TODIM Method Research Articles

Web Application Development for TODIM Method Automation and Alternatives Evaluation

The TODIM method (Tomada de Decisao Interativa Multicriterio), which in Portuguese means “Interactive and Multicriteria Decision Making”, is a process of evaluation alternatives, with various academic and professional uses. The current project focuses on the first approach, considering students, professors and investigators as the main beneficiaries and target audience. There is a shortage of software that automate the TODIM method, therefore it is proposed to develop a web application mainly using Python, HTML and JavaScript programming languages that can satisfy this necessity. To guarantee a uniformity in the results obtained by this program, samples of results obtained by this method by other researchers are taken as a basis and guide. To develop the application, the complete functioning of TODIM as an alternative evaluation approach must be understood. In a general view, TODIM uses pairwise comparisons between decision criteria while eliminating the inconsistencies that arise from such comparisons. Thus, the main idea is to measure the degree of dominance in each alternative over the others using the prospective value function. As result, it calculates the overall and partial degrees of dominance of each alternative to finally lead to a classification or “ranking” of the best alternatives.

An FMEA decision support model for hotel risk assessment based on the risk tolerance of multi-type travelers and online reviews

As a reliability management tool, failure mode and effect analysis (FMEA) is widely used to solve the problem of risk assessment in all trades and professions. Considering the opinions interaction and the diversity of risk tolerance of experts, this paper constructs a decision-support model of FMEA based on dynamic interaction of opinions and risk tolerance. Firstly, word frequency statistics and Word2Vec analysis are applied on 14,194 online reviews collected from TripAdvisor.com to identify major risk factors. Secondly, the consensus opinion of risk is reached through the dynamic interaction of opinions. Furthermore, the weight problem of risk factors is solved by a linear programming model with the goal of minimum individual regret, and the priority of risk is determined by an improved TODIM method considering risk tolerance. Through simulation experiments, sensitivity analysis and comparative analysis, the effectiveness and superiority of the proposed method are verified, and the theoretical research of FMEA method is enriched. This study provides a direction for the future improvement of hotel services based on understanding the preferences and interactions of multi-type travelers.

A Group Intuitionistic Fuzzy Exponential TODIM Method Considering Attribute Interactions Applied to Green Building Material Supplier Selection

Green building, driven by the goal of sustainable development, has prompted extensive attention to be paid to the environmental impact of its materials. However, some of the traditional methods of evaluating building material suppliers and attribute systems are not able to adapt to the new issues arising from the green context. This paper aims to provide a new solution for selecting green building material suppliers to enhance the green efficiency of buildings. Specifically, this paper presents a framework for evaluating and selecting suppliers of green building materials that meet the criteria of environmental friendliness and sustainability. A comprehensive evaluation attribute system is established, encompassing cost, quality, service level, delivery capability, and green and sustainable ability. Additionally, a group decision-making method based on the exponential TODIM (an acronym in Portuguese for Interactive and Multi-attribute Decision Making) and intuitionistic fuzzy numbers is developed to integrate expert opinions from diverse domains. Intuitionistic fuzzy numbers represent an extension of traditional fuzzy sets, offering a means of more fully and accurately responding to the inherent vagueness and hesitancy of human thinking. They can often prove invaluable when faced with problems containing uncertainty. Moreover, to obtain more precise attribute weights, the λ-fuzzy measure, Choquet integral, and Shapley value are employed to consider attribute interactions. Subsequently, a selection case involving six timber suppliers was proposed. Subsystem analysis was employed to ascertain the relative strengths and weaknesses of the various suppliers, with a view to facilitating future improvements. The findings indicated that green and sustainability capability attributes exert a considerable influence on the selection of green building material suppliers. Consequently, suppliers distinguished under this standard may encounter challenges in attaining exemplary rankings. Comparative analysis and robustness analysis have demonstrated the efficacy, superiority, and stability of the proposed framework. The findings of this paper can provide a reference for companies engaged in or planning to develop green buildings and help them choose green building material suppliers, which can help them achieve the expected green building efficiency and promote the sustainable development of the industry.

