A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming

This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.

Multi-Criteria Wildfire Risk Hazard Assessment in GIS Environment: Projection for the Future and Impact on RES Projects Installation Planning

It is alarming for the fact that Wildfires number, severity and consequently impact have significantly increased during the last years, an aftermath of the Climate Change. One of the most affected areas worldwide is Mediterranean, due to the unique combination of its type of vegetation and demanding climatic conditions. This research is focused on the Region of Epirus in Greece, an area with significant natural vegetation and a range of geomorphological aspects. In order to estimate the Wildfire Risk Hazard, several factors have been used: geomorphological (slope, aspect, elevation, TWI, Hydrographic network), social (Settlements and landfils, roads, overhead lines and substations), environmental (land cover) and climatic (Fire Weather Index). Through a multi-criteria decision analysis (MCDA) and an analytic hierarchy process (AHP) in a GIS environment, the Wildfire Risk Hazard has been estimated not only for current conditions but also for future projections for the near future (2031-2060) and the far future (2071-2100). The selected case study includes the potential impact of the Wildfires to the installed (or targeted to be installed) RES projects in the studied region.

GIS-Based Multi-Criteria Decision Analysis (MCDA) and Analytical Hierarchy Process (AHP) Techniques to Derive Flood Risks Management on Rice Productivity in Gishari Marshland

Floods are phenomenon with significant socio-economic implications mainly for human loss, agriculture, livestock, soil loss and land degradation, for which many researchers try to identify the most appropriate methodologies by analyzing their temporal and spatial development. This study therefore attempts to employ the GIS-based multi-criteria decision analysis and analytical hierarchy process techniques to derive the flood risks management on rice productivity in the Gishari Agricultural Marshland in Rwamagana district, Rwanda. Here, six influencing potential factors to flooding, including river slope, soil texture, Land Use Land Cover through Land Sat 8, rainfall, river distance and Digital Elevation Model are considered for the delineation of flood risk zones. Data acquisition like Landsat 8 images, DEM, land use land cover, slope, and soil class in the study area were considered. Results showed that if the DEM is outdated or inaccurate due to changes in the terrain, such as construction, excavation, or erosion, the predicted flood patterns might not reflect the actual water flow. This could result unexpected flood extents and depths, potentially inundating rice fields that were not previously at risk and this, expectedly explained that the increase 1 m in elevation would reduce the rice productivity by 0.17% due to unplanned flood risks in marshland. It was found that the change in rainfall distribution in Gishari agricultural marshland would also decrease the rice productivity by 0.0018%, which is a sign that rainfall is a major factor of flooding in rice scheme. Rainfall distribution plays a crucial role in flooding analysis and can directly impact rice productivity. Oppositely, another causal factor was Land Use Land Cover (LULC), where the Multivariate Logistic Regression Model Analysis findings showed that the increase of one unit in Land Use Land Cover would increase rice productivity by 0.17% of the total rice productivity from the Gishari Agricultural Marshland. Based on findings from these techniques, the Gishari Agricultural Marshlands having steeped land with grassland is classified into five classes of flooding namely very low, low, moderate, high, and very high which include 430%, 361%, 292%, 223%, and 154%. Government of Rwanda and other implementing agencies and major key actors have to contribute on soil and water conservation strategies to reduce the runoff and soil erosion as major contributors of flooding.

Diagnostic and economic value of carcinoembryonic antigen,carbohydrate antigen 19-9,and carbohydrate antigen 72-4 in gastrointestinal cancers

BACKGROUND The diagnostic and economic value of carcinoembryonic antigen(CEA),carbohydrate antigen 19-9(CA19-9)and CA72-4 for gastrointestinal malignant tumors lacked evaluation in a larger scale.AIM To reassess the diagnostic and economic value of the three tumor biomarkers.METHODS A retrospective analysis of all 32857 subjects who underwent CEA,CA19-9,CA72-4,gastroscopy and colonoscopy from October 2006 to May 2018 was conducted.Then,we assessed the discrimination and clinical usefulness.Total cost,cost per capita and cost-effectiveness ratios were used to evaluate the economic value of two schemes(gastrointestinal endoscopy for all people without blood tests vs both gastroscopy and colonoscopy when blood tests were positive).RESULTS The analysis of 32857 subjects showed that CEA was a qualified biomarker for colorectal cancer(CRC),while the diagnostic efficiencies of CA72-4 were catastrophic for all gastrointestinal cancers(GICs).Regarding early diagnosis,only CEA could be used for early CRC.The combination of biomarkers didn’t greatly increase the area under the curve.The economic indicators of CEA were superior to those of CA19-9,CA72-4 and any combination.At the threshold of 1.8μg/L to 10.4μg/L,all four indicators of CEA were lower than those in the scheme that conducted gastrointestinal endoscopy only.Subgroup analysis implied that the health checkup of CEA for people above 65 years old was economically valuable.CONCLUSION CEA had qualified diagnostic value for CRC and superior economic value for GICs,especially for elderly health checkup subjects.CA72-4 was not suitable as a diagnostic biomarker.

