Uncertain Preferences Research Articles

Classification-based consensus model considering quantum interference in linguistic distribution environment

Multi-attribute group classification (MAGC) is widely used in dealing with a variety of practical problems. However, cognitive biases, resulting from factors such as irrational behaviors, epistemic uncertainty, and interference phenomena, may critically affect the consensus reaching process (CRP) of MAGC. To eliminate such influences, this study proposes an ordinal classification consensus model in a linguistic environment based on quantum probability theory (QPT), with the aim of classifying the alternatives into several predefined ordinal classifications accepted by a majority of experts. First, the linguistic distribution assessments (LDAs), which can depict the quantitative distribution and qualitative vagueness, are used to express the uncertain preference of experts. Second, the LDAs best-worst method (BWM) and LDAs maximizing deviation model (MDM) are developed to identify the subjective and objective weight of attributes, and then these two types of attributes weight are integrated by quantum-like Bayesian networks (QLBN). Third, a maximum consensus model (MCM), maximizing the consensus level of ordinal classification results of experts, is provided to determine the parameters of QLBN. When the consensus level is lower than the predetermined threshold, a minimum adjustment distance model (MADM) is designed to guide the preference-modification of experts to derive the consensus classification of alternatives. Finally, a risk assessment case study is conducted to verify the feasibility and effectiveness of the proposed method. Sensitivity analysis and comparison analysis are performed to verify the feasibility and effectiveness of the proposed method

Evaluating risk of IoT adoption in the food supply chain using an integrated interval-valued spherical fuzzy generalised TODIM method

The existing literature has shown that the Internet of Things (IoT) has proven to be beneficial for managing operations in the food supply chain. However, the potential failures resulting from these new technologies have not been thoroughly examined. Therefore, the aim of this study is to create a new framework for analyzing the risks associated with implementing IoT in the food supply chain. To achieve this, we introduce an extended failure mode and effect analysis framework using an integrated generalised Toma de Decisão Iterativa Multicritério (TODIM) method within the interval-valued spherical fuzzy setting. Initially, we developed a risk structure consisting of four dimensions and sixteen sub-factors to facilitate the implementation of IoT technology in the food supply chain. We then introduced an interval-valued spherical fuzzy-weighted Bonferroni mean operator to gather expert opinions and create a group risk matrix considering the interaction between the input risk data. Subsequently, we proposed a newly developed interval-valued spherical fuzzy TODIM method based on the Logarithmic percentage change-driven objective weighting (LOPCOW) method to evaluate and rank the risks associated with IoT application in the food supply chain. This method can capture the bounded rational decision behavior of experts and the uncertain preference of risk parameters. Based on the identified risk factors, we implemented a proposed risk analysis framework in line with the preferences of the experts. The results indicate that "human resource risk" and "uncertainty in technology adoption" are the most and least significant risks, respectively. We also conducted sensitivity and comparison studies to test the reliability and rationality of the proposed framework. The main findings can assist policymakers and managers in mitigating and minimizing the risks connected with IoT applications in the food supply chain. Additionally, these outcomes can aid stakeholders in making well-informed decisions about resource allocation for risk management.

The influence of externality in the graph model for conflict resolution under fuzzy preferences

The Graph Model for Conflict Resolution (GMCR) is a flexible and comprehensive methodology for systematically investigating strategic conflicts. However, most existing studies solely focus on internal conflicts among decision makers (DMs), often disregarding the influence of external stakeholders (ESs) on DMs’ preferences. Consequently, this leads to insufficient stability in equilibrium outcomes. The objective of this study is to address the conflict issue faced by DMs with subjective uncertain preferences who are influenced by externality. Building upon the framework of GMCR, this study proposes the graph model for conflict resolution with fuzzy preference based on externality (FEGMCR) which introduces fuzzy numbers to measure both uncertain preferences of DMs and uncertain expectations of ESs. Furthermore, four forms of stability are extended-- Fuzzy Nash Stability based on externality (FER), Fuzzy General Metarationality based on externality (FEGMR), Fuzzy Symmetric Metarationality based on externality (FESMR), and Fuzzy Sequential Stability based on externality (FESEQ). The optimal equilibrium is achieved by dynamically adjusting the weight of the impact of externalities. Finally, the method is applied to the case of plastic ban in Hainan. It is found that the expectations of ESs do change the preferences of DMs and affect the final equilibrium, which provides a sustainable solution for the issue.