Promoting the sustainable development of CCUS projects: A multi-source data-driven location decision optimization framework

Carbon Capture, Utilization, and Storage (CCUS) technology is vital for achieving global carbon reduction targets. However, the uncertainties in technology and economic viability are influenced by location. To promote the sustainable development of CCUS technology, the study proposes a data-driven framework for optimizing location decisions. Firstly, the framework considers multiple factors, including geospatial data on resources, risks, power production, transportation, and environment. It also evaluates qualitative and quantitative data across economic, social, environmental, and technological dimensions. Secondly, the two-stage model is conducted as follows: Using Geographic Information System (GIS) technology, the first stage identifies suitable regions for CCUS projects, while the second stage prioritizes these regions using the TODIM method. Further, validated in China, the Junggar Basin, Tarim Basin, Ordos Basin, Sichuan Basin, and Bohai Rim Basin are identified as suitable for CCUS deployment. The Huaneng Luohuang Power Plant is the most conducive location for CCUS projects as pilot demonstrations. Final sensitivity analysis, scenario analysis, and comparative analysis have respectively affirmed the stability, dynamism, and reliability of the model. These analyses have also been instrumental in elucidating the final preferred outcomes under various decision-making preferences and strategic orientations. The framework for decision-making and data-driven priority model for CCUS projects layout proposed in the study can provide technical support and practical evidence for decision-makers in planning CCUS projects and formulating supportive policies.

Optimization and ranking of the input parameter settings of sustainable grinding using cashew nut shell liquid as cutting fluid

The current work advocates the use of Cashew Nut Shell Liquid/Oil (CNSL), an oil extract of the leftover cashew nut shells, as a novel environment-friendly cutting fluid in sustainable machining operations. The tribological characteristics of CNSL obtained on a pin-on-disc tribometer are found to be better compared to the traditionally used cutting fluid. Experiments are conducted on the surface grinder with EN8 material, considering input parameters, such as cutting fluid type, grinder speed and grade, work speed, and depth of cut, with Surface Roughness (Ra) and Grinding Temperature (Temp) being the responses. Input parameter optimization is performed using Taguchi’s statistical models. A total of 36 investigative and six validation experiments are conducted, and a prediction model is proposed. When Ra and Temp are optimized simultaneously, the prediction value of Ra is 0.071 μm, and the corresponding value of Temp is 31.6 °C for which the experimental values are 0.072 μm and 32 °C respectively. This work also applies the TODIM (TOmada de Decisao Interativa Multicriterio, in the Portuguese language), a multi-attribute decision-making method for ranking the input parameter settings. The study reveals that the performance of CNSL is better than that of a traditional cutting fluid, and the TODIM method can be successfully applied to rank the input parameter settings.

A trust relationship network-based consensus model in large-scale TODIM group decision-making

PurposeIn large-scale group decision-making (LSGDM) situations, existing TODIM group decision-making methods often fail to account for the influence of social network relationships and the bounded rationality of decision-makers (DMs). To address this issue, a new TODIM-based group decision-making method is proposed that considers the current trust relationships among DMs in a large-scale trust relationship network.Design/methodology/approachThis method consists of two main stages. In the first stage, the large-scale group is partitioned into several sub-clusters based on trust relationships among DMs. The dominance degree matrix of each sub-cluster is then aggregated into the large-scale group dominance degree. In the second stage, after aggregating the large-scale group dominance degree, the consensus index is calculated to identify any inconsistent sub-clusters. Feedback adjustments are made based on trust relationships until a consensus is reached. The TODIM method is then applied to calculate the corresponding ranking results. Finally, an illustrative example is applied to show the feasibility of the proposed model.FindingsThe proposed method is practical and effective which is verified by the real case study. By taking into account the trust relationships among DMs in the core process of LSGDM, it indeed has an impact on the decision outcomes. We also specifically address this issue in Chapter Five. The proposed method fully incorporates the bounded rationality of DMs, namely their tendency to accept the opinions of trusted experts, which aligns more with their psychology. The two-stage consensus model proposed in this paper effectively addresses the limitations of traditional assessment-based methods.Originality/valueThis study establishes a two-stage consensus model based on trust relationships among DMs, which can assist DMs in better understanding trust issues in complex decision-making, enhancing the accuracy and efficiency of decisions, and providing more scientific decision support for organizations such as businesses and governments.

