Multiple attribute two-sided matching decision-making model with uncertain preferences considering prospect value factors and its application

Determination of the optimal bridge scheme is crucial in the preliminary design stage of bridge construction, and the scientific decision results directly affect the construction and implementation of the whole project. At present, the determination of bridge schemes in mountainous areas is mainly based on empirical judgment, and few theoretical methods can be adopted. Therefore, a comprehensive evaluation model was built for mountainous bridge type scheme by the basic AHP theory, grey relational analysis, and TOPSIS. The model comprehensively considered the various factors affecting the selection of bridge type from the aspects of economy, technology, and society, and 12 evaluation indexes were selected to build a comprehensive evaluation system for the bridge type scheme in mountainous areas. Weight vector of valuation indexes of bridge type was calculated by AHP to reduce the influence of human subjective factors. Then, a weighted grey correlation coefficient decision matrix was constructed by fuzzy mathematics theory and grey correlation analysis, and the relative closeness coefficient between the alternative schemes and the Grey correlation ideal solution was calculated by TOPSIS. Finally, the optimal bridge type scheme was determined based on the relative closeness coefficient. The evaluation model was used to judge three alternative bridge type schemes (A1-A3) of a highway in the mountainous area of Pu'an County, Guizhou Province. The relative closeness coefficients of continuous PC T beam bridge (A1), PC continuous rigid frame bridge (A2), and PC dwarf-tower cable-stayed bridge (A3) were respectively 0.597 7, 0.315 6, and 0.400 3, indicating the first scheme is the best optimized bridge type. Thus, the first bridge scheme was applied to actual bridge construction and achieved good economic and social values. The results show that the evaluation model provides a feasible theoretical method for the decision-making of mountain bridge type.

Total knee arthroplasty (TKA) provides substantial pain relief and functional improvement in advanced knee osteoarthritis, yet up to 20% of patients remain dissatisfied despite technically successful procedures. Traditional preoperative assessments overlook psychological determinants influencing surgical decision-making and postoperative satisfaction. Prospect Theory—emphasizing loss aversion and perceived gains—offers a novel behavioral framework to explain these outcomes. A retrospective observational study included 500 patients with Kellgren–Lawrence grade III–IV osteoarthritis; 300 underwent TKA and 200 declined surgery. Preoperative and postoperative assessments included EQ-5D, Satisfaction With Life Scale (SWLS), and Global Perceived Effect (GPE). Psychological parameters were evaluated using a Prospect Theory–based model quantifying perceived gains, perceived risks, and loss aversion (α = 0.88, β = 0.88, λ = 2.25). Statistical analyses comprised t-tests, chi-square tests, correlations, and logistic regression to identify predictors of surgical decision and satisfaction. Patients who declined surgery demonstrated higher loss aversion (7.1 ± 1.9) compared to surgical patients (4.3 ± 2.1, p < 0.001). Perceived gain scores were greater in the TKA group (8.2 ± 1.4 vs. 5.9 ± 1.6, p < 0.001). Loss aversion correlated negatively with surgical acceptance (r = –0.655, p < 0.001), while perceived gain correlated positively (r = 0.746, p < 0.001). Among surgical patients, EQ-5D mobility improved from 0.41 ± 0.22 to 0.78 ± 0.19, pain decreased by –3.4 points, and anxiety/depression by –2.1 points (all p < 0.001). Logistic regression identified loss aversion (OR 0.62, 95% CI 0.51–0.74) and perceived gain (OR 1.48, 95% CI 1.28–1.71) as independent predictors of surgical acceptance. Overall satisfaction was 82% at 12 months. Psychological factors, particularly loss aversion and perceived gains, significantly influence both the decision to undergo TKA and postoperative satisfaction. The Prospect Theory–based model accurately predicted surgical acceptance and recovery trajectories, underscoring the potential of integrating behavioral economics into preoperative counseling and shared decision-making. • Up to 20% of TKA patients remain dissatisfied despite technical success. • Prospect Theory explains decision-making through loss aversion and perceived gains. • Higher loss aversion was strongly linked to declining surgery. • Perceived gains predicted surgical acceptance and postoperative satisfaction. • A Prospect Theory model accurately predicted decisions and recovery outcomes. • Integrating behavioral economics may improve counseling and reduce dissatisfaction.

