Multi-attribute Decision Research Articles

χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}-linguistic sets and its application for the linguistic multi-attribute group decision making

The information in the real world often contains many properties such as fuzziness, randomness, and approximation. Although existing linguistic collections attempt to solve these problems, with the emergence of more and more constraints and challenges, this information cannot fully express the problem, leading to an increasing demand for methods that can contain multiple uncertain information. In this paper, we comprehensively consider the various characteristics of information including membership degree, credibility and approximation based on rough sets, and propose the concept of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}-linguistic sets (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LSs), which depend on original data rather than prior knowledge and effectively solve the problem of incomplete information representation. At the same time, the corresponding theories such as the comparison method and operational rules have also been proposed. Subsequently, we construct a new χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}-linguistic VIKOR (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LVIKOR) method for multi-attribute group decision making (MAGDM) problem with χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LSs, and apply it to the risk assessment of COVID-19. Through comparative analysis, we discuss the effectiveness and superiority of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LSs.

Research on Case Reasoning Multi-attribute Group Decision-making Method Based on Hesitant Fuzzy Set

In this study, a hesitant fuzzy set-based case-based reasoning integration method is proposed for the multi-attribute group decision-making problem with unknown attribute weights and mixed forms of attribute values. First, from two perspectives, traditional distance measure and information theory, a multi-objective optimization model is constructed using the distance similarity measure and information entropy of each type of attributes to determine the attribute weights. Secondly, considering the hybrid and nonlinear characteristics of case data, based on the principle of symmetric interaction entropy and TOPSIS method, a global similarity measure based on symmetric interaction entropy is proposed and a case inference algorithm suitable for hesitant fuzzy environment is designed. Finally, by analyzing the arithmetic cases of the target case in the case base, the most similar historical cases to the target case are retrieved to determine the decision-making scheme, and the practicality and feasibility of the decision-making method are verified. The results show that considering hesitant fuzzy theory for case-based reasoning research will help improve the accuracy and reliability of decision-making and provide more effective support for multi-attribute group decision management.

Entropy for q-rung linear diophantine fuzzy hypersoft set with its application in MADM

A notable advancement in fuzzy set theory is the q-rung linear diophantine fuzzy set. The soft set theory was expanded into the hypersoft set theory. By combining both the q-rung linear diophantine fuzzy set and hypersoft set, this study describes the notion of q-rung linear diophantine fuzzy hypersoft set that can handle multi sub-attributed q-rung linear diophantine fuzzy situations in the real world. Furthermore, some of its algebraic operations such as union, intersection and complement are described in this study. In addtion, the entropy measure of the q-rung linear diophantine fuzzy hypersoft set is established as it is helpful in determining the degree of fuzziness of q-rung linear diophantine fuzzy hypersoft sets. A multi-attribute decision making algorithm based on suggested entropy is presented in this study along with a numerical example of selecting a suitable wastewater treatment technology to demonstrate the effectiveness of the proposed algorithm in real-life situations. A comparative study was undertaken that describes the validity, robustness and superiority of the proposed algorithm and notions by discussing the advantages and drawbacks of existing theories and algorithms. Overall, this study describes a novel fuzzy extension that prevails over the existing ones and contributes to the real world with a valid real-life multi-attribute decision making algorithm that can cover many real-world problems that are unable to be addressed by the existing methodology.

A novel three-way classification and ranking approach based on regret theory and TOPSIS

In multi-attribute decision-making (MADM) problems, attribute types typically include benefit attributes and cost attributes. In most existing MADM studies, attribute types are converted to the same type to reduce the effect of diverse attribute types on decision results, inevitably leading to the loss of original information. In view of this, this paper presents a novel three-way decision (TWD) approach based on regret theory (RT) and TOPSIS to handle MADM problems in fuzzy environments without converting attribute types. Firstly, RT is employed to analyze the process of acquiring the relative revenue function for benefit attributes and the relative loss function for cost attributes. Then, we combine RT and TOPSIS method to estimate the conditional probability. Based on two attribute types, we develop the corresponding TWD models. One is to establish a TWD model that maximizes expected revenues based on benefit attributes, and the other is to establish a TWD model that minimizes expected losses based on cost attributes. Subsequently, we introduce the notion of integrated decision domains and investigate the ranking methods for alternatives that belong to the same (or different) integrated decision domains. Finally, we validate the effectiveness and performance of our method through case study and experimental analyses.