Indexing habitat suitability and human-elephant conflicts using GIS-MCDA in a human-dominated landscape

Concerns for biodiversity loss, wildlife conservation, and habitat destruction have dominated the policy agenda worldwide for decades. Unsustainable human-induced development and negative interaction between humans and wildlife have emerged as predominant issues globally. The present study deals with human and elephant conflicts (HEC) in the Polpitigama Divisional Secretariat, Sri Lanka, which is located in the Kahalla-Pallekele elephant corridor and connects Wilpattu and Kaudulla wildlife sanctuaries. The research objectives are identifying spatial patterns of elephant habitat suitability and probable risk zones for HEC. The elephant habitat suitability and HEC risk zones were identified on spatial and temporal scales using Geographic Information System integrating Multi-Criteria Decision Analysis. Different factors, including habitat suitability, distance to roads, distance to croplands, distance to forests and protected areas, settlements, and population density, were considered to determine HEC risk zones in the area. Topography, water, and vegetation criteria are considered when determining elephant habitat suitability. The results of the Analytic Hierarchy Process run the spatially explicit model. The results revealed that of the total area, 15.3% is very highly suitable for elephant habitats, while the least suitable areas contribute only 4%. About 33.8% of the area is moderately suitable for elephants. The risk map indicates that 23.7% of the total area is under very high risk for HEC, and the least risk areas only account for 5.4%. About 26.2% of the area falls under the moderate risk zone for HEC. Since the model considered three aspects of HEC, it will help policymakers in wildlife conservation to avoid and minimize the HEC.

Liver fibrosis index-based nomograms for identifying esophageal varices in patients with chronic hepatitis B related cirrhosis

BACKGROUND Esophageal varices(EV)are the most fatal complication of chronic hepatitis B(CHB)related cirrhosis.The prognosis is poor,especially after the first upper gastrointestinal hemorrhage.AIM To construct nomograms to predict the risk and severity of EV in patients with CHB related cirrhosis.METHODS Between 2016 and 2018,the patients with CHB related cirrhosis were recruited and divided into a training or validation cohort at The First Affiliated Hospital of Wenzhou Medical University.Clinical and ultrasonic parameters that were closely related to EV risk and severity were screened out by univariate and multivariate logistic regression analyses,and integrated into two nomograms,respectively.Both nomograms were internally and externally validated by calibration,concordance index(C-index),receiver operating characteristic curve,and decision curve analyses(DCA).RESULTS A total of 307 patients with CHB related cirrhosis were recruited.The independent risk factors for EV included Child-Pugh class[odds ratio(OR)=7.705,95%confidence interval(CI)=2.169-27.370,P=0.002],platelet count(OR=0.992,95%CI=0.984-1.000,P=0.044),splenic portal index(SPI)(OR=3.895,95%CI=1.630-9.308,P=0.002),and liver fibrosis index(LFI)(OR=3.603,95%CI=1.336-9.719,P=0.011);those of EV severity included Child-Pugh class(OR=5.436,95%CI=2.112-13.990,P<0.001),mean portal vein velocity(OR=1.479,95%CI=1.043-2.098,P=0.028),portal vein diameter(OR=1.397,95%CI=1.021-1.912,P=0.037),SPI(OR=1.463,95%CI=1.030-2.079,P=0.034),and LFI(OR=3.089,95%CI=1.442-6.617,P=0.004).Two nomograms(predicting EV risk and severity,respectively)were well-calibrated and had a favorable discriminative ability,with C-indexes of 0.916 and 0.846 in the training cohort,respectively,higher than those of other predictive indexes,like LFI(C-indexes=0.781 and 0.738),SPI(C-indexes=0.805 and 0.714),ratio of platelet count to spleen diameter(PSR)(C-indexes=0.822 and 0.726),King’s score(C-indexes=0.694 and 0.609),and Lok index(C-indexes=0.788 and 0.700).The areas under the curves(AUCs)of the two nomograms were 0.916 and 0.846 in the training cohort,respectively,higher than those of LFI(AUCs=0.781 and 0.738),SPI(AUCs=0.805 and 0.714),PSR(AUCs=0.822 and 0.726),King’s score(AUCs=0.694 and 0.609),and Lok index(AUCs=0.788 and 0.700).Better net benefits were shown in the DCA.The results were validated in the validation cohort.CONCLUSION Nomograms incorporating clinical and ultrasonic variables are efficient in noninvasively predicting the risk and severity of EV.