Reasonable selection of black-start scheme is significant to fast restoration of power system after a large-scale blackout. Firstly, this paper introduces the prospect theory to solve the problem that the influence of decision-makers' experience and knowledge on the evaluation results is neglected in the traditional black-start scheme evaluation method. Secondly, in order to avoid the subjectivity of artificially determining the weight, this paper adopts the objective comprehensive weight determination method based on CRITIC method, and obtains the objective weights of indicators by calculating the Gini coefficient and Kendall coefficient. The comprehensive prospect theory and the CRITIC method combine subjectivity and objectiveness to obtain a more comprehensive and reasonable evaluation result. Thirdly, this paper improves the TOPSIS method. On the one hand, the relative entropy is introduced to solve the problem that the vertical line nodes in the positive and negative ideal solutions cannot effectively be distinguished in the traditional TOPSIS. On the other hand, the gray correlation is introduced to measure the curve edge coupling degree, so that the evaluation result is more precise. Finally, an evaluation examples is given to verify the rationality and effectiveness of the proposed method.

A three-way decision method based on prospect theory under probabilistic linguistic term sets

In their 1982 article, Kelso and Crawford proposed a gross substitutes condition for the existence of core (and equilibrium) in a two-sided matching model. Since then, this condition has often been used in the literature on matching models and equilibrium models in the presence of indivisibilities. In this paper we prove that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is an M♮-concave function defined on the unit-hypercube, which is a discrete concave function recently introduced by Murota and Shioura (1999).

As the need for environmental protection and resource sustainability has increased in recent times, wastewater treatment has become increasingly important. In this paper, a group decision-making model for plans selection in wastewater treatment is proposed. In order to deal with uncertainties and multiple attributes in wastewater treatment, an intuitionistic fuzzy set is employed to evaluate wastewater treatment plans effectively. A distance measure is defined to obtain an objective weight measuring the expert’s judgment. More specifically, experts first use group decision-making on the various plans with an intuitionistic fuzzy set. Meanwhile, Due to the decision-makers psychological behavior, the prospect theory is applied. Next, the various plans are ranked by The Order of Preference by Similarity to Ideal Solution (TOPSIS) method and prospect theory. Finally, an illustrative example of wastewater treatment plans selection is used to verify the proposed model.

The problem of bilateral matching of teams and scientific and technical talents is studied in new R&amp;D institutions with different forms of uncertain assessment information. A decision method is proposed based on a combination of grey correlation and cloud model. The method firstly applies interval grey numbers to characterize uncertain assessment score information and cloud models to characterize uncertain linguistic assessment information; secondly, the two different pieces of information are converted into grey correlation coefficients by applying grey correlation analysis methods to the assessment values, so as to solve indicator weights, and assemble assessment data based on indicator weights and cloud models; finally, the bilateral matching model is constructed and the matching results are solved based on the cloud model data features and the dual objectives of maximum satisfaction and minimum uncertainty. The case analysis and method comparison show that the method is feasible and effective.

PurposeOn the basis of the time series of the land area economy and marine economy data during 1996-2015, the authors study the relationship between land area economy and marine economy, and divides the relational schema of the land-sea economy by doing causality test of land-sea economy, grey correlation degree analysis and relational schema analysis of the land-sea economy in coastal provinces and cities. The paper aims to discuss these issues.Design/methodology/approachThe paper uses methods such as Granger causality test and grey correlation degree analysis to preliminarily demonstrate the relationship of land-sea economy.FindingsWith Granger causality test, we can draw that there is a causal relationship between the land area economy and marine economy. Further with the relational schema analysis, we can draw that the relationship between marine economy and land economy in 11 coastal provinces and cities can be summed up into four kinds of patterns such as land-sea weak type, land-sea strong type, sea strong land weak type and land strong sea weak type.Practical implicationsFor the government and related disaster management departments, when policies are made and relevant measures are taken in the process of planning economic layout of land-sea economy, similar policies or measures may be taken for the same type of provinces, in order to improve administrative efficiency.Originality/valueThe development and utilization between land economy and marine economy has a certain contradiction, which must be balanced to realize the balanced development of land economy and marine economy. Therefore, it is necessary to comprehensively assess the grey relational analysis of land-sea economy, in order to provide the basis for reasonable policies.