Project Investment Decision Under Uncertain Information

With the change of environment and market, the current investment project decision is facing a more complex environment, the competition of enterprises intensifies, the decision complexity increases, and the demand for scientific decision is increasing. The advantage of multi-attribute decision making in investment project decision is increasingly prominent. This paper studies the application of multi-attribute decision making under triangular fuzzy uncertainty information in investment decision making. Considering the decision makers' risk aversion and preference attitude in multi-stage decision making process, a dynamic reference point setting method based on stage development characteristics is proposed. Considering that the attribute value and attribute value will produce compensation in the decision-making process, the attribute value difference formula is constructed to reduce the decision-making bias, and on this basis, an improved TODIM method is proposed. The triangular fuzzy number uncertainty information is introduced to evaluate the attributes of each scheme in each decision stage, and the information is aggregated by the aggregation operator. Combining the dynamic multi-attribute decision model, the practical problem is solved. The practicability and feasibility of this method are demonstrated by the example analysis and method comparison.

A hybrid spherical fuzzy logarithmic decomposition of criteria importance and alternative ranking technique based on Adaptive Standardized Intervals model with application

This study presents a hybrid fuzzy Multi-Attribute Group Decision Making (MAGDM) model with application to commercial insurance selection. The proposed hybrid model uses Spherical Fuzzy (SF) sets using Yager t-norm and t-conorm operations. The Logarithmic Decomposition of Criteria Importance (LODECI) method is used for criterion weighting due to its efficacy in stabilizing scenarios that may challenge other weighting techniques. For alternative ranking, the study employs the Alternative Ranking Technique based on Adaptive Standardized Intervals (ARTASI), offering enhanced flexibility in handling uncertainties inherent in expert evaluations. The combination of these methods and the utilization of SF sets gives rise to the proposed SF-LODECI-ARTASI hybrid model. The paper systematically delineates the procedural steps involving SF sets, Yager t-norm and t-conorm operations, SF-LODECI, and SF-ARTASI methods. Subsequently, the developed hybrid model is applied to a case study of commercial insurance selection, supported by a numerical example. The research application results emphasize the consistency of these findings with other alternative methods. Additionally, sensitivity scenarios are constructed to scrutinize the robustness of the proposed hybrid model. The study concludes by elucidating implications and contributions to the existing literature.

Probability numbers for multi-attribute decision-making

In the face of increasingly complex data forms and decision-making problems, the uncertainty of information poses a major challenge to multi-attribute decision-making methods. How to effectively organize information and serve realistic decision-making problems has attracted extensive attention in the academic circles. In view of this, based on the distribution law of random variables, we put forward the basic concept of probability numbers and construct a general framework, including the concepts of type, order, item, isomorphism and isomerism, same domain and same distribution of probability numbers. On this basis, we further define the expectation and variance formula of probability numbers, and its operation rules are defined for the same type of probability numbers. To compare the dominance and inferiority of probability numbers further accurately, we put forward the concepts of dominance degree and comparability degree of probability numbers, so that decision makers can realize the ranking of probability numbers by calculating the comprehensive dominance degree. In view of the related concepts of probability numbers, we summarize the properties and theorems of probability numbers and prove them. In addition, a probability numbers-based multi-attribute decision-making framework model is proposed to solve the multi-attribute decision-making problem. Decision makers can select appropriate sub-models to construct personalized multi-attribute decision-making methods according to actual needs. At the end of the paper, we apply the method to the multi-attribute decision case of campus express stations evaluation and verify the scientificity and rationality of the evaluation method. The concept of probability numbers and its decision model proposed in this paper extend the concept category of numbers, enrich the multi-attribute decision-making method based on probability numbers, and have certain reference significance for further research of uncertain decision theory and method.

