A min-max optimization approach for weight determination in analytic hierarchy process

A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absolute difference between the weight vector obtained from each column and the ideal weight vector. By transformation, the. constrained min- max optimization problem is converted to a linear programming problem, which can be solved using either the simplex method or the interior method. The Karush-Kuhn- Tucker condition is also analytically provided. These control thresholds provide a straightforward indication of inconsistency of the pairwise comparison matrix. Numerical computations for several case studies are conducted to compare the performance of the proposed method with three existing methods. This observation illustrates that the min-max method controls maximum deviation and gives more weight to non- dominate factors.

Analytic Hierarchy Process for Technological Risks in the Process of Innovative Drug Development in China

Objective To identify the critical risks in the process of innovative drug research and development,and to provide reference for improving the efficiency of innovative drug development and risk control in China.Methods Expert investigation and analytic hierarchy process were used to determine the weights of different risks.Results and Conclusion The research and analysis results showed that the risks at different stages of development had different effects on the success rate of drug development,among which the risk at the drug discovery stage influenced the most.In the drug discovery stage,inappropriate target selection had the greatest impact on the success rate of drug development.The lack of appropriate cell tissue or animal models had the greatest impact on the success rate of drug development from the discovery of a compound to the application for clinical trials.The difference in changes between nonclinical and clinical studies had the greatest impact on the success rate of drug development from early clinical studies to pivotal clinical studies.Incorrect dose selection had the greatest impact on the success rate of drug development from pivotal clinical studies to marketing authorization applications.The biggest impact from the marketing authorization application to the approval stage was inadequate communication with regulators.After investigating the weight of risk factors in the process of innovative drug development based on scientific methods,a new perspective for the risk control of new drug development and improving the research and development efficiency is provided.

Assessment and Application of Beach Quality Based on Analytic Hierarchy Process in Yangkou Beach, Qingdao

The whole-beach quality assessment is the basis of building and preserving beautiful beaches.The beach quality assessment index system and assessment standard have been established based on the attributes of beaches(including the width,slope,landform,and types),sorting coefficient,and softness degree of surface sediment.The assessment weight of each index for quality evaluation was analyzed using the analytic hierarchy process,and comprehensive scores of selected beach profiles were calculated in accordance with the light assessment standard.A beach quality evaluation model based on index weight and scores was established in this paper.The factors of 12 profiles of Yangkou Beach in Qingdao City were surveyed to carry out a quality assessment,and the comprehensive scores of each profile were calculated in accordance with the evaluation model.The results showed that the quality of Yangkou Beach can be divided into four ratings:excellent,good,medium,and poor.The excellent-quality area includes a wide and flat dry beach zone and soft,flat,and clean intertidal and subtidal zones covered with well-sorted fine sand,and leisure sports,such as volleyball,running,and swimming,are suitable for tourists.The good-quality area features a slightly narrow and dry beach zone,moderately soft and uneven intertidal and subtidal zones covered with fine sand and a small tidal gully,and a small amount of foreign matter;leisure sports,such as walking and running,are suitable for tourists.This study recommends the building of fixed drainage ditches or underground culverts to reduce the tidal gully.The medium-quality area consisted of a narrow and dry beach zone,moderately soft and uneven intertidal and subtidal zones covered by poorly sorted medium sand,a tide ditch,and a small amount of foreign matter.In this area,walking is suitable for tourists.Sand should be supplemented in the intertidal zone.The poor-quality area contained a very narrow and dry beach zone covered with poor-sorted gravel,a very chaotic intertidal zone with a considerable amount of foreign matters,such as bricks and rocks,wide tidal ditches,and an uneven subtidal zone with some reefs;leisure sports are unsuitable here.Thus,foreign matter and reefs should be removed,and the dry beach zone should be supplemented with sand.Therefore,the beach quality assessment is a very useful tool for building beautiful beaches.

Quality Evaluation of Threshing and Redrying Process Based on Analytic Hierarchy Process

Improving the stability of the homogenization process to achieve the homogeneity of tobacco products is one of important targets for the redrying industry.According to the specification for threshing and redrying process,a total of 14 indicators in three categories that affect the quality of the threshing and redrying process were selected.Using analytic hierarchy process,combined with expert experiences,a judgment matrix was constructed to conduct consistency test.The weights of indices in production were obtained.This will help in evaluating the actual production quality,finding the weak links of process and adjusting the parameters of the corresponding links in a targeted manner,thereby improving the quality of production process.