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.

Supplier selection of complex equipment in a military-civilian collaborative two-tier supply network with uncertain preference: A matching perspective

Complex equipment refers to special equipment that differs from general equipment. The collaborative development work of complex equipment in the military-civilian integration context involves numerous suppliers. We consider a two-tier supply network composed of different suppliers that participate in the development work to assemble complex equipment that cooperate with a main-manufacturer regarding spare parts. However, in terms of spare parts, a substitution relationship exists in assembly work for complex equipment. Hence, selecting a suitable supplier from the matching process between suppliers and spare parts under a military-civilian integration background is essential. This study considers three main analyses to obtain a suitable supplier for the development work of complex equipment. First, we construct a two-stage model to acquire the necessary evaluation dimension for subsequent processes. Second, we examine the evaluated attributes for the matching process based on entropy-group-DEMATEL analysis. Third, we perform information aggregation for the uncertain preference information between spare parts and suppliers using a Bonferroni mean operator. Finally, an illustrative example is presented to demonstrate the whole efficiency. Through the aforementioned analysis, we can select a suitable supplier that could participate in complex equipment military-civilian collaborative development work.

Envy-Free House Allocation under Uncertain Preferences

Envy-freeness is one of the most important fairness concerns when allocating items. We study envy-free house allocation when agents have uncertain preferences over items and consider several well-studied preference uncertainty models. The central problem that we focus on is computing an allocation that has the highest probability of being envy-free. We show that each model leads to a distinct set of algorithmic and complexity results, including detailed results on (in-)approximability. En route, we consider two related problems of checking whether there exists an allocation that is possibly or necessarily envy-free. We give a complete picture of the computational complexity of these two problems for all the uncertainty models we consider.

Grey preference for analyzing the influence of externality within the graph model for conflict resolution

Externality may have uncertain influence on decision makers (DMs). To address the conflicts with uncertain preference and externality, this study adopts the general grey number to measure the uncertain value of DMs’ option statements influenced by externality. It constructs adjustable grey preference influenced by externality (GPE), which can be dynamically adjusted according to the influence of externality. Subsequently, the study defines four equilibrium solutions for the graph model for conflict resolution based on grey preference influenced by externality (GPE-GMCR). Finally, the method is applied to a commercial bank operating conflict triggered by the Silicon Valley Bank (SVB) collapse in the United States, resulting in optimal results for conflict resolution. Specifically, the new model provides a practical tool for DMs, managers and policy makers to address conflicts arising from DMs’ uncertain preference under the influence of externality in complex environments.

Influence measure-based large-scale group decision making with linear uncertain preference relations

This research focuses on the problem of large-scale group decision-making (LSGDM) based on influence measure under linear uncertain preferences. The value of this research is that it improves the performance of the current clustering algorithms, increases the efficiency of consensus reaching for major decision-making events, thus reducing the cost of feedback adjustments, and at the same time reflecting the risk attitude of the decision-makers (DMs) during situations of uncertainty. First, an approach for measuring the influence of the DMs is presented. Based on the influence measure, a clustering method is proposed to classify the experts into subgroups. Then, a method for determining the weights of the subgroups is developed by combining the influence and credibility of the subgroup leader as well as the intra-subgroup consensus level. Subsequently, a feedback adjustment method is provided to reduce the disagreement among the DMs by considering the unit adjustment cost and the corresponding adjustment willingness of the DMs. Further, based on the trust risk and credibility of the DMs, a dual management mechanism of non-cooperative behavior is established to hasten consensus. Finally, a case study is presented to demonstrate the practicality of the suggested approach, while simulation experiments and comparative analysis are conducted to verify the model.