A probability-exponential method of converting Z-numbers and its systematic applications in multi-attribute decision making

Z-numbers contain fuzzy restrictions, credibility measures, and probability distributions to effectively represent uncertain information. Converting Z-numbers to fuzzy numbers facilitates extensive applications (such as multi-attribute decision-making (MADM)), thus becoming valuable for research purposes. Regarding Z-number conversions, the original method never considers the association probability, while probabilistic strategies offer better informatization. Recently, a probability-driven conversion starts with a linear transformation of the centroid difference between the fuzzy restriction and probabilistic distribution. However, it has the invalidation weakness of edge information due to underlying non-normalization. To improve this probability-linear conversion, a Z-number conversion is proposed by using underlying probability-exponential descriptions, and this new method is further applied to MADM. At first, the current probability-linear conversion is analyzed based on the initial non-probabilistic conversion, and its intrinsic weakness and correctional improvement are revealed. Then, the novel probability-exponential conversion resorts to an exponential characterization of centroid difference between the restriction and distribution, and it gains information enrichment due to underlying normalization. The refined method preserves the inherent characteristics of Z-numbers more effectively, facilitating their application in subsequent engineering practices. This is especially pertinent in decision-making systems based on expert input and initial value problems. The proposed method for converting Z-numbers aims to minimize information loss in transitions between Z-numbers and classical fuzzy numbers. This approach will be further explored in future research. Furthermore, the probability-exponential conversion induces an ExpTODIM algorithm for MADM, called PE-ExpTODIM. Three Z-number conversions (i.e., the non-probabilistic, probability-linear, and probability-exponential types) and three decision algorithms (i.e., ExpTODIM, EDAS, MOORA) are combined to establish a 3 × 3 framework of Z-number-driven MADM. Finally, the systematical 9 algorithms are applied to the problem of site selection of carbon storage. They are validated by criss-cross contrast analyses and statistical significance tests. Thus, PE-ExpTODIM exhibits the desired optimization. The last technology of statistical testing is original, ingenious, and valuable for MADM.

Enhanced MADM framework for fuzzy comprehensive evaluation of attack ability of basketball defenders with the triangular fuzzy neutrosophic numbers

With the continuous improvement of modern basketball technology, higher requirements have been put forward for the personal abilities of basketball players. As the core of an organization, the offensive ability of a defender largely determines the team’s performance. Therefore, it is necessary to objectively evaluate the attacking ability of defenders. Traditional techniques cannot objectively reflect the true level of players due to their strong subjectivity. Therefore, establishing a scientific evaluation technique is particularly important. The fuzzy comprehensive evaluation of attack ability of basketball defenders is viewed as the multi-attribute decision-making (MADM). In this paper, the triangular fuzzy neutrosophic number cross-entropy (TFNN-CE) technique is designed with help of cross-entropy and triangular fuzzy neutrosophic sets (TFNSs). Furthermore, Then, TFNN-CE technique is addressed to solve the MADM. Finally, a numerical example for fuzzy comprehensive evaluation of attack ability of basketball defenders is given and some comparisons are conducted to r illustrate advantages of the designed technique. The main contribution of this paper is addressed: (1) The TFNN-CE technique is addressed under TFNSs; (2) the TFNN-CE technique is addressed for MADM under TFNSs; (2) the TFNN-CE technique for fuzzy comprehensive evaluation of attack ability of basketball defenders is addressed; (3) Through the several efficient comparisons, it is addressed that TFNN-CE technique is effective for fuzzy comprehensive evaluation of attack ability of basketball defenders.

