A Modified TOPSIS Method utilizing the Gray Correlation Analysis

BackgroundBy analyzing 23 evaluation indicators included in 14 national basic public health service programs in a region of Hohhot City, Inner Mongolia Autonomous Region, China, the performance of basic public health services in the region in 2021 were analyzed to clarify the implementation and conduct of relevant programs. We also use this study as a basis to radiate the work of municipal basic public health services centered on the region and the outstanding problems reflected and to provide theoretical contents and suggestions that can be referred to for the same regions in central and western China as well as worldwide.MethodsUsing the TOPSIS method as the basis for the data analysis method, the evaluation indexes are ranked in terms of their proximity to the idealized target, and combined with the entropy value method, Technique for order preference by similarity to an ideal solution (TOPSIS) and rank-sum ratio (RSR) were used to rank 14 basic health care providers by grade. A comprehensive evaluation of the performance of basic public health services in a region of Hohhot City, Inner Mongolia Autonomous Region in 2021 was conducted through a joint model of entropy -weighted TOPSIS and RSR, making full use of the characteristics and advantages of the fuzzy joint, and conducting a comprehensive analysis from the perspective of the ratio weight and the method of graded calculation, making the study more distinguishable and measureable.ResultsIn this study, for the regional basic public health services, a total of 23 evaluation indicators of basic public health service projects were included, among which the top three indicators with the weight of the entropy value method indicators were found to include the rate of Chinese medicine health management for the elderly, the rate of health management for the elderly, and the BCG vaccination rate after the analysis of the weight of the indicators; After the entropy-weighted TOPSIS evaluation showed that the Ci values of the regions were found to be between 0.378 and 0.715 through the calculation of the positive and negative ideal values of each indicator; RSR staging method evaluation showed that three community health centers (X2, X10, X12) had excellent evaluations of basic public health services; The number of evaluations as poor and moderate are 2 (X3, X9) and 9 (X1, X4, X5, X6, X7, X8, X11, X13, X14), respectively; Finally, the results of the entropy-weighted TOPSIS method and the fuzzy joint model of RSR staging method are basically consistent with the overall trend of the above two methods, and the reliability and credibility of the research results are high.ConclusionThe entropy-weighted TOPSIS and RSR joint model can evaluate the effectiveness of basic public health services in a more comprehensive and holistic way. The results of the RSR staging results and the related weight ratio analysis show that the basic public health service programs in Hohhot, Inner Mongolia Autonomous Region are relatively balanced, but there are some differences; The same genus of elderly Chinese medicine health management rate, health management rate of the elderly, BCG vaccination rate several indicators accounted for a higher weight, its correlation with the key population-related items is high, suggesting that the future key population health service items should be focused on, and future research should be suggested from two key research.

The safety issue during bridge construction and operation has become a major concern for the society. This research focuses on how to conduct integral health-status assessment for bridges in operation on the basis of test and monitoring data. The result of the assessment will be the foundation of bridge maintenance, damage repair and reinforcement decision-making. Bridge state assessment origins in America, where bridge management systems were developed to give comprehensive assessment and help make daily management and maintenance decision for medium and small bridges. Afterward, different bridge health-status evaluation methods have been developed. For small and medium bridges, bridge assessment is usually conducted by applying assessment code. For complicated bridge, such code could not reflect the complexity of the structure. Another assessment method is reliability method. Reliability method is based on theory of probability and fully considers the uncertainty of structures. Analytic Hierarchy Process (AHP) is proposed in the 1970s to conduct multi-criteria decision-making combining qualitative and quantitative factors. (Saaty 2008) Bridge state assessment is a typical multicriteria decision-making problem. In the assessment model, multiple assessment indexes should be taken into consideration, including quantitative indexes and qualitative indexes. When the AHP assessment model is built and the weight of each index is derived, the evaluation value of the base indexes of the model should be derived and then be integrated by a certain relationship to get an integrated evaluation value representing the general state of the bridge. This research focuses on the evaluation value of base level indexes and the integrated evaluation method. The base level indexes of the bridge health-status assessment model are all from field test and monitoring directly. They need to be transformed to unified non-dimensional evaluation value. Considering the fuzziness and uncertainty of the evaluation process and transformation process, fuzzy grading is used to give a quantitative description of the base index’s evaluation. Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is a multiple attribute decision making method, which was developed for ranking and evaluation of limited number of alternatives (Yoon & Hwang 1995). Under AHP assessment framework, an improved fuzzy TOPSIS method has been proposed to conduct overall assessment of bridges. An integrated evaluation method is proposed by improving TOPSIS method and adapting it to bridge health-status assessment. The improvements include: ① absolutization of positive and negative ideal solution value; ② establishment of the virtual ideal solutions; ③ calculation of variable weight of base-level indexes considering the impact of the variation of the base-level indexes ④ fuzzy assessment based on level sets; ⑤ defuzzificaiton and standardization treatment of the assessment result. A case study applying the proposed fuzzy TOPSIS methodis introduced. This implementation verifies the feasibility and utility of the proposed method.

