objective weighting method, or the combined weighting method, the research mainly focuses on deterministic multiattribute decision-making, mostly transforming fuzzy information into deterministic information for decision-making, which will lose a lot of information. Due to the differences of objective information data, a combined weighting method in different cases was proposed in this study. The original weight information and the prior information of standardized evaluation can be fully utilized in this model. The results indicate that when decision makers have preferences for different weighting methods, the combined weighting method can be determined according to the preference information of decision makers.

Contingency response decision of network public opinion emergencies based on intuitionistic fuzzy entropy and preference information of decision makers

A multi-attribute group decision-making (MAGDM) method based on intuitionistic fuzzy preference information is proposed for the multi-attribute intuitionistic fuzzy group decision-making problem where the decision-makers weight and attribute weight are completely unknown and the decision-maker has preference information for the scheme. Firstly, an intuitionistic fuzzy interval judgment matrix is established to describe the original data of the key decision indicators for multiple network public opinion emergencies that erupt simultaneously. Secondly, the attribute weights are determined based on the improved intuitionistic fuzzy entropy construction method, and the expert weights are determined by using objective decision information, taking into account the intuitionistic fuzzy entropy of decision matrix. MAGDM can not only synthesize experts' professional experience in different aspects, but also avoid experts' decision-making errors caused by insufficient domain knowledge. It is necessary to continuously adjust the expert weight based on decision-making information to make the comprehensive decision-making information more accurate. Thirdly, a scheme preference model and an attribute weight optimization model are established to determine the ranking method of intuitionistic fuzzy interval values. Then, a modified distance measure of intuitionistic fuzzy sets (IFSs) is introduced to make the evaluation result more accurate and reasonable when it comes to solving the deviation between the evaluation value and ideal solution of each scheme. Finally, the effectiveness and practicability of the proposed decision-making method are verified by an example of emergency crisis severity, It assists decision makers in selecting and implementing the optimal emergency response plan in a timely and efficient manner, which improves the emergency treatment efficiency of network public opinion crisis, helps emergency departments to better deal with the network public opinion crisis, improves the ability of public opinion guidance and control, and provides a new method and idea for multi-attribute intuitionistic fuzzy group decision-making problem.

A Data Envelopment Analysis or Goal Programming Model with Fuzzy Preferences of Decision Makers

Due to the complexity and uncertainty involved in real world decision problems, the determination and interpretation of Decision Makers' preference relations remain a challenging task for them. This paper develops a novel procedure for incorporating preference information in the efficiency analysis of Decision Making Units. The efficiency of Decision Making Units is defined in the spirit of Data Envelopment Analysis, complemented with Decision Maker's preference information. Our procedure begins by aiding the different decision making group members to express their incomplete fuzzy preferences by using a multiple objective linear programming approach for generating a common set of weights in the DEA framework.

Compromise solutions for stochastic multicriteria acceptability analysis with uncertain preferences and nonmonotonic criteria

AbstractAs one of the most popular multiple criteria decision‐making (MCDM) methods, the stochastic multicriteria acceptability analysis (SMAA) is powerful in dealing with the uncertain preference information of decision makers. However, how to find compromise solutions for MCDM problems remains an open question in the SMAA family. A compromise solution refers to an alternative that is the closest to the ideal solution. In this paper, we propose an improved SMAA method, called the SMAA with compromise solutions (SMAA‐CO), to determine compromise solutions for MCDM problems with the uncertain preferences of decision makers and conflicting criteria. The SMAA‐CO uses nonmonotonic additive value functions to depict decision makers’ ideal values for reference points. We apply the proposed method to capture multiple decision makers’ uncertain preference information. An illustrative example concerning supplier selection in the pulp and paper industry is used to show the applicability of the proposed method. Some managerial insights are given.

S-CoEA: Subproblems Co-Solving Evolutionary Algorithm for Uncertain Optimization.