The selection of reform models for provincial rural credit cooperatives unions in China using an extended CPT-TODIM method based on novel type-2 fuzzy numbers

The selection of a suitable reform model for provincial rural credit cooperatives unions (PRCCUs) is a pivotal aspect of China’s ongoing financial reform endeavors. This involves optimizing internal processes, enhancing efficiency, minimizing operational costs, elevating service quality, strengthening financial innovation capabilities, and promoting the healthy growth of rural financial markets. However, current research on this matter primarily concentrates on qualitative analysis. As of yet, a scientifically grounded decision-making framework from a quantitative standpoint has not been developed. This absence of quantitative analysis results in inaccuracies in research findings, thereby hindering the practical applicability of outcomes. To tackle this formidable challenge, we propose an innovative quantitative analysis framework employing the multi-criteria group decision-making method. This framework, which builds upon the cumulative prospect theory (CPT), the TODIM method, and the most recent advances in type-2 fuzzy numbers (T2FNs), is referred to as the T2FNs-CPT-TODIM. Initially, we define a novel score function, followed by the introduction of a fresh method for computing the distance between the T2FNs. Subsequently, our model pioneers an exclusive weight allocation strategy for decision-makers, grounded in the principles of Dice Similarity. Furthermore, the objective weights of criteria can be computed utilizing the Distance Correlation-based CRITIC approach. We then optimize the rankings by applying the advantage of gains and losses preference in the CPT-TODIM. Ultimately, we apply our proposed model to the practical task of selecting the optimal reform model for a specific PRCCU. Thorough comprehensive sensitivity and comparative analyses, the results validate the theoretical robustness and practical efficacy of our proposed method.

Multi-attribute decision-making research on investment suitability assessment of hydropower-wind-photovoltaic-storage complementary system based on dynamic social network

The hydropower-wind-photovoltaic-storage (HWPS) complementary system is one of the essential ways for China to build a new type of power system and to realize the dual-carbon goal. However, China's HWPS complementary system is still in the exploratory stage, and it is important to propose a rational multi-attribute decision-making (MADM) framework for investment suitability assessment based on completed hydropower plants. Therefore, this study first established a limitation indicator system for preliminary screening hydropower plants and an HWPS investment suitability assessment indicator system containing six dimensions: nature, market, infrastructure, land, society, and environment. Second, the weights among experts were determined based on the dynamic social network, and a mechanism for updating expert weights was proposed. Again, triangular intuitionistic fuzzy number (TIFN) was used to quantify the qualitative indicators and combined the weights according to the best-worst method (BWM) and criteria importance through intercriteria correlation (CRITIC) methods. Finally, the TODIM (an acronym in Portuguese for interactive and MADM) method was used for scheme suitability assessment with sensitivity analysis and method comparison. The results show that 62 eligible hydropower plants were preliminarily screened out of 647 completed medium- and large-scale hydropower plants in China by combining GIS technology. Natural factors are the most important of the six dimensions, followed by social factors. According to the suitability assessment results of TODIM, #23 hydropower station has the highest suitability for HWPSCS investment, which provides a reference for the layout of China's HWPS complementary system. With different decision makers' risk preferences and different MADM methods, #23 hydropower plant is still the best investment option, which proves the effectiveness of the MADM framework proposed in this study.