Interval neutrosophic fuzzy decision making is an important part of decision making under uncertainty, which is based on preference order. In this study, a new multi-valued interval neutrosophic fuzzy multiple attribute decision making method has been developed by integrating the DEMATEL (decision making trial and evaluation laboratory) method and the TOPSIS (the technique for order preference by similarity to an ideal solution) method. Evaluation values are given in the form of multi-valued interval neutrosophic fuzzy values. By using DEMATEL, dependencies among attributes can be modeled, and attribute weights are determined. The normalized Euclidean distance and the normalized Hamming distance between multi-valued interval neutrosophic fuzzy values are defined. Alternatives are ranked by using the TOPSIS method based on the distance measures. The truck selection problem in the logistics industry is presented to illustrate the feasibility and practical advantages of the proposed method. Some comparisons of the new method with other methods are also made.

Ensuring safe and efficient evacuation in university dormitories is crucial for minimizing risks during emergencies. This study develops a comprehensive safety evacuation scheme evaluation model by integrating the entropy weight method (EMW) and the technique for order preference by similarity to an ideal solution (TOPSIS). The model aims to provide an objective and systematic approach to evaluate and rank evacuation schemes for university dormitories. A set of evaluation indicators, encompassing building scale, building design and layout, emergency equipment and facilities, personnel factors and emergency management, evacuation effectiveness and safety, management and support, is established. The EWM is employed to calculate the weight of each indicator, reflecting its relative importance. The TOPSIS method is then applied to measure the closeness of each evacuation scheme to the ideal solution, enabling comparative ranking. A case study conducted in 8 university dormitories validates the model’s practicality and effectiveness. The results demonstrate that the proposed model offers a robust decision-making tool for university administrators, aiding in optimizing evacuation plans and enhancing safety during emergencies.

Comparative studies on using RSM and TOPSIS methods to optimize residential air conditioning systems

Technique for order preference by similarity to an ideal solution (TOPSIS) is an effective technique to solve multi-criteria decision-making problem. It aims to select the alternative, which has the “shortest distance” from positive ideal solution (PIS) and the “farthest distance” from negative ideal solution (NIS). Nevertheless, much literature has demonstrated that the solution calculated by TOPSIS only is the compromise of PIS and NIS, and it is of great restriction in dealing with the practical problems which have diverse demands and properties. Therefore, in the presented model, an optimism coefficient is defined to expand the physical meaning of the standard TOPSIS. Decision-makers (DMs) can describe their attitudes toward risk and profit by changing the value of optimism coefficient. Furthermore, intuitionistic fuzzy number is introduced to measure the evaluations (linguistic values) of DMs to alternatives under diverse criteria. Intuitionistic fuzzy weighted averaging operator is used for fusing the judgments of all DMs. Finally, a conclusion can be safely obtained that the proposed model is stable and validity from the illustrative examples and sensitivity analysis.

