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Concept: Arithmetical hierarchy


River water quality sampling frequency is an important aspect of the river water quality monitoring network. A suitable sampling frequency for each station as well as for the whole network will provide a measure of the real water quality status for the water quality managers as well as the decision makers. The analytic hierarchy process (AHP) is an effective method for decision analysis and calculation of weighting factors based on multiple criteria to solve complicated problems. This study introduces a new procedure to design river water quality sampling frequency by applying the AHP. We introduce and combine weighting factors of variables with the relative weights of stations to select the sampling frequency for each station, monthly and yearly. The new procedure was applied for Jingmei and Xindian rivers, Taipei, Taiwan. The results showed that sampling frequency should be increased at high weighted stations while decreased at low weighted stations. In addition, a detailed monitoring plan for each station and each month could be scheduled from the output results. Finally, the study showed that the AHP is a suitable method to design a system for sampling frequency as it could combine multiple weights and multiple levels for stations and variables to calculate a final weight for stations, variables, and months.

Concepts: Algorithm, Decision theory, Decision making software, Operations research, Analytic Hierarchy Process, Analytical hierarchy, Weight, Arithmetical hierarchy


Sustainability assessments of coastal beach exploitation are difficult because the identification of appropriate monitoring methodologies and evaluation procedures is still ongoing. In particular, the most suitable procedure for the application of sustainability assessment to coastal beaches remains uncertain. This paper presents a complete sustainability assessment process for coastal beach exploitation based on the analytic hierarchy process (AHP). We developed an assessment framework consisting of 14 indicators derived from the three dimensions of suitability, economic and social value, and ecosystem. We chose a wind power project on a coastal beach of Yancheng as a case study. The results indicated that the wind power farms on the coastal beach were not completely in keeping with sustainable development theory. The construction of the wind power farms had some negative impacts. Therefore, in the design stage, wind turbines should be designed and planned carefully to minimize these negative impacts. In addition, the case study demonstrated that the AHP was capable of addressing the complexities associated with the sustainability of coastal beaches.

Concepts: Assessment, Sustainability, Analytic Hierarchy Process, Renewable energy, Wind power, Wind farm, Wind turbine, Arithmetical hierarchy


This paper proposes a two-stage group decision making approach to urban landscape management and planning supported by the analytic hierarchy process. The proposed approach combines an application of the consensus convergence model and the weighted geometric mean method. The application of the proposed approach is shown on a real urban landscape planning problem with a park-forest in Belgrade, Serbia. Decision makers were policy makers, i.e., representatives of several key national and municipal institutions, and experts coming from different scientific fields. As a result, the most suitable management plan from the set of plans is recognized. It includes both native vegetation renewal in degraded areas of park-forest and continued maintenance of its dominant tourism function. Decision makers included in this research consider the approach to be transparent and useful for addressing landscape management tasks. The central idea of this paper can be understood in a broader sense and easily applied to other decision making problems in various scientific fields.

Concepts: Decision making, Decision theory, Management, Decision making software, Analytic Hierarchy Process, Analytical hierarchy, Plan, Arithmetical hierarchy


In average-risk individuals aged 50 to 75 years, there is no difference in life-years gained when comparing colonoscopy every 10 years vs. annual fecal immunochemical testing (FIT) for colorectal cancer screening. Little is known about the preferences of patients when they have experienced both tests.

Concepts: Hierarchy, Analytical hierarchy, Arithmetical hierarchy


The Yellow River Delta (YRD), located in Yellow River estuary, is characterized by rich ecological system types, and provides habitats or migration stations for wild birds, all of which makes the delta an ecological barrier or ecotone for inland areas. Nevertheless, the abundant natural resources of YRD have brought huge challenges to the area, and frequent human activities and natural disasters have damaged the ecological systems seriously, and certain ecological functions have been threatened. Therefore, it is necessary to determine the status of the ecological environment based on scientific methods, which can provide scientifically robust data for the managers or stakeholders to adopt timely ecological protection measures. The aim of this study was to obtain the spatial distribution of the ecological vulnerability (EV) in YRD based on 21 indicators selected from underwater status, soil condition, land use, landform, vegetation cover, meteorological conditions, ocean influence, and social economy. In addition, the fuzzy analytic hierarchy process (FAHP) method was used to obtain the weights of the selected indicators, and a fuzzy logic model was constructed to obtain the result. The result showed that the spatial distribution of the EV grades was regular, while the fuzzy membership of EV decreased gradually from the coastline to inland area, especially around the river crossing, where it had the lowest EV. Along the coastline, the dikes had an obviously protective effect for the inner area, while the EV was higher in the area where no dikes were built. This result also showed that the soil condition and groundwater status were highly related to the EV spatially, with the correlation coefficients −0.55 and −0.74 respectively, and human activities had exerted considerable pressure on the ecological environment.

Concepts: Ecology, Natural environment, Hierarchy, Soil, Estuary, Analytical hierarchy, Yellow River, Arithmetical hierarchy


Rooted deeply in medical multiple criteria decision-making (MCDM), risk assessment is very important especially when applied to the risk of being affected by deadly diseases such as coronary heart disease (CHD). CHD risk assessment is a stochastic, uncertain, and highly dynamic process influenced by various known and unknown variables. In recent years, there has been a great interest in fuzzy analytic hierarchy process (FAHP), a popular methodology for dealing with uncertainty in MCDM. This paper proposes a new FAHP, bimodal fuzzy analytic hierarchy process (BFAHP) that augments two aspects of knowledge, probability and validity, to fuzzy numbers to better deal with uncertainty. In BFAHP, fuzzy validity is computed by aggregating the validities of relevant risk factors based on expert knowledge and collective intelligence. By considering both soft and statistical data, we compute the fuzzy probability of risk factors using the Bayesian formulation. In BFAHP approach, these fuzzy validities and fuzzy probabilities are used to construct a reciprocal comparison matrix. We then aggregate fuzzy probabilities and fuzzy validities in a pairwise manner for each risk factor and each alternative. BFAHP decides about being affected and not being affected by ranking of high and low risks. For evaluation, the proposed approach is applied to the risk of being affected by CHD using a real dataset of 152 patients of Iranian hospitals. Simulation results confirm that adding validity in a fuzzy manner can accrue more confidence of results and clinically useful especially in the face of incomplete information when compared with actual results. Applying the proposed BFAHP on CHD risk assessment of the dataset, it yields high accuracy rate above 85% for correct prediction. In addition, this paper recognizes that the risk factors