LogTODIM framework for MAGDM with neutrosophic sets: Energy conservation and emission reduction case

The significant acceleration of China’s urbanization process has greatly promoted economic development. At the same time, the massive construction of urban buildings has also caused many problems such as environmental pollution and increased energy consumption. Therefore, in architectural design, it is particularly important to pay attention to the sustainable development of the environment, handle the relationship between good people and nature under the guidance of the concept of green development, and focus on the recycling of resources. Focusing on resource utilization in architectural design and based on certain planning can better control the construction process of urban buildings, save energy consumption, reduce construction costs, and contribute to the green development of cities. The comprehensive evaluation of energy conservation and emission reduction of construction projects is a classical MAGDM problems. Recently, the Logarithmic TODIM (LogTODIM) method has been employed to cope with MAGDM issues. The single-valued neutrosophic sets (SVNSs) are used as a tool for characterizing uncertain information during the comprehensive evaluation of energy conservation and emission reduction of construction projects. In this paper, the single-valued neutrosophic number Logarithmic TODIM (SVNN-LogTODIM) method is built to solve the MAGDM under SVNSs. In the end, a numerical case study for comprehensive evaluation of energy conservation and emission reduction of construction projects is given to validate the proposed method.

ExpTODIM-driven framework for 2-tuple linguistic neutrosophic MAGDM with applications to teaching quality evaluation in higher education

Since the new century, the main theme of my country’s higher education is to improve the quality of teaching. To this end, the education administrative department and the vast number of colleges and universities have done a lot of work. Looking back, this teaching quality construction involving thousands of colleges and universities across the country has attracted much attention from all walks of life. The government as the organizer promotes the active participation of colleges and universities in the form of teaching evaluation under the leadership of administrative authority and the “quality engineering” project with resources and reputation, which has played a huge role in improving the teaching quality of colleges and universities. The teaching quality evaluation in higher education is a classical multi-attribute group decision-making (MAGDM) issue. Recently, the Exponential TODIM (ExpTODIM) method has been used to cope with MAGDM issues. The 2-tuple linguistic neutrosophic sets (2TLNSs) are used as a tool for characterizing uncertain information during the teaching quality evaluation in higher education. In this paper, the 2-tuple linguistic neutrosophic number ExpTODIM (2TLNN-ExpTODIM) is built to solve the MAGDM under 2TLNSs. In the end, a numerical case study for teaching quality evaluation in higher education is given to validate the proposed method. The main contribution of this paper is constructed: (1) the Exponential TODIM (ExpTODIM) method is extended to the PLTSs; (2) the 2-tuple linguistic neutrosophic number ExpTODIM (2TLNN-ExpTODIM) is built to solve the MAGDM under 2TLNSs; (3) Finally, a numerical case study for teaching quality evaluation in higher education is given to validate the proposed method.

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.

TODIM-PROMETHEE method for tourism landscape planning design scheme evaluation based on the virtual reality technology under spherical fuzzy sets

How to explore the potential value of landscape, realize the organic combination of tourism landscape, enrich landscape elements and enhance tourism experience has become an important topic of tourism landscape planning and design, which is also a practical problem that needs to be solved urgently in the process of tourism landscape development and planning in different regions of China. The tourism landscape planning design scheme evaluation based on the virtual reality technology a typical multi-attribute group decision-making (MAGDM) problem. With the complexity of economic activities, uncertain information has an increasing impact on production activities. However, due to the ambiguity and uncertainty of human cognition, the factors affecting the risk of things cannot be accurately expressed. Therefore, selecting spherical fuzzy sets (SFSs) can make the expression of information more accurate and complete. On basis of the TODIM method and the PROMETHEE method, in this study, spherical fuzzy number TOMIM-PROMETHEE (SFN-TOMIM-PROMETHEE) method is implemented to solve the MAGDM problem under SFSs. Furthermore, CRITIC method under SFSs is implemented to determine relative weights. Then a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology is selected to illustrate the effectiveness and practicality of the method. Finally, the comparative analysis shows that the SFN-TOMIM-PROMETHEE method under SFSs is an effective method to deal with MAGDM problems. The main contribution of this paper is managed: (1) the TODIM and PROMETHEE technique was extended to SFSs; (2) CRITIC technique is employed to manage the weight values under SFSs. (3) the SFN-TOMIM-PROMETHEE technique is founded to manage the MAGDM under IVPFSs; (4) a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology and comparison analysis are constructed to verify the feasibility and effectiveness of the SFN-TOMIM-PROMETHEE technique.