METHOD FOR BRIDGE BEARING CAPACITY ASSESSMENT BASED ON ANALYTIC HIERARCHY PROCESS

By analyzing the existing methods for the bridge bearing capacity assessment, an analytic hierarchy pro cess estimation model with a variable weight and fuzzy description is proposed based on the nondestructive infor mation. Considering the actual strength, the bearing capacity is first calculated from its design state, and then modified based on the detection information. The modification includes the section reduction and the structure deterioration. The section reduction involves the concrete section and the steel cross-section reduction. The structure deterioration is decided by six factors, i.e. , the concrete surface damage, the actual concrete strength, the steel corrosion electric potential, the chloride ion content, the carbonization depth, and the protective layer depth. The initial weight of each factor is calculated by the expert judgment matrix using an analytic hierarchy process. The consistency approximation and the error transfer theory are used. Then, the variable weight is in- troduced to expand the influences of factors in the worse state. Finally, an actual bridge is taken as an example to verify the proposed method. Results show that the estimated capacity agrees well with that of the load test, thus the method is objective and credible

Mathematical Model of Weight in Evaluation System

Having studied the property of compare matrix, this paper establishes a mathematical model of minimizing the sum of Euclidean norm (SEN) by means of the least square method. It is proved that the non linear program model can be transformed into linear a

Application of combination weighting method in contract risk's evaluation of third party logistics

First,the analytical hierarchy process(AHP),which stands for the subjective weighting method,and the entropy method,which stands for the objective weighting method,are chosen to calculate the index weights of the contract risks of third party logistics(TPL),respectively.Then,they can determine the combination weights using the combination weighting method.Second,using the combination weights,the contract risks of TPL are evaluated through the fuzzy comprehensive evaluation method.According to the combination weights,the most important risk factor of the contract risks of TPL is choosing sub-contractors.The results are basically consistent with the facts and show that the weights determined by the combination weighting method can avoid the man-made deviations of the subjective weighting method on the one hand,and prevent results opposite to the reality brought about by the objective weighting method on the other hand.Meanwhile,the results of the fuzzy comprehensive evaluation are that the contract risks of TPL are at a high risk level.Roughly this matches real situations,and it indicates that the combination weighting method can generate the comprehensive assessment more scientifically and more reasonably as well.

Analytic Hierarchy Process for Evaluating Flipped Classroom Learning

In reality,the flipped classroom has gained popularity as a modern way of structuring teaching,where lectures move from in-class procedures to digitally-based assignments,freeing up the debate,and practice exercises class time.Therefore,it is essential to implement and analyze a way of teaching that will improve student performance.The paper aims to develop a model of the method of teaching science in Iraqi schools,and to assess whether teaching flipped classroom affects the achievement,motivation,and creative thinking of students by using the methodology of Multi-Criteria Decision Making(MCDM)in the Analytic Hierarchy Process(AHP).The AHP approach includes several steps,including setting assessment criteria and their weights,and by assessing the methodology of the flipped classroom as compared to the conventional cognitive learning process.An experiment was carried out in Iraqi secondary schools to examine the attitude of the students towards the subject of Chemistry.The findings have indicated that the students and teachers favored flipped classroom learning more than conventional cognitive learning.The study took the following parameters compared to the traditional approach:teaching techniques,learning flexibility,teaching aids effectiveness,student participation and working environment.This paper indicates that the teachers in Iraqi schools will be able to improve and do more preparation to shift towards flipped learning in the classroom.

Information Security Testing Model Based on Variable Weights Fuzzy Comprehensive Evaluation

Nowadays,clear evaluation models and methods are lacking in classified protection of information system,which our country is making efforts to promote.The quantitative evaluation of classified protection of information system security is studied.An indicators system of testing and evaluation is established.Furthermore,a model of unit testing and evaluation and a model of entirety testing and evaluation are presented respectively.With analytic hierarchy process and two-grade fuzzy comprehensive evaluation,the subjective and uncertain data of evaluation will be quantitatively analyzed by comprehensive evaluation.Particularly,the variable weight method is used to model entirety testing and evaluation.It can solve the problem that the weights need to be adjusted because of the relationship role which enhances or reduces security of information system.Finally,the paper demonstrates that the model testing and evaluation can be validly used to evaluate the information system by an example.The model proposed in this paper provides a new valuable way for classified protection of information system security.

Weighting indicators of building energy efficiency assessment taking account of experts' priority

Analytic hierarchy process(Group AHP) is combined with two different methods of assigning experts' priority to weight indicators in building energy efficiency assessment.One is to assign the experts' priority averagely,and the other is to use cluster analysis to assign experts' priority.The results show that,1) Different expert's priority assigns result in great different weights of indicators in building energy efficiency assessment,therefore,the method of assigning experts' priority should be taken into account carefully while weighting indicators of building energy efficiency assessment using Group AHP;2) Three indicators are found to be overwhelmingly important in residential building energy efficiency assessment in the hot summer and cold winter zone in China.They are 'Outdoor & indoor shadow','Heating & air-conditioning facilities' and 'Insulation of envelope';3) The method combining cluster analysis with Group AHP to weight indicator of building energy efficiency assessment has the advantage of finding overwhelming important indicator,whereas,some less important indicators have a tendency to be ignored.A useful reference is provided for building energy conservation including policy revision and energy efficient residential building design.