Eigenvector Method for Ranking Alternatives with Vague Value Measurements

An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.

Canadian children’s and youth’s adherence to the 24-h movement guidelines during the COVID-19 pandemic: A decision tree analysis

Purpose:The purpose of this study was to use decision tree modeling to generate profiles of children and youth who were more and less likely to meet the Canadian 24-h movement guidelines during the coronavirus disease-2019(COVID-19)outbreak.Methods:Data for this study were from a nationally representative sample of 1472 Canadian parents(Meanage=45.12,SD=7.55)of children(511 years old)or youth(1217 years old).Data were collected in April 2020 via an online survey.Survey items assessed demographic,behavioral,social,micro-environmental,and macro-environmental characteristics.Four decision trees of adherence and non-adherence to all movement recommendations combined and each individual movement recommendation(physical activity(PA),screen time,and sleep)were generated.Results:Results revealed specific combinations of adherence and non-adherence characteristics.Characteristics associated with adherence to the recommendation(s)included high parental perceived capability to restrict screen time,annual household income ofCAD 100,000,increases in children’s and youth’s outdoor PA/sport since the COVID-19 outbreak began,being a boy,having parents younger than 43 years old,and small increases in children’s and youth’s sleep duration since the COVID-19 outbreak began.Characteristics associated with non-adherence to the recommendation(s)included low parental perceived capability to restrict screen time,youth aged 1217 years,decreases in children’s and youth’s outdoor PA/sport since the COVID-19 outbreak began,primary residences located in all provinces except Quebec,low parental perceived capability to support children’s and youth’s sleep and PA,and annual household income ofCAD 99,999.Conclusion:Our results show that specific characteristics interact to contribute to(non)adherence to the movement behavior recommendations.Results highlight the importance of targeting parents’perceived capability for the promotion of children’s and youth’s movement behaviors during challenging times of the COVID-19 pandemic,paying particular attention to enhancing parental perceived capability to restrict screen time.

Utilizing comprehensive decision analysis methods to determine an optimal planting pattern and nitrogen application for winter oilseed rape

Oilseed rape is one of the most important oil crops globally.Attaining the appropriate cultivation method(planting pattern and nitrogen level)is necessary to achieve high yield,quality and resource utilization efficiency.However,the optimal method for oilseed rape varies across countries and regions.The objective of the present study was to determine an appropriate cultivation method,including planting pattern and nitrogen application,for winter oilseed rape in northwestern China.Two planting patterns:ridge film mulching and furrow planting(RFMF)and flat planting(FP),and six nitrogen(N)amounts:0(N0),60(N60),120(N120),180(N180),240(N240),and 300(N300)kg N ha–1 were applied across three growing seasons(2014–2017).Three comprehensive decision analysis methods:principal component analysis,grey correlation degree analysis and the combined entropy weight and dynamic technique for order preference by similarity to ideal solution method were used to evaluate the growth and physiological indicators,nutrient uptake,yield,quality,evapotranspiration,and water use efficiency of winter oilseed rape.Planting pattern,nitrogen amount and their interaction significantly affected the indicators aforementioned.The RFMF pattern significantly increased all indicators over the FP pattern.Application of N also markedly increased all the indicators except for seed oil content,but the yield,oil production and water use efficiency were decreased when N fertilizer exceeded 180 kg N ha–1 under FP and 240 kg N ha–1 under RFFM.The evaluation results of the three comprehensive decision analysis methods indicated that RFMF planting pattern with 240 kg N ha–1 is an appropriate cultivation method for winter oilseed rape in northwestern China.These findings are of vital significance to maximize yield,optimize quality and improve resource use efficiencies of winter oilseed rape.