Existing techniques on dealing with uncertain optimization problems (UOPs) mostly rely on the preference information of decision makers (DMs) or the knowledge involved in probability distributions on uncertainties. Actually, accurate preferences and distribution information of uncertainties are hard to obtain due to the lack of knowledge. Besides, it is risky to make assumptions on this information to handle uncertainties when DMs do not have sufficient knowledge about the problem. This article attempts to treat UOPs in an a posteriori manner and proposes a subproblem co-solving evolutionary algorithm (EA) for UOPs, namely, S-CoEA. It decomposes a UOP into a series of correlated subproblems by using the proposed decomposition strategy embedded with an original ordered weighted-sum (OWS) operator. These subproblems are formulated in different aggregation forms of sampled function values and represent different preferences on uncertainties. They are co-solved in parallel by using information from neighboring subproblems. The sampling strategy is used to gather the distribution information of uncertain functions and alleviate the detrimental effects of uncertainties. A sample-updating scheme based on historical information is presented to further improve the performance of S-CoEA. The proposed S-CoEA is compared with two state-of-the-art competitors, including the EA with the exponential sampling method (E-sampling) and the population-controlled covariance matrix self-adaptation evolution strategy (pcCMSA-ES). Numerical experiments are conducted on a series of test instances with various characteristics and different strength levels of uncertainties. Experimental results show that S-CoEA outperforms or performs competitively against competitors in the majority of 26 continuous test instances and four test cases of discrete redundancy allocation problems.

Are the Portuguese public hospitals sustainable? A triple bottom line hybrid data envelopment analysis approach

AbstractThe harmonious interaction between humans and the biosphere determines how sustainable existence and coexistence are. However, when social challenges appear, sustainability is heavily compromised. Health is one of the areas affected by such challenges, with the delivery of health services being ensured by health systems. Consequently, understanding how sustainable health services are, especially those that consume the majority of resources—hospitals—is indispensable for a sustainable future. For this reason, we propose using a hybrid data envelopment analysis (DEA) approach to study hospital sustainability in Portugal under environmental, social, and economic perspectives, in cooperation with the Portuguese Ministry of Health. In particular, the proposed methodology incorporates the preference information of decision makers (via the construction of utility scales and the determination of Möbius coefficients) and criteria interactivity, due to the integration of the Choquet multiple criteria preference aggregation model in the DEA approach. In the end, despite approximately 30% of the sampled 29 assessed hospitals were deemed as efficient across the three perspectives in 2018, only 1 was entirely sustainable.

Does Preference Always Help? A Holistic Study on Preference-Based Evolutionary Multiobjective Optimization Using Reference Points

The ultimate goal of multiobjective optimization is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory tradeoffs among multiple conflicting criteria. This can be realized by leveraging DM's preference information in evolutionary multiobjective optimization (EMO). No consensus has been reached on the effectiveness brought by incorporating preference in EMO (either a priori or interactively) versus a posteriori decision making after a complete run of an EMO algorithm. Bearing this consideration in mind, this article: 1) provides a pragmatic overview of the existing developments of preference-based EMO (PBEMO) and 2) conducts a series of experiments to investigate the effectiveness brought by preference incorporation in EMO for approximating various SOI. In particular, the DM's preference information is elicited as a reference point, which represents her/his aspirations for different objectives. The experimental results demonstrate that preference incorporation in EMO does not always lead to a desirable approximation of SOI if the DM's preference information is not well utilized, nor does the DM elicit invalid preference information, which is not uncommon when encountering a black-box system. To a certain extent, this issue can be remedied through an interactive preference elicitation. Last but not the least, we find that a PBEMO algorithm is able to be generalized to approximate the whole PF given an appropriate setup of preference information.

A Robust Interactive Desirability Function Approach for Multiple Response Optimization Considering Model Uncertainty

To solve multiple response optimization problems that often involve incommensurate and conflicting responses, a robust interactive desirability function approach is proposed in this article. The proposed approach consists of a parameter initialization phase and calculation and decision-making phases. It considers a decision maker's preference information regarding tradeoffs among responses and the uncertainties associated with predicted response surface models. The proposed method is the first to consider model uncertainty using an interactive desirability function approach. It allows a decision maker to adjust any of the preference parameters, including the shape, bound, and target of a modified robust function with consideration of model uncertainty in a single and integrated framework. This property of the proposed method is illustrated using a tire tread compound problem, and the robustness of the adjustments for the approach is also considered. The new method is shown to be highly effective in generating a compromise solution that is faithful to the decision maker's preference structure and robust to uncertainties associated with model predictions.