Research on the Weight of Index for the Assessment Standard for Green Store Building

Assessment standard for green store building of national standard has been compiled. The index has been given by experts' subjective assignment based on experience. Analytic hierarchy process has been used,making questionnaires of experts,using pairwise comparison and calculating the weight of each index. The weight of index in assessment would not only make quantitative evaluation on the whole situation of green store buildings,but also provide the foundation for compilation and revision.

Innovative Product Design Based on Customer Requirement Weight Calculation Model

In the processes of product innovation and design, it is important for the designers to find and capture customer＇s focus through customer requirement weight calculation and ranking. Based on the fuzzy set theory and Euclidean space distance, this paper puts forward a method for customer requirement weight calculation called Euclidean space distances weighting ranking method. This method is used in the fuzzy analytic hierarchy process that satisfies the additive consistent fuzzy matrix. A model for the weight calculation steps is constructed; meanwhile, a product innovation design module on the basis of the customer requirement weight calculation model is developed. Finally, combined with the instance of titanium sponge production, the customer requirement weight calculation model is validated. By the innovation design module, the structure of the titanium sponge reactor has been improved and made innovative.

Research on consistency measurement and weight estimation approach of hybrid uncertain comparison matrix

The consistency measurement and weight estimation approach of the hybrid uncertain comparison matrix in the analytic hierarchy process （AHP） are studied. First, the decision-making satisfaction membership function is defined based on the decision making＇s allowable error. Then, the weight model based on the maximal satisfactory consistency idea is suggested, and the consistency index is put forward. Moreover, the weight distributing value model is developed to solve the decision making misleading problem since the multioptimization solutions in the former model. Finally, the weights are ranked based on the possibility degree approach to obtain the ultimate order.

A preliminary study on criteria weights for a library's digital resource selection:From the viewpoints of both users and librarians

Through investigating both users' and librarians' perceptions of the relative importance of the major criteria governing the selection of digital resources, we attempted to develop a criterion weight framework for a library's selection of digital resources, which can meet both the users' requirements and the library's goal of developing digital collections. The respective weight of each specific criterion is decided through the Analytic Hierarchy Process(AHP) Method. The findings of this study indicate that, when assigning weights to the selection criteria, it is important to consult the opinions of a wide crosssection of people, especially the views of different users. As a result, the digital resource selection system characterized by the criteria weights can reflect more comprehensively the users' requirements, and meanwhile it enables librarians' more rational selection of digital resources.

Water-conserving mining influencing factors identification and weight determination in northwest China

Water-conserving mining is an effective way to alleviate the contradiction between fragile ecological environment and high-intensity coal mining in the arid and semi-arid region of northwest China. It needs to consider the engineering and geological conditions, hydrogeological conditions and mining methods of coal seams. From the three aspects, this paper systematically analyzes the influencing factors and establishes an identification model with multi-level structures. The model includes three primary factors (including the engineering and geological conditions, hydrogeological conditions and mining methods), nine secondary factors (including overlying strata thickness, aquiclude, mining parameters and etc.), sixteen third-tier factors (including the faults, aquiclude thickness and effective mining height and etc.) and twelve fourth-tier factors (including the fault throw exp on ent, aquiclude permeability and coal pillar sizes and etc.). On the basis, the analytic hierarchy process is used to build the judgment matrix and obtain the weight of each influencing factor. The results indicate that the overlying strata thickness, aquiclude and effective mining height are the most import a nt factors among the primary factors of engineering and geological conditions, hydrogeological conditions and mining methods, respectively. The research results could provide theoretical references for the water-conserving mining of coal resources in northwest China.

A methodological approach for weighting factors in land suitability assessment: a tool for facilitating spatial planning

The increasing demand for infrastructural facilities in hill areas needs efficient spatial planning at the local level through land suitability assessment,which is influenced by a number of factors. There has been little systematic empirical work for identification and evaluation of the factors affecting spatial planning decisions in hill areas. The present study focuses on identifying the critical factors for land suitability assessment at the local level in hill areas and determining their percentage influence, which has been done in two stages. In the first stage, the comprehensive list of 21 factors from the reported literature was prepared which was further condensed to the critical factors. In the second stage, the percentage influence of the critical factors was calculated by analyzing the experts’ opinions collected through a questionnaire survey. Analytic Hierarchy Process(AHP) was used for the analysis of the questionnaire for weighting the critical factors. The slope was identified with the highest weight followed by aspect, surface runoff, elevation, and vegetation,whereas groundwater table, existing utilities,accessibility, soil type, and land use have comparatively less weights. The results of the study were used for the identification of locations for builtup facilities of an educational campus located in hill areas of Himachal Pradesh, India.