Prospect Theory-Based q-Rung Orthopair Fuzzy TODIM Method for Risk Assessment of Renewable Energy Projects

Prospect Theory-Based q-Rung Orthopair Fuzzy TODIM Method for Risk Assessment of Renewable Energy Projects

Utilizing multicriteria decision‐making approach for material selection in hybrid polymer nanocomposites for energy‐harvesting applications

AbstractFlexible and cost‐effective poly(vinylidene fluoride) (PVDF)‐based composites having excellent piezo performance are quite interesting for developing actuators, sensors, and nanogenerators. In this work, a hybrid PVDF‐based nanocomposite consisting of a fixed quantity of titanium dioxide (TiO2) and varying quantities of reduced graphene oxide (rGO) for increased mechanical and piezoelectric performance is reported for the first time. Compared to pure PVDF, there is a significant enhancement in mechanical properties for hybrid nanocomposites. The highest piezoelectric voltage as well as current values of 10.2 V and 0.78 μA are recorded for a hybrid nanocomposite containing 1 wt% of rGO for continuous finger‐tapping operation. A multicriteria decision‐making (MCDM)‐based material selection and optimization technique called TODIM is applied, and a sensitivity study is carried out to select the best material for mechanical energy harvesting applications. A hybrid nanocomposite based on PVDF‐TiO2 with 1% rGO loading is the most suitable material according to the TODIM (an acronym in Portuguese for Interactive Multicriteria Decision Making) approach.Highlights PVDF‐TiO2‐rGO nanocomposites are fabricated by solvent casting. TODIM optimization technique is applied for the best material selection among samples. Material ranking consistency shows the reliability of the TODIM method. Conductive rGO increases interfacial polarization, resulting in enhanced ε values. An increment of 88% and 104% in tensile strength and elastic modulus, respectively.

A flexible group decision-making method for informationization teaching ability evaluation of university teachers integrating ExpTODIM and GRA under interval neutrosophic environment

Today, information technology has penetrated into various fields of universities, and the development of information technology in teaching, scientific research, management, and services has become a catalyst for promoting changes in universities. In terms of teaching informatization, the Internet provides a powerful tool for knowledge dissemination and a huge platform for learning and communication between university teachers and students. Knowledge sharing has become easier, and the era of mutual interaction between teachers and students has arrived. University teachers need to quickly face this challenge, adapt to the new teaching and learning environment, improve their own literacy, enhance their information-based teaching ability, change their teaching behavior, and thereby improve the quality of university education and meet the needs of society for talent cultivation. The informationization teaching ability evaluation of university teachers is a classical MAGDM problems. Recently, the Exponential TODIM(ExpTODIM) and (grey relational analysis) GRA method has been used to cope with MAGDM issues. The interval neutrosophic sets (INSs) are used as a tool for characterizing uncertain information during the informationization teaching ability evaluation of university teachers. In this manuscript, the interval neutrosophic number Exponential TODIM-GRA (INN-ExpTODIM-GRA) method is built to solve the MAGDM under INSs. In the end, a numerical case study for informationization teaching ability evaluation of university teachers is given to validate the proposed method.

A Decision‐Making Approach Incorporating TODIM Method and Sine Entropy in q‐Rung Picture Fuzzy Set Setting

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision‐making) for decision‐making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision‐making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision‐making processes, we introduce novel entropy and distance measures for q‐rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen‐Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real‐life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision‐makers facing complex and uncertain decision‐making problems.