Development and validation of a prognostic nomogram model for Chinese patients with primary small cell carcinoma of the esophagus

BACKGROUND Primary small cell carcinoma of the esophagus(PSCE)is a highly invasive malignant tumor with a poor prognosis compared with esophageal squamous cell carcinoma.Due to the limited samples size and the short follow-up time,there are few reports on elucidating the prognosis of PSCE,especially on the establishment and validation of a survival prediction nomogram model covering general information,pathological factors and specific biological proteins of PSCE patients.AIM To establish an effective nomogram to predict the overall survival(OS)probability for PSCE patients in China.METHODS The nomogram was based on a retrospective study of 256 PSCE patients.Univariate analysis and multivariate Cox proportional hazards regression analysis were used to examine the prognostic factors associated with PSCE,and establish the model for predicting 1-,3-,and 5-year OS based on the Akaike information criterion.Discrimination and validation were assessed by the concordance index(C-index)and calibration curve and decision curve analysis(DCA).Histology type,age,tumor invasion depth,lymph node invasion,detectable metastasis,chromogranin A,and neuronal cell adhesion molecule 56 were integrated into the model.RESULTS The C-index was prognostically superior to the 7th tumor node metastasis(TNM)staging in the primary cohort[0.659(95%CI:0.607-0.712)vs 0.591(95%CI:0.517-0.666),P=0.033]and in the validation cohort[0.700(95%CI:0.622-0.778)vs 0.605(95%CI:0.490-0.721),P=0.041].Good calibration curves were observed for the prediction probabilities of 1-,3-,and 5-year OS in both cohorts.DCA analysis showed that our nomogram model had a higher overall net benefit compared to the 7th TNM staging.CONCLUSION Our nomogram can be used to predict the survival probability of PSCE patients,which can help clinicians to make individualized survival predictions.

The Application of Optimum Decision in Oilfield Development

The major steps of oilfield development are given in this paper. The optimal model of oilfield development is built and the methods of optimum decision analysis are studied. The solution and analysis of the optimal tactics have been set up according to the data collected in the oilfield.

Scenario-based approach for project portfolio selection in army engineering and manufacturing development

The decisions concerning portfolio selection for army engineering and manufacturing development projects determine the benefit of those projects to the country concerned.Projects are typically selected based on ex ante estimates of future return values,which are usually difficult to specify or only generated after project launch.A scenario-based approach is presented here to address the problem of selecting a project portfolio under incomplete scenario information and interdependency constraints.In the first stage,the relevant dominance concepts of scenario analysis are studied to handle the incomplete information.Then,a scenario-based programming approach is proposed to handle the interdependencies to obtain the projects,whose return values are multi-criteria with interval data.Finally,an illustrative example of army engineering and manufacturing development shows the feasibility and advantages of the scenario-based multi-objective programming approach.

A group consensus model for evaluating real estate investment alternatives

Background:Individual decision-making largely influences the effectiveness of decisions and benefits of investments.Methods:In this article,a consensus model for group decision-making(GDM),based on the analytic hierarchy process(AHP),is developed to gather group ideas and analyze the real estate investment environment under multi-criteria problems.Twelve evaluation procedures of the developed model,which increase the convergence of the opinions of multiple experts,are proposed.Results:An empirical case about the real estate investment environment is applied to certify the feasibility of this developed model.Conclusions:the evaluation procedures have been fully observed with several rounds of discussions,and have manifested the experiences of experts.Besides,the evaluation results are in accordance with real-world situations,which demonstrates that our developed model is a feasible analysis tool for real estate investors to obtain better profits and lower risk.

Multiobjective Decision Making: the Combined Approach

In this paper, a new approach for generating all or partly efficient solutions called the Combined Approach is developed. The property of efficient solutions generated by the combined approach and its relationships with other four approaches: weighting approach, sequential approach, ε-constraint approach and hybrid approach, are discussed. Based on this combined approach, a decision-making support method called the Combined Decision-Making Method (CDMM) for multiobjective problems is developed, which is an interactive process with the decision maker. Only the aspiration levels, which reflect the decision maker's satisfying degrees for corresponding objectives, are needed to be supplied by the decision maker step by step as he will. This interactive way for objectives can easily be accepted. Finally, the application of the proposed decision making method in the resource allocation problem is discussed, and an example for the production decision analysis of the solar energy cells given.