Purpose The selection of alliance partners occurs in a highly uncertain environment, characterized by the uncertainty related to the parties themselves and ambiguities in evaluation criteria and weights. Moreover, it is crucial to fully consider the psychological expectations of the parties involved in the partner selection process. The authors focus on the problem of partner selection, considering the psychological expectations of decision makers (DMs) under uncertain information. Design/methodology/approach Interval grey numbers (IGNs) provide an effective solution to this problem. Firstly, the authors incorporate the psychological expectations of parties into the decision-making framework and utilize IGNs to represent the evaluation and expectation information of universities and enterprises. Then, the authors employ cumulative prospect theory (CPT) to construct prospect value matrices for universities and enterprises and solve the partner selection two-sided matching (TSM) model with the objectives of minimizing losses and maximizing the number of matching pairs. Findings Through comparison, it is evident that the proposed method effectively incorporates the psychological expectations of DMs, addresses the challenges of cooperative matching under uncertain information and improves both the satisfaction and stability of the matching outcomes. By integrating the psychological expectations of the parties involved, the proposed matching scheme achieves a satisfaction level of 0.99, with comparatively high robustness. Originality/value In this paper, the authors propose a novel method for alliance partner selection under uncertainty, based on psychological expectations. IGNs are used to represent evaluation and expectation information of DMs, aligning with real-world ambiguity. CPT is then applied to calculate gains and losses based on loss aversion and to determine criteria weights for maximizing prospect values. Furthermore, a TSM method is proposed to enhance satisfaction and stability. Additionally, the proposed method is validated through a real-case scenario and compared with another method.

Using the daily temperature data of 95 meteorological stations from Sichuan-Chongqing Region and its surrounding areas, this paper adopted these methods (e.g., linear regression, trend coefficient, geographical statistics, gray relational analysis and spatial analysis functions of GIS) to analyze the relations of temperature variability with topography, latitude and longitude. Moreover, the rank of gray correlation between temperature variability and elevation, longitude, latitude, topographic position and surface roughness also was measured. These results indicated: (1) The elevation affected temperature variability most obviously, followed by latitude, and longitude. The slope of the linear regression between temperature change rate and elevation, latitude and longitude was 0.4142, 0.0293 and −0.3270, respectively. (2) The rank of gray correlation between temperature change rate and geographic factors was elevation > latitude > surface roughness > topographic position > longitude. The gray correlation degree between temperature change rate and elevation was 0.865, followed by latitude with 0.796, and longitude with 0.671. (3) The rate of temperature change enhanced with the increase of elevation. Especially, the warming trend was significant in the plateau and mountain areas of western Sichuan, and mountain and valley areas of southwestern Sichuan (with the warming rate of 0.74°C/10a during the 1990s). However, there was a weak warming trend in Sichuan Basin and its surrounding low mountain and hilly areas. (4) The effects of latitude on temperature change rate presented the specific regulation, which the warming rate of low-latitude areas was more significant than that of high-latitude areas. However, they were consistent with the regulation that the increasing of low temperature controlled most of the warming trend, due to the effects of terrain and elevation on annual mean temperature. (5) Basically, temperature variability along longitude direction resulted from the regular change of elevation along longitude. It was suggested that, in Sichuan-Chongqing Region, special features of temperature variability largely depended on the terrain complexity (e.g., undulations, mutations and roughness). The elevation level controlled only high or low annual mean temperature and the range of temperature change rate in the macro sense.