A method for group decision-making based on determining weights of decision makers using TOPSIS

This study aims to improve the structural strength and reduce the weight of a full-suspension electric-assisted bike frame using a multi-objective optimization approach. A comprehensive and major design framework is implemented, integrating the uniform design of experiments, Kriging interpolation, entropy weight method, technique for order preference by similarity to an ideal solution (TOPSIS), and a genetic algorithm. Five geometric parameters of the bike frame are selected as control factors in the uniform design. Finite element analysis is conducted to simulate impact displacements under the EN 15194 standard test conditions. Each simulation evaluates frame performance across various parameter combinations. The proposed optimization strategy is validated through falling-mass and falling-frame impact simulations, achieving respective improvements of 4.53% and 5.29% over the original design. Furthermore, the optimized frame demonstrates a weight reduction of 52.51 g. A full factorial design and analysis of variance are employed to identify the most influential parameters, and a comprehensive sensitivity analysis evaluates the relative impact of each factor on the objective functions. These results confirm the effectiveness of the proposed optimization method in producing a stronger and lighter bike frame.

A multi-objective decision method is proposed based on the combining orthogonal test, entropy weight method (EWM) with TOPSIS (technique for order preference by similarity to an ideal solution) in this article. The method is more objective and efficient than traditional methods in the design of green residential buildings. A villa in Nanjing was taken as an example, and the cost, building energy consumption, and daylight factors were used as decision-making indexes. A total of six control factors were selected: terrain elevation, window area, building orientation, the opening ratio of exterior windows, roof structure, and window glass material. Each factor was designed with three levels. First, a design scheme index system was constructed, and the orthogonal experimental design was used to select representative design schemes. Then, the EWM and the TOPSIS method were used to determine the weight of each index, a comprehensive evaluation of the residential building design scheme was conducted, and, finally, the optimal scheme was confirmed via range analysis. The results show that the multi-objective decision-making model based on the orthogonal experiment EWM-TOPSIS is suitable for green residential building design and the optimal solution obtained is “15 m elevation, a 1200 × 1500 mm size vacuum glass, an orientation of 170° and an external window opening ratio 45% with a 40 mm thick expanded insulation board roof”.

Providing service continuity to the end users with best quality is a very important issue in the next generation wireless communications. With the evolution of the mobile devices towards a multimode architecture and the coexistence of multitude of radio access technologies (RAT's), the users are able to benefit simultaneously from these RAT's. However, the major issue in heterogeneous wireless communications is how to choose the most suitable access network for mobile's user which can be used as long as possible for communication. To achieve this issue, this paper proposes an intelligent network selection strategy which combines two multi attribute decision making (MADM) methods such as analytic network process (ANP) and the technique for order preference by similarity to an ideal solution (TOPSIS) method. The ANP method is used to find the differentiate weights of available networks by considering each criterion and the TOPSIS method is applied to rank the alternatives. Our new strategy for network selection can dealing with the limitations of MADM methods which are the ranking abnormality and the ping-ponf effect.

Conservation tillage is crucial for rehabilitating degraded cropland, securing crop production and lessening greenhouse gas (GHG) emissions. Yet, the optimal nitrogen (N) application level that balances crop productivity with environmental effects following long‐term conservation tillage remains unclear. Based on a 9‐year conservation tillage experiment of black soil in Northeast China, an in situ microplot experiment was conducted from 2021 to 2023, including six N fertilization levels: 240 (N240, conventional N fertilization level by local farmers), 210 (N210), 180 (N180), 150 (N150), 120 (N120) and 0 kg N ha −1 (N0, control). The systematic effects of N fertilization on crop production, N fertilizer agronomic efficiency (NAE), GHG emissions and N balance were evaluated by using TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). N fertilization significantly enhanced crop production ( p < 0.05), especially maize grain yield was increased by 27.7%–36.2% in high N fertilization treatments (N180, N210 and N240) over that for N0. The NAE increased with the increase of N fertilization and exhibited a positive nonlinear correlation with the N fertilization level elevating ( R 2 = 0.61), whereas no notable variation in NAE was found across high N fertilization treatments. Moreover, global warming potential (GWP) showed an upward trend with the increase of N fertilization, while greenhouse gas intensity (GHGI) did not show a consistent trend. Analysis of the annual N balance suggested that, except for the N deficit observed in N0. Based on the TOPSIS method, the integrated evaluation showed that N180 ranked first with the total score of 0.61. Overall, from the perspective of crop production, nutrient utilization and the environment, an N fertilization level of 180 kg N ha −1 after long‐term conservation tillage is beneficial for ensuring food security while mitigating global change. This study provided scientific data for optimizing N management and promoting sustainable development of the black soil granary in Northeast China.