Game Analysis for the Pricing Strategy in Manufacturer-Retailer Supply Chains

Supply Chain Management(SCM) is the term used to de sc ribe the management of the flow of materials, information and funds across the e ntire supply chain, from suppliers to component producers to final assemblers to distribution(warehouses and retailers) and ultimately to the consumers.This pap er studies the coordinated problem for a manufacturing and retailing supply chai n. Differentiating from traditional joint optimization in the literature, the ap proach applies game theory structure as the researching framework to address the problem of coordinating the pricing decisions of the manufacturer and retailer. Three co-op pricing models are developed and discussed which are based on two noncooperative games and one cooperative game. They are a Stakelberg’s two-sta ge game model, a simultaneously move game model and an cooperative game model, r espectively. The results obtained by the sufficient comparisons and discusses te ll us that the noncooperative equilibriums are lower efficiently than joint coop erative equilibrium. In order to get the efficient cooperative mechanism, we int roduce the Pareto efficiency concept and obtain so-called feasible Pareto effic ient set of pricing schemes (contract curve). The cooperative mechanism based on the curve would be solid and stable. These and orther related managerial issues are explored in this paper.

Genecological zones and selection criteria for natural forest populations for conservation:the case of Boswellia papyrifera in Ethiopia

Rapid changes in land-use in the Combretum–Terminalia woodlands of northwestern Ethiopia are mainly due to the increases in commercial farming and immigration.We used integrated ecological and social data collection techniques,including subdivision of the vegetation zone,vegetation survey,focus group discussions and key informant interviews,to identify genecological zones and set criteria for selection of viable populations of Boswellia papyrifera(Del.)Hochst in Ethiopia for conservation.Interviews of senior experts were supported with a rating method and involved 43 respondents and focused on identifying and weighting criteria and indicators of selection in a participatory way to prioritize populations for conservation.Using mean annual rainfall data,we reclassified the Combretum–Terminalia woodland vegetation region into three moisture zones(wet,moist and dry),and designated them as genecological zones for B.papyrifera conservation.A total of 35 woody species were identified at Lemlem Terara site in Metema district,and the Shannon diversity index and evenness were 2.01 and of 0.62,respectively.There were 405 adult trees,and 10 saplings and3314 seedlings per ha.The trees were medium-sized with overall mean diameter at breast height(dbh) of 16.9(±9.5)cm.Seedling recruitment was poor due to grazing,crop production and fire incidences.Through a multi-criteria decision analysis,five criteria and 20 quantitative indicators were identified and weighted to prioritize populations for conservation.These criteria in their descending order of importance are(1) forest ecosystem health and vitality,(2)forest cover and population structure of B.papyrifera,(3)productive function of the forest,(4) biological diversity in the forest,and(5) socioeconomic benefits of the forest to communities.Multivariate tests in the general linear model revealed significant differences among researchers and nonresearchers in rating the criteria and indicators,but not among foresters and nonforesters.Hence,participatory multi-criteria decision analysis should involve people from various institutions to rectify decisions on conservation of the species.Careful evaluation of the investment policy environment and engaging those government bodies that are responsible to allocate the dry forests for commercial farming is recommended before the proposed criteria are applied to select populations for conservation,thus ensuring subsequent use of the outcomes of such exercises and better reconciling conservation and agricultural production increment goals.

Competence Set Analysis Under Risk and Uncertainty

The competence set analysis technology can be applied to solve the decision making problems successfully and satisfactorily. This paper mainly focuses on the expanding strategy research and development of the competence set under risk and uncertainty. A systematic expression of the competence set analysis is described, several expanding principles and strategies with regard to several different cases are presented, and their applications in the personnel training program are discussed, some conclusions and suggestions to be developed in a further work are included.

Three-Dimensional Computerized Tomography-Assisted Identification of Necrotic Volume, Distribution, Shape and Prognosis of Collapse in ONFH