In order to analyse the influence of different performance indexes on the working reliability of a tractor multi‐way valve. The grey correlation theory is introduced into the reliability analysis of multi‐way valves. Combined with the multi‐way valve failure mode, the reliability index is proposed, and then a grey relational model and the reliability evaluation sequence of multi‐way valves are established. The reliability of multi‐way valve is analysed by traditional grey relational analysis and improved weighted grey correlation analysis, respectively. Although both methods produced the same optimal prototype, the dynamic identification coefficient introduced by the latter can effectively suppress the influence of singular values on the correlation sequence in the prototype sequence. The analysis process is simplified, and the accuracy of calculation is improved. Meanwhile, the identification degree of the sequence of the prototype is increased. In addition, the improved weighted grey relational analysis method uses the entropy weight method to assign weight coefficients. This method can reflect the influence degree of different sequence points on the overall correlation degree objectively and improve the reliability of the analysis results. Finally, the correctness of the optimal prototype is verified by comparing the experimental data. The reliability evaluation standard of the tractor multi‐way valve is obtained.

Purpose – The purpose of this paper is to deal with interval grey-stochastic multi-attribute decision-making problems. It proposes a VIKOR method based on prospect theory in which probabilities and the attribute value are both grey numbers. Design/methodology/approach – In the prospect theory the results values and probability weight are used while the utility and probability values in the expected utility theory, which the more realistically reflect and describe the decision makers on the optimal process. VIKOR method makes the decision acceptable superiority and decision process stability. At the same time, a new interval grey number entropy is put forward, which is used to calculate the index weight of unknown. Findings – The paper provides a VIKOR method based on prospect theory in which probabilities and the attribute value are both grey numbers. And the validity and feasibility of the method are illustrated by an example. Research limitations/implications – Although VIKOR is much closer to PIS than TOPSIS, at the same time VIKOR method can get the compromise solution with priority, researchers are encouraged to carry on comparative study further. Practical implications – The paper includes interval grey-stochastic multi-attribute decision-making method and implications. The validity and feasibility of the method are illustrated by a case. Originality/value – This paper proposes a VIKOR method based on prospect theory in which probabilities and the attribute value are both interval grey numbers. At the same time, a new interval grey number entropy is put forward, which is used to calculate the index weight of unknown.

In this study, financial performances of certain selected non-life insurance companies operating in Turkey between 2014-2018 are compared with two multi-criteria decision-making methods. The analytical hierarchy process is integrated into the grey relational analysis. First, the weights of the financial ratios are computed with the analytical hierarchy process, and then the companies are ranked by grey relational analysis using the weights found. The grey relational analysis results in which the financial ratios are taken as equally weighted are compared with the results in which the weights found with the help of the analytical hierarchy process. It is realized that the grey relational analysis results are affected by the weight of the financial ratios calculated with the analytical hierarchy process. In addition, it is observed that the ranking obtained by the combination of grey relational analysis and analytical hierarchy process is more compatible with the data in the financial reports.

In recent years, cultural and creative industry park is becoming a kind of hot industry to promote industrial restructuring and to improve the quality of urban space. For this reason, cultural and creative industrial parks are planning to build across the country. Currently, cultural and creative industrial parks that develop better than others thank to the government’s overall planning, construction, marketing, and management. At the same time, the new cultural and creative industry parks face enormous challenges, such as how to have together the cultural and creative industries and related groups or how to have area cultural creativity. And it is frequently regarded as a multiattribute group decision-making (MAGDM) process. Thus, a novel MAGDM process is needed to tackle it. Depending on the conventional grey relational analysis (GRA) method and intuitionistic fuzzy sets (IFSs), this paper designs a novel intuitive distance-based IF-GRA method for development potentiality evaluation of cultural and creative garden. First of all, some necessary theories related to IFSs are briefly reviewed. In addition, since subjective randomness frequently exists in determining criteria weights, the weights of criteria are decided objectively by utilizing the CRITIC method. Afterwards, relying on novel distance measures between IFSs, the GRA method is extended to the IFSs to calculate assessment score of each alternative. Eventually, an application about development potentiality evaluation of cultural and creative garden and some comparative analysis is given. The results think that the designed method is useful for development potentiality evaluation of cultural and creative garden.

Prospect theory based method for heterogeneous group decision making with hybrid truth degrees of alternative comparisons