An intuitive fuzzy multi-attribute decision making method based on a herding psychology improved score function for trading decisions

The amount of used new energy vehicle transactions is increasing quickly as the social economy matures, yet prices are typically low, making it increasingly difficult to select a fair trading system. Enhancing the score function is crucial in order to account for how different people’s attitudes affect the outcome of decisions and to choose an acceptable trading strategy that is applicable to other scenarios and has a favorable impact on transaction flow. The choice of a trading scheme for new energy-using vehicles is usually regarded as a multi-attribute decision problem. In this paper, the Intuitionistic Fuzzy Hybrid Averaging (IFHA) operator integration operator with an improved score function is proposed based on the influence of herd mentality on decision-makers. In order to examine the correlation between the score function and the decision outcome using the Spearman rank correlation coefficient, an application to a real situation and some comparative analyses are provided. The outcomes demonstrate that the decision-making process for used car trading schemes can make use of the proposed improved score function.

Multi-attribute decision making for deep learning-based typhoon disaster assessment

Emergency rescue decisions in case of a typhoon disaster can be considered multi-attribute decision-making problems. Considering the need for the timeliness and authenticity of decision-making information sources after such a disaster, this study proposed using learning methods to process real-time online data and interval-valued neutrosophic numbers (NNs) to express the classification results. Using Typhoon Hagupit as an example, a trained text classification model was used to classify real-time data (online comments), following which the classification results were used as weights to convert these data into interval-valued NNs. Finally, the technique for order of preference by similarity to ideal solution (TOPSIS) method was adopted to rank the extent of damage caused by the typhoon in each region; the sorting results were consistent with the official statistical data, proving the effectiveness of the proposed method. A detailed sensitivity analysis was conducted to determine the optimal parameter settings of the classification model. Furthermore, the proposed method was compared with existing methods in terms of data conversion and deep learning efficiency; the results confirmed the superior capabilities of the proposed method. Notably, the proposed method can provide support to disaster management professionals in their post-disaster emergency relief work.

An enhanced decision making model for industrial robotic selection using three factors: Positive, abstained, and negative grades of membership

Traditional packaging industries that lack automation often grapple with a spectrum of challenges that impede operational efficiency, productivity and overall competitiveness. To maintain quality and safety, the food industry must transition from manual to robotic packaging processes. The most suitable robot for executing such task is identified via a new hybrid fuzzy Stratified Multi-Attribute Decision-Making (S-MADM). This model comprises Fuzzy-PIvot Pairwise RElative Criteria Importance Assessment (F-PIPRECIA) and Stratified Network Mapping (SNM). The Hesitant T-Spherical Fuzzy (HT-SF) set effectively tackles the uncertainty associated with the selection process by introducing three factors, namely, positive, abstained, and negative grades of membership. A case study is presented to demonstrate the novel fusion model and determine the optimal food packaging robot. A total of twelve criteria are selected from the literature based on the decision-maker’s judgment. Among the seven industrial robots, the ”Delta robot” gained the highest ranking (71%), followed by the ”Scara robot” (56%), and the ”Multi-Axis Gantry” (49%). Delta robots, with spider-like limbs, can move gently and accurately at fast speeds, with heavy motors fixed on the frame, allowing for lightweight moving parts. The proposed SNM technique helps to enhance the effectiveness of these alternatives by analyzing the possible, inefficient, and highly influential states of the system. The sensitivity study confirms this analysis and the system’s durability while the comparative study verifies the effectiveness and feasibility of the proposed technique than existing MADM models. This paradigm enables company stakeholders to invest in an industrial robot that not only delivers better results but also efficiently overcome barriers associated with manual packaging procedures.

Multiattribute Decision-Making in Wargames Leveraging the Entropy–Weight Method in Conjunction With Deep Reinforcement Learning

With the development of society, intelligent games have gradually become a hot research field. The paper proposes an algorithm that combines the multi-attribute decision-making and reinforcement learning methods to apply to multi-agents' decision-making for wargaming AI (artificial intelligence). This algorithm solves the problem of the agent's low rate of winning against specific rules and its inability to quickly converge during intelligent wargame training. At the same time, a multi-attribute decision-making method based on Entropy-Weight method was proposed to obtain the normalized weighting for each attribute that feeds into a deep reinforcement learning model. A simulation experiment confirms that the RNM-PPO (Real Number Multi-attribute decision-making-PPO) algorithm of multi-attribute decision-making combined with reinforcement learning presented in the paper is significantly more intelligent than the pure reinforcement learning algorithm.