Comprehensive Evaluation of Flower Border Application Value of New and Superior Plants in Hefei Area

An analytic hierarchy process(AHP)was employed to assess the applicability of 18 new and superior varieties of flowers in Hefei City flower border applications.A total of 12 indicators were selected from three distinct aspects of adaptability,ornamental characteristics and use traits,in order to establish a comprehensive evaluation model.The results demonstrate that grade I(J≥2.685)exhibits excellent application value,encompassing six species of plants,such asHydrangeamacrophylla‘Endless Summer’;grade II(2.684≤J≤2.420)is also of notable application value,encompassing five species of plants,such asCallistemonrigidus;grade III(2.419≤J≤2.615)is of average application value,including five species of plants,such asCrocosmiacrocosmiflora;grade IV(J≤2.16)is of relatively poor application value.The evaluation results may be utilized as a theoretical reference for the promotion of new and superior varieties in the flower border of Hefei.

Comprehensive Evaluation of Application Value of Wild Flower Resources in Flower Border in Hefei City

In order to further understand and better develop and utilize wild flower resources in Hefei City,a comprehensive evaluation model of landscape value of wild flowers in the application of flower border was constructed by field investigation and analytic hierarchy process(AHP).The application value of wild flowers in Hefei was evaluated by selecting evaluation indicators from three aspects of ornamental value,adaptability and resource potential.

Establishment of an indicator framework for global One Health Intrinsic Drivers index based on the grounded theory and fuzzy analytical hierarchy-entropy weight method

Background:One Health has become a global consensus to deal with complex health problems.However,the pro‑gress of One Health implementation in many countries is still relatively slow,and there is a lack of systematic evalua‑tion index.The purpose of this study was to establish an indicator framework for global One Health Intrinsic Drivers index(GOH-IDI)to evaluate human,animal and environmental health development process globally.Method:First,82 studies were deeply analyzed by a grounded theory(GT)method,including open coding,axial coding,and selective coding,to establish a three-level indicator framework,which was composed of three selective codes,19 axial codes,and 79 open codes.Then,through semi-structured interviews with 28 health-related experts,the indicators were further integrated and simplifed according to the inclusion criteria of the indicators.Finally,the fuzzy analytical hierarchy process combined with the entropy weight method was used to assign weights to the indi‑cators,thus,forming the evaluation indicator framework of human,animal and environmental health development process.Results:An indicator framework for GOH-IDI was formed consisting of three selective codes,15 axial codes and 61 open codes.There were six axial codes for“Human Health”,of which“Infectious Diseases”had the highest weight(19.76%)and“Injuries and Violence”had the lowest weight(11.72%).There were four axial codes for“Animal Health”,of which“Animal Epidemic Disease”had the highest weight(39.28%)and“Animal Nutritional Status”had the low‑est weight(11.59%).Five axial codes were set under“Environmental Health”,among which,“Air Quality and Climate Change”had the highest weight(22.63%)and“Hazardous Chemicals”had the lowest weight(17.82%).Conclusions:An indicator framework for GOH-IDI was established in this study.The framework were universal,balanced,and scientifc,which hopefully to be a tool for evaluation of the joint development of human,animal and environmental health in diferent regions globally.

GIS Based Landslide Susceptibility Mapping with Application of Analytical Hierarchy Process in District Ghizer, Gilgit Baltistan Pakistan

District Ghizer is a rugged mountainous territory which experiences several landslides each year. There are 16 major landslide areas and 53 villages that are at high risk to hazards. Keeping in view the severity of natural hazards, the present study was designed to generate landslide susceptibility map based on twelve causative factors viz., slope, aspect, elevation, drainage network, Stream Power Index (SPI), Topographic Wetness Index (TWI), lithological units, fault lines, rainfall, road network, land cover and soil texture. Soil texture was determined by particle size analysis and data for other factors were acquired from freely available sources. Analytical Hierarchy Process (AHP) was employed to identify major landslide causative factors in the district Ghizer. Further, a temporal assessment from 1999 till 2015 was generated to assess the impact of land cover change on landslides. It indicated that the barren soil/ exposed rocks and glaciers have reduced while the vegetation and water classes have shown increment. The total area that lies in moderate to very high landslide susceptible zones was 74.38%, while slope is the main landslide causative factor in the district Ghizer. Validation of the susceptibility map showed 88.1% of the landslides in the study area had occurred in the moderate to very high susceptible zones.