A Method Based on Bivariate Almost Stochastic Dominance for Multiple Criteria Group Decision Making With Probabilistic Dual Hesitant Fuzzy Information

Probabilistic dual hesitant fuzzy sets (PDHFSs) are sound information granules to describe decision maker's aleatory and epistemic uncertainty in multiple criteria group decision making (MCGDM) process. In this paper, a bivariate almost stochastic dominance-based PROMETHEE-II method is presented to solve probabilistic dual hesitant fuzzy MCGDM problems which consider correlation averse behavior of decision makers. First, probabilistic dual hesitant fuzzy power Bonferroni mean (PDHFPBM) operator and probabilistic dual hesitant fuzzy power geometric Bonferroni mean (PDHFPGBM) operator are proposed to acquire collective preference information of decision makers. Second, based on the defined bivariate almost stochastic dominance (BASD) and BASD degree, qualitative and quantitative relationships between two probabilistic dual hesitant fuzzy elements (PDHFEs) with corresponding to all criteria are obtained. Third, distance-based correlation coefficient method for computing combined weight with respect to all criteria is proposed. Finally, a BASD-based PROMETHEE-II method is developed to determine the ranking results. Three illustrative examples followed by comparative analysis are included to show the practicality and effectiveness of the proposed method.

Multi-Objective Service Selection and Scheduling with Linguistic Preference in Cloud Manufacturing

Service management in cloud manufacturing (CMfg), especially the service selection and scheduling (SSS) problem has aroused general attention due to its broad industrial application prospects. Due to the diversity of CMfg services, SSS usually need to take into account multiple objectives in terms of time, cost, quality, and environment. As one of the keys to solving multi-objective problems, the preference information of decision maker (DM) is less considered in current research. In this paper, linguistic preference is considered, and a novel two-phase model based on a desirable satisfying degree is proposed for solving the multi-objective SSS problem with linguistic preference. In the first phase, the maximum comprehensive satisfying degree is calculated. In the second phase, the satisfying solution is obtained by repeatedly solving the model and interaction with DM. Compared with the traditional model, the two-phase is more effective, which is verified in the calculation experiment. The proposed method could offer useful insights which help DM balance multiple objectives with linguistic preference and promote sustainable development of CMfg.

Interactive Decomposition Multiobjective Optimization Via Progressively Learned Value Functions

Decomposition has become an increasingly popular technique for evolutionary multiobjective optimization (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice, a decision maker (DM) might only be concerned in her/his region of interest (ROI), i.e., a part of the PF. Solutions outside that might be useless or even noisy to the decision-making procedure. Furthermore, there is no guarantee that the preferred solutions will be found when many-objective problems. This paper develops an interactive framework for the decomposition-based EMO algorithm to lead a DM to the preferred solutions of her/his choice. It consists of three modules, i.e., consultation, preference elicitation, and optimization. Specifically, after every several generations, the DM is asked to score a few candidate solutions in a consultation session. Thereafter, an approximated value function, which models the DM's preference information, is progressively learned from the DM's behavior. In the preference elicitation session, the preference information learned in the consultation module is translated into the form that can be used in a decomposition-based EMO algorithm, i.e., a set of reference points that are biased toward the ROI. The optimization module, which can be any decomposition-based EMO algorithm in principle, utilizes the biased reference points to guide its search process. Extensive experiments on benchmark problems with three to ten objectives fully demonstrate the effectiveness of our proposed method for finding the DM's preferred solutions.

A New Model for Deriving the Priority Weights from Hesitant Triangular Fuzzy Preference Relations

Fuzzy preference relation is a common tool to express the uncertain preference information of decision maker in the process of decision making. However, the traditional fuzzy preference relation will fail under hesitant fuzzy environment as the membership has a single value. In addition, it is very difficult to obtain the precise membership values. Therefore, a new model of fuzzy preference relation is proposed in this paper. Firstly, the concept of hesitant triangular fuzzy preference relation is defined and its properties are investigated based on the concepts of hesitant fuzzy set, hesitant triangular fuzzy set, fuzzy preference relation, and hesitant fuzzy preference relation. Then, the steps of applying this novel model are offered for the case of determining the weights of failure modes. Finally, an example is used to illustrate the proposed model.