Multi-Criteria Evaluation of the Effectiveness of Computer Crime Disclosure Under Ecuadorian Legal Regulations

Decision-making based on multiple criteria is common in various contexts, recognized for its high complexity in seeking viable solutions. Computer crimes encompass any act with criminal intent that seeks to cause harm or put at risk a legally protected interest using computer tools. This study aims to determine whether residents of Santo Domingo are aware of computer crimes established in Ecuadorian legislation, employing multicriteria evaluation techniques and the TODIM and PROMETHEE methods. These methodologies are complemented by neutrosophic single-value sets, based on neutrosophic logic, to effectively manage the indeterminate and inconsistent information typical in real-world scenarios. In this way, the utility of these techniques for addressing complex problems in daily life and in various social domains is demonstrated.

Simulation-Based Optimized Weighting TODIM Decision-Making Approach for National Oil Company Global Benchmarking

The oil and gas industry has played a dominant role in developed and developing economies. In particular, the rise of national oil companies (NOCs) in recent decades has led to significant changes in this industry. With the control of most of the world's oil reserves, NOCs sit at the epicenter of the country's economy and impact other political and social spheres. Moreover, the performance of NOCs affects the global oil and gas markets. To evaluate this performance, this study implements a global-scale multicriteria ranking process. The considered criteria include production, operational efficiency, financial performance, and home country attributes. To achieve this goal, a novel simulation-based integrated approach was presented in this study. This approach uses the best-worst method and its nonlinear model to determine the optimal weights of the criteria. In the next stage, a simulation-based TODIM method was applied to rank the NOCs. The simulation results found threshold values of the loss attenuation coefficient, where the rank of the alternatives is disturbed. This finding helped to group NOCs based on rank and response to the psychological behavior of decision makers.

A fuzzy Pythagorean TODIM method for sustainable ABC analysis in inventory management

This paper aims to improve the ABC analysis method used for inventory management by applying the Pythagorean Fuzzy TODIM approach. ABC analysis is one the well-known and widely used inventory classification techniques which divides inventory items into three categories according to their importance and value. However, the traditional ABC analysis does not consider the imprecision and vagueness of real-world inventory data, which can lead to inaccurate results and poor inventory management decisions. The proposed approach enhances the traditional ABC analysis by incorporating fuzzy numbers to be considered in real-world inventory data. The improved ABC analysis helps companies to optimize inventory levels, reduce costs, improve customer service, and increase overall operational efficiency. To check for the reliability and effectiveness of the developed model under different scenarios sensitivity analysis is conducted. Additionally, the comparative analysis among other existing models further demonstrates the model's accuracy. The model prepared shows that the Pythagorean Fuzzy TODIM approach is superior to the conventional ABC analysis in terms of reliability and dealing with the uncertain inventory data. Overall, this paper provides a novel and effective approach to inventory management and offers valuable insights for practitioners and researchers in the field.

Stochastic group preference acceptability analysis for interval-valued multiplicative preference relations based on TODIM method

Among many decision problems, interval-valued multiplicative preference relation (IMPR) is widely utilized due to its ability to express uncertain information. A new approach to solve group decision making (GDM) with IMPRs is proposed in this paper, named stochastic group preference acceptability analysis with TODIM (SGPAA-TODIM) method, by combining TODIM method (an acronym in Portuguese of Interactive and multi-criteria Decision Making) with stochastic multi-criteria acceptability analysis (SMAA-2). It effectively circumvents information loss and considers the weight and risk preferences of experts. Firstly, the stochastic multiplicative preference relation is defined through stochastic simulation employing a certain density function, and its priority weight vector is determined using the logarithmic least squares method (LLSM). Then, the priority preference comprehensive matrix is proposed by extracting information of priority vectors. Moreover, the novel SGPAA-TODIM method is developed to analyze the stochastic parameter spaces, with the optimal rank determined based on the analysis of acceptability degrees associated with dominance rank. Finally, to demonstrate the validity and applicability of the proposed method, numerical examples are given.