A new decision analysis framework for multi-attribute decision-making under interval uncertainty

In decision-making analysis, the description on decision makers' risk attitude under uncertainty is a focus topic. This paper presents a novel decision analysis framework that considers uncertainty and risk using the cumulative prospect theory. The proposed approach describes uncertain preference information using interval-valued fuzzy sets, maintaining this representation without converting intervals into crisp numbers throughout the entire process. To quantify the distance between interval-valued fuzzy sets, we introduce a comprehensive interval-valued distance model that accounts for multiple situations determined based on the relative positions between intervals. Afterwards, some related theorems about the proposed interval-valued distance model are explored mathematically. Then, with the aid of different reference points and interval-valued distance model, the overall interval-valued prospect value of each alternative is investigated. Finally, an Enhanced Minimax Regret-based (EMR) approach is developed to compare and rank the obtained overall interval-valued prospect values. An illustrative example, accompanied by detailed discussions, is provided to demonstrate the flexibility and superiority of the proposed decision analysis framework.

Demystifying the Stability and the Performance Aspects of CoCoSo Ranking Method under Uncertain Preferences

This paper attempts to demystify the stability of CoCoSo ranking method via a comprehensive simulation experiment. In the experiment, matrices of different dimensions are generated via Python with fuzzy data. Stability is investigated via adequacy and partial adequacy tests. The test passes if the ranking order does not change even after changes are made to entities, and the partial pass signifies that the top ranked alternative remains intact. Results infer that CoCoSo method has better stability with respect to change of alternatives compared to criteria; and CoCoSo method shows better stability with respect to partial adequacy test for criteria.

Probabilistic consistency of stochastic multiplicative comparison matrices based on Monte Carlo simulation

Stochastic multiplicative comparison matrices (SMCMs) are widely accepted due to their flexibility in measuring various types of decision-makers' uncertain preferences by treating the judgment as a random variable. However, few existing consistency indices for SMCMs account for the influence of uncertainty of SMCMs on consistency. This may lead to some contradictions in consistency measurement for SMCMs. This paper proposes a probabilistic consistency index (PCI) considering the uncertainty of SMCMs from a statistical perspective. The index satisfies the property of invariance under the permutation of the labels of objects. The influence of uncertainty on the PCI is discussed in detail by numerical simulation. In addition, the perfect consistency and acceptable consistency of SMCMs based on the PCI are introduced, and a general threshold determination algorithm for acceptable consistency of SMCMs based on Monte Carlo simulation is designed considering the uncertainty, the distribution and the order of an SMCM. Subsequently, a consistency improvement method for SMCMs based on stochastic programming is proposed, which preserves the original preference of decision-makers to the greatest extent. Finally, examples are given to illustrate the significance of the consistency verification by using the PCI, and the most likely preference structure is used as the ranking for SMCMs.

Idlefish or not? Online platform’s strategy of secondhand marketplace introduction in the presence of consumer’s uncertain preferences and strategic behavior

Idlefish or not? Online platform’s strategy of secondhand marketplace introduction in the presence of consumer’s uncertain preferences and strategic behavior

Multi-stage multi-criteria group decision making method based on hierarchical criteria interaction and trust rejection threshold under uncertain preference information

In the face of complex and changeable group decision-making problems, making satisfactory decisions is always difficult, which is deeply affected by information such as different stages, criteria, experts and alternatives. Thus, this study aims to develop an effective multi-stage multi-criteria group decision making (MSMCGDM) method to solve the multi-stage group decision making problems with various information. Firstly, through the introduction of trust rejection threshold, a Cross Calibration method is proposed to calculate experts' weights, considering the social influence of experts in the same stage as well as different stages. Then, based on the extend DEMATEL and Shapley approaches, the DE-Shapley method is constructed to obtain criteria weights considering the hierarchical criteria interaction according to the evaluation information on criteria. Furthermore, inspired by the adjacency matrix, the relationship matrix on alternatives and the concept of alternative sets are proposed to consider the acceptability of alternatives in different stages. Afterwards, elastic mechanism in proposed framework is put forward to deal with the unexpected situations when implementing the optimal alternative set. Finally, two scenarios on snowmelt flood are presented to demonstrate the application of the proposed method, sensitive analysis and comparative analyses are conducted to highlight the advantages of our proposed method.