A novel approach towards multiattribute decision making using q-rung orthopair fuzzy Dombi–Archimedean aggregation operators

When dealing with real-life problems, the q-rung orthopair fuzzy set is a core concept because the qth power of the membership and non-membership degrees is less than or equal to one. The process of selecting and evaluating alternatives based on several criteria or characteristics is known as multi-attribute decision-making (MADM) problems. The overview of the attribute values is a significant problem in MADM. It must be done in an accurate, consistent, and meaningful way. q-rung orthopair fuzzy numbers (q-ROFNs) are more flexible and powerful for representing uncertain or fuzzy information than other fuzzy number systems such as intuitionistic fuzzy numbers or Pythagorean fuzzy numbers. The paper introduces a new operator within the q-ROF framework or environment. This operator combines the characteristics of Dombi and Archimedean operations. These two operations likely have defined rules and properties within the q-ROF environment. The paper then proceeds to propose some weighted aggregation operators (AOs) based on the Dombi and Archimedean operations under q-ROF. These weighted AOs are likely used for combining or aggregating multiple attributes or criteria in decision-making processes. The paper explores the properties of these operators, which could include aspects like monotonicity, idempotence, or other desirable mathematical properties. Furthermore, the paper emphasizes applying the proposed operators within the q-ROF environment to MADM. This suggests that operators may be used in decision-making scenarios involving multiple attributes or criteria. The paper provides a procedure or methodology for applying the proposed operators in such decision-making processes. Lastly, the paper presents a practical example related to human resource selection. It demonstrates how the suggested strategy can be employed in real-world scenarios with its decision steps and the new operator. The example aims to demonstrate the viability and efficacy of the suggested strategy in solving decision-making problems related to human resource selection.

Evaluation of the Contaminated Area Using an Integrated Multi-Attribute Decision-Making Method

Air pollution affects public health and the environment, creating great concern in developed and developing countries. In India, there are numerous reasons for air pollution, and festivals like Diwali also contribute to air contamination. Determining the polluted region using several air contaminants is significant and should be analyzed carefully. This study aims to analyze the air quality in Tamil Nadu, India, during the Diwali festival from 2019 to 2021, based on multiple air pollutants. The study models the impact of air pollution as a Multi-Attribute Decision-Making (MADM) problem. It introduces a hybrid approach, namely the Analytical Hierarchy Process-Entropy-VlseKriterijumska Optimizacija I Kompromisno Resenje (AHP-Entropy-VIKOR) model, to analyze and rank the areas based on the quality of air. A combined approach of AHP and entropy is employed to determine the weights of multiple air pollutants. The VIKOR approach ranks the areas and identifies the areas with the worst air quality during the festival. The proposed model is validated by performing the Spearman’s rank correlation with two existing MADM methods: Combinative Distance Based Assessment (CODAS) and Weighted Aggregates Sum Product Assessment (WASPAS). Sensitivity analysis is carried out to assess the effects of the priority weights and the dependency of the pollutants in ranking the regions. The highest air pollution level during the festival was seen in Cellisini Colony (2019), Rayapuram (2020), T. Nagar and Triplicane (2021) in their respective year. The results demonstrate the consistency and efficiency of the proposed approach.

Multi-attribute group decision making method for sponge iron factory location selection problem using multi-polar fuzzy EDAS approach

This paper presents new averaging operators, such as mpF Einstein weighted averaging (mpFEWA), mpF Einstein ordered weighted averaging (mpFEOWA), mpF Einstein hybrid weighted averaging (mpFEHWA), mpF Einstein weighted geometric (mpFEWG), and mpF Einstein hybrid weighted geometric (mpFEHWG), as well as new Einstein operations (mpFNs) for handling multi-polar fuzzy numbers. We evaluate these operators for idempotency, boundedness, monotonicity, and commutativity, and we design them to deal with multi-polar fuzzy numbers (mpFNs). Furthermore, the study investigates the use of these operators in MAGDM settings, namely mpFEWA and mpFEWG operators, to expand on this. Additionally, it proposes a procedure for determining the best site for a sponge iron production plant by use of the created MAGDM method. The EDAS method, which stands for “Evaluation based on Distance from Average Solution,” verifies that the solutions are effective. Finally, the suggested model highlights the benefits and possible improvements provided by these creative strategies by comparing the new approach to conventional methods and evaluating its efficiency and practicality.