Objective: We constructed 3D-model of ONFH in computer according to three-dimensional computerized tomography (3D-CT) data. We determined the location and volume of necrosis to investigate its clinical efficacy. Method: Totally 92 hips (59 cases) with ONFH (44 males, 15 females) were included, with mean age of 37.5 years (range from 26 to 58). Totally 20 cases (35 hips) were induced by corticosteroid (CTSs), 31 (49 hips) induced by alcohol, 4 (4 hips) induced by trauma and 4 (4 hips) idiopathic. All the hips were categorized into stage ARCO II. Finally diagnosed by MRI, all hips were scanned by CT to acquire data in DICOM format. The images were imported into software to extract 3D-shape of femoral heads, necrotic foci, their volumes and distribution in each quadrant. Deviation of volumes between digital image and biopsy specimen was analyzed by SAS9.1 package. Correlativity between collapse and volume of necrosis under specific pathogeneses was also analyzed. Among the cases necessitating total hip arthroplasty (THA) due to advancing to ARCO III, we randomly selected 8 of them to perform 3D-CT scanning thrice prior to surgical operation. Total femoral heads harvested were torn asunder. Cubic capacity of femoral heads and necrotic foci were hereby measured and compared with those acquired from digital models. Result: Through the digital model, necrotic foci were found mainly locating within the super lateral portion of femoral head, coinciding with those observed in biopsy specimen. Average volumetric ratio of digitally acquired necrosis focus/femoral head in 58 collapsed hips was 36.8%. The ratio of the 34 hips without collapse was 17.3%. In collapsed femoral heads, the distribution of necrosis focus was 23.4% in quadrant 1 (q1), 23.6% in q2, 12.1% in q3, 14.4% in q4, 9.0% in q5, 11.8% in q6, 1.6% in q7 and 3.9% in q8. In femoral heads without collapse, the distribution was 34.2% in q1, 29.6% in q2, 11.8% in q3, 11.3% in q4, 6.0% in q5, 6.0% in q6, 0.5% in q7 and 0.4% in q8. As for the average cubic capacities of femoral heads and necrotic foci, those acquired from the digital model and biopsy specimen had no significant difference in matched-pairs test (t = -1.49, P = 0.179 for femoral heads and t = -1.52, P = 0.172 for necrotic foci). There was significant difference (F = 2.720, P = 0.035 P was respectively 0.0001 and 0.0005). Decision tree model showed that 94.6% (53/56) hips would progress into collapse if the volumetric ratio of necrotic tissue was over 23.48%. Otherwise, if distribution in q2 was over 45.13%, 83.3% (5/6) hips would progress into collapse. No collapse (0/30) would occur if the distribution of necrotic tissue in q2 was under 45.13%. Conclusion: Digital 3D-model reconstructed from CT scanning can precisely incarnate spatial orientation of necrotic foci in femoral head. Multinomial logistic regression and decision-making tree shows that volumetric ratio of necrotic tissues plays an important role in anticipating collapse of femoral head.

Uncertainty and Its Description in Decision Models

Various perspectives in uncertainty are briefly summarized in this paper, and the classification of uncertainties is discussed. The descriptions of different classes of uncertainty are also presented. Furthermore, a risk representation model for decision-making analysis is provided.

Holistic approach of GIS based Multi-Criteria Decision Analysis(MCDA) and WetSpass models to evaluate groundwater potential in Gelana watershed of Ethiopia

Appropriate quantification and identification of the groundwater distribution in a hydrological basin may provide necessary information for effective management,planning and development of groundwater resources.Groundwater potential assessment and delineation in a highly heterogeneous environment with limited Spatiotemporal data derived from Gelana watershed of Abaya Chamo lake basin is performed,using integrated multi-criteria decision analysis(MCDA),water and energy transfer between soil and plant and atmosphere under quasi-steady state(WetSpass)models.The outputs of the WetSpass model reveal a favorable structure of water balance in the basin studied,mainly using surface runoff.The simulated total flow and groundwater recharge are validated using river measurements and estimated baseflow at two gauging stations located in the study area,which yields a good agreement.The WetSpass model effectively integrates a water balance assessment in a geographical information system(GIS)environment.The WetSpass model is shown to be computationally reputable for such a remote complex setting as the African rift,with a correlation coefficient of 0.99 and 0.99 for total flow and baseflow at a significant level of p-value<0.05,respectively.The simulated annual water budget reveals that 77.22%of annual precipitation loses through evapotranspiration,of which 16.54%is lost via surface runoff while 6.24%is recharged to the groundwater.The calibrated groundwater recharge from the WetSpass model is then considered when determining the controlling factors of groundwater occurrence and formation,together with other multi-thematic layers such as lithology,geomorphology,lineament density and drainage density.The selected five thematic layers through MCDA are incorporated by employing the analytical hierarchy process(AHP)method to identify the relative dominance in groundwater potential zoning.The weighted factors in the AHP are procedurally aggregated,based on weighted linear combinations to provide the groundwater potential index.Based on the potential indexes,the area then is demarcated into low,moderate,and high groundwater potential zones(GWPZ).The identified GWPZs are finally examined using the existing groundwater inventory data(static water level and springs)in the region.About 70.7%of groundwater inventory points are coinciding with the delineated GWPZs.The weighting comparison shows that lithology,geomorphology,and groundwater recharge appear to be the dominant factors influence on the resources potential.The assessment of groundwater potential index values identify 45.88%as high,39.38%moderate,and 14.73%as low groundwater potential zones.WetSpass model analysis is more preferable in the area like Gelana watershed when the topography is rugged,inaccessible and having limited gauging stations.