The process of bridges seismic retrofitting in the highway network is extremely costly and time consuming. In addition, the constraint on resources prevents the retrofitting of all the bridges at the same time. Besides, the bridges must be prioritized with simultaneous consideration of multiple criteria, including technical and socioeconomic aspect. This study intends to identify the major criteria and consider them simultaneously for prioritization of highway bridges additionally provides an effective technique for weighing these criteria. In this research, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method as a Multi-Criteria Decision-Making (MCDM) model is applied. TOPSIS method enables decision makers to deal with problems involving a large number of alternatives (bridges) and criteria. This methodology reduces multiple alternative (bridge) performances into a single value (ranking score) to facilitate the decision-making process for determination of the most suitable bridges for retrofitting. Suggested criteria include structural vulnerability, seismic hazard, anticipated service life, average daily traffic, interface with other lifelines, alternative routes and bridge importance. Moreover, relative importance (weight) of the criteria is assigned using Analytic Hierarchy Process (AHP) technique. The proposed method is applied to a real case of the Isfahan highway network.

Application of TOPSIS method in evaluating the effects of supply vane angle of a task/ambient air conditioning system on energy utilization and thermal comfort

Knowledge always constitutes the primary productive force for the social and economic development of the country, and consequently innovation has become a new development theme in most countries worldwide.Characterized by high profitability and high growth, Chinese high-tech industries show a rapid growth trend in size and effectiveness, which have been the supporting force and cornerstone for the national economy to promote the upgrading of products and industrial structures.In this study, a combination of Criteria Importance through Intercriteria Correlation (CRITIC) and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method was proposed to evaluate the innovation capacity of high-tech industries.A total of 25 three-level evaluation indicators were established to construct a high-tech industry innovation capacity indication system.The CRITIC method was used to calculate the weight of each indicator, and the TOPSIS method was used to make comprehensive decisions on the high-tech industries of 31 provinces in China.Results show that the development trends of high-tech industries vary greatly in the 31 provinces of China.The top five indicators are the rate-of renovation and reformation projects completed and put into use; the amount of investment in renovation and reformation; the rate of projects completed and put into use; the gross value of production and operation output at current prices; and the expenditure of large and medium-sized high-tech enterprises on technology reformation.These indicators are the critical factors affecting the ranking of high-tech industries at the provincial level.Guangdong ranks first, followed by Jiangsu and Zhejiang, sequentially.The differences in economic and geographical factors initially result in the regional distribution imbalance of high-tech industries, typically "the eastern preceding over the middle, and the middle preceding over the western."Conclusions provide significantly valuable references in expanding the indication system for a comprehensive evaluation of the independent innovation capacity of high-tech enterprises, which also show valuable references in suggesting measures for the government and enterprises to improve the independent innovation capacity of high-tech enterprises.

Multi-criteria decision making with hesitant fuzzy information is a new research topic since the hesitant fuzzy set was firstly proposed. This paper investigates a multi-criteria decision making problem where the weight information is partially known. We firstly propose the hesitant fuzzy positive ideal solution and the hesitant fuzzy negative ideal solution. Motivated by the TOPSIS (Technique for Order Preference by Similarity to an ideal Solution) method, we definite the satisfaction degree of an alternative, based on which several optimization models are derived to determinate the weights. Subsequently, in order to make a more reasonable decision, we introduce an interactive method based on some optimization models for multi-criteria decision making problems with hesitant fuzzy information. Finally, a practical example on evaluating the service quality of airlines is provided to illustrate our models and method.