A novel routing method for dynamic control in distributed computing power networks

Driven by diverse intelligent applications, computing capability is moving from the central cloud to the edge of the network in the form of small cloud nodes, forming a distributed computing power network. Tasked with both packet transmission and data processing, it requires joint optimization of communications and computing. Considering the diverse requirements of applications, we develop a dynamic control policy of routing to determine both paths and computing nodes in a distributed computing power network. Different from traditional routing protocols, additional metrics related to computing are taken into consideration in the proposed policy. Based on the multi-attribute decision theory and the fuzzy logic theory, we propose two routing selection algorithms, the Fuzzy Logic-Based Routing (FLBR) algorithm and the low-complexity Pairwise Multi-Attribute Decision-Making (lPMADM) algorithm. Simulation results show that the proposed policy could achieve better performance in average processing delay, user satisfaction, and load balancing compared with existing works.

Research on Protective Reuse of Industrial Heritage Based on Multi-Attribute Decision Making Method: Taking Six Heritage Sites in Qingdao as an Example

Research on Protective Reuse of Industrial Heritage Based on Multi-Attribute Decision Making Method: Taking Six Heritage Sites in Qingdao as an Example

Multi-attribute decision making based on VIKOR with probabilistic linguistic term sets: An application to the risk evaluation of foreign direct investment.

The multiple global environments have triggered changes in the international environment, leading to a sharp decline of foreign direct investment (FDI) compared to pre-pandemic level. To evaluate the investment risk of FDI and make optimal investment decision becomes the most important issue for investors. This paper focuses on the evaluation of investment risk for FDI. First, an index system for risk evaluation of FDI is constructed. Then, we introduce the probabilistic linguistic entropy and cross entropy measures, based on which, a programming model is developed to identify the objective attribute weights. A composite weight derivation method, which takes both the objective attribute weights and the subjective attribute weights into account, is further introduced. In view of attributes' uncertainty and fuzziness and the conflicting characteristics of some attributes, the VIKOR (the Serbian name: VlseKriterijumska Optimizacija I Kompromisno Resenje, means multi-criteria optimization and compromise solution) method is used to evaluate the risk of FDI under the probabilistic linguistic environment. Furthermore, a case study is presented to illustrate the proposed method. The comparative analysis and some further discussions verify the validity of the proposed method for the FDI risk evaluation.

Ground collision avoidance system with multi-trajectory risk assessment and decision function

AbstractThe traditional ground collision avoidance system (GCAS) makes avoidance decisions based on predicted collision time, without considering the impact of terrain environment and dynamic changes in load factor on avoidance decisions. This increases the risk of ground collisions for the aircraft. To solve the problem, a GCAS with multi-trajectory risk assessment and decision function is proposed. Firstly, a variety of predicted flight avoidance trajectories are established within the final manoeuvering capability of the aircraft. Secondly, for each predicted trajectory, the uncertain length between adjacent prediction points is used to construct a rectangular distance bin, and the terrain data below the avoided trajectory is extracted. Finally, the regret theory is used to establish a multi-attribute avoidance decision model to evaluate and prioritise the risk of collision avoidance trajectories, to provide effective collision avoidance decision for pilots. The algorithm is tested and verified with real digital elevation model and simulated flight data, and compared with traditional GCAS. Simulation results show that the proposed algorithm can comprehensively consider manoeuvering performance and threatening terrain, and provide safe and effective avoidance decisions for pilots.