RkHit: Representative Query with Uncertain Preference

A top-k query retrieves the k tuples with highest scores according to a user preference, defined as a scoring function. It is difficult for a user to precisely specify the scoring function. Instead, obtaining the distribution on scoring functions, i.e., the preference distribution, has been extensively explored in many fields. Motivated by this, we introduce the uniform (r,k)-hit (UrkHit) problem. Given a preference distribution, UrkHit aims to select a representative set of r tuples to maximize the probability of containing a tuple attractive to the user. We say a tuple attracts a user, if it is a top-k tuple for the scoring function adopted by the user. Further, we generalize UrkHit and propose the (r,k)-hit (rkHit) problem with an additional penalty function to model the user satisfaction with the tuple ranked i-th. rkHit aims to maximize the expected user satisfaction with the representative set. In 2D space, we design an exact algorithm 2DH for rkHit, indicating rkHit is in P for d=2. We show that rkHit is NP-hard when d\ge3. In 3D space, assuming a uniform preference distribution, we propose a (1-1/e)-approximation algorithm 3DH based on space partitioning. In addition, we propose an approximate algorithm MDH suitable for any dimension and distribution, which creatively combines the ideas of sampling and clustering. It relaxes the approximation guarantee slightly. Comprehensive experiments demonstrate the efficiency and effectiveness of our algorithms.

A Minimum-Cost Consensus Model in Social Networks Derived From Uncertain Preferences

The influence of mutual interaction behaviors on the opinions and consensus process has gradually emerged due to the information sharing in social networks. Currently, the cost of making individual decisions and the similarity between experts’ decision behaviors are relatively less addressed in the social network decision process. Therefore, in this study, a consensus approach with the trust relationships and adjustment cost is proposed to fill in such a gap. The method is divided into three stages: 1) trust propagation; 2) weight allocation; and 3) consensus reaching. In the trust propagation phase, uninorm is extended to the uncertain theory and employed in the transmission and integration problems of trust relationships. In the weight allocation stage, the comprehensive weight is assigned based on network structure and strength of relationship. In the consensus-reaching process, two levels of consensus are considered: 1) consensus among individuals and 2) consensus between individuals and the collective group, and chance-constrained programming models are constructed to obtain collective decision opinions. Moreover, a comparative analysis is performed to clarify the effectiveness and advancement of the proposed consensus method.

Probabilistic ordinal regression methods for multiple criteria sorting admitting certain and uncertain preferences

We propose a family of probabilistic ordinal regression methods for multiple criteria sorting. They employ an additive value function model to aggregate the performances on multiple criteria and the threshold-based procedure to derive the class assignments of alternatives. The Decision Makers (DMs) can provide certain and uncertain assignment examples concerning a subset of reference alternatives, expressing the confidence levels using linguistic descriptions. On the one hand, we introduce Bayesian Ordinal Regression to derive a posterior distribution over a set of all potential sorting models by defining a likelihood for the provided preference information and specifying a prior of the preference model. This distribution emphasizes the potential differences in the models’ abilities to reconstruct the DM’s classification examples and thus is robust to the DM’s potential cognitive biases in her judgments. We also develop a Markov Chain Monte Carlo algorithm to summarize the posterior distribution of the preference model. On the other hand, we adapt Subjective Stochastic Ordinal Regression to sorting problems. It builds a probability distribution over the space of all value functions and class thresholds compatible with the DM’s certain holistic judgments. The ambiguity in representing incomplete and potentially uncertain preference information by the assumed sorting model is quantified using class acceptability indices. We investigate the performance and robustness of the introduced approaches through an extensive experimental study involving real-world datasets. We also compare them against novel methods based on mathematical programming that handle potential inconsistencies in uncertain preferences in the traditional way by minimizing the misclassification error or the number of misclassified reference alternatives.

Consensus Reaching in Group Decision Making With Linear Uncertain Preferences and Asymmetric Costs

Consensus reaching process (CRP), as an essential part of group decision making (GDM), can facilitate more effective consensus by taking human behaviors into account. Extending the established research on uncertain minimum cost consensus models (MCCMs), this article continues to adopt linear uncertainty distributions (LUDs) to represent decision-maker’s (DM’s) preference, but considers asymmetric costs into a new framework of CRP, where DM’s preference and weight are both adjusted according to democratic consensus. Moreover, in light of the uncertain distance measure, two novel optimization-based consensus models are built in this article: one is to obtain a minimum cost consensus by simultaneously considering asymmetric costs, aggregation function, and consensus measure; while the other provides a more flexible way to address GDM problems without presetting a specific consensus level (CL) threshold. Some 0–1 binary variables are further introduced to reduce the calculation complexity resulted from piecewise functions in the new multicoefficient goal programming models. Finally, an illustrative example and further discussion reveal the feasibility and superiority of our new method.

A two-level groups consensus reaching process for selecting suppliers of complex equipment under uncertain environment

With the development of complexity in complex equipment, the selection of suppliers referred to several groups. How to select the suppliers for the complex equipment under several groups becomes an important topic. To solve the problem, a two-level consensus reaching process is designed to select the suppliers of the complex equipment in uncertain environments. First, considering the fuzzy environment of selection, the cloud model, which could reflect the fuzziness and randomness, is used to present the uncertain preferences of the decision-makers. Then, considering the negotiation and interaction of two groups, the bi-level consensus reaching process is established to present the master-slave features of complex equipment. Third, to solve the proposed bi-level model, the improved artificial bee colony is proposed, which adopts the gray wolf algorithm’ searching mechanism and levy flying method. The adopted strategies could enhance the searching power of artificial bee colony. Finally, a case study is used to verify the advantages of our study.

Three-way Preference Completion via Preference Graph

With the personal partial rankings from agents over a subset of alternatives, the goal of preference completion is to infer the agent’s personalized preference over all alternatives including those the agent has not yet handled from uncertain preference of third parties. By combining the partial rankings of the target agent and the partial rankings from third parties to settle some disagreement with three-way preference completion, which includes a general strategy, an optimal strategy, and a pessimistic strategy, it forms the weighted preference graph. Technically, to settle the disagreement and obtain the completed preference of the target agent in the weighted preference graph, maximum likelihood estimation (MLE) under Mallows is proposed and validated theoretically by removing edges with the minimum weight in the weighted preference graph. However, it is not easy to locate the edges with the minimum weight efficiently in a big graph. Hence, an optimal MLE algorithm and three greedy MLE algorithms are proposed to process the MLE. Furthermore, these proposed algorithms are experimentally validated and compared with each other by both the synthetic dataset and the Flixter dataset.

Water Eutrophication Evaluation Based on the Improved Projection Pursuit Regression Model Under the Hesitant Fuzzy Environment

The water eutrophication restricts the development of economy and society in China, which attracts increasing attention. It also affects the health and ecological environment. The evaluation of water eutrophication is very complicated due to the dynamic variability of the water quality data. This paper adopts the hesitant fuzzy set (HFS) to depict the massive data of samples and uncertain preference information of experts, which reduces the complexity of calculation and avoids the loss of information. After that, we construct the projection index function based on the main factors of water eutrophication. The particle swarm optimization (PSO) algorithm is applied to determine the global optimal projection direction by optimizing the projection index function. Therefore, we construct an improved projection pursuit regression (PPR) model. Finally, the water eutrophication evaluation of several lakes in China is used to demonstrate the improved PPR model. Also, the comparative analysis and contribution rate analysis are conducted to validate its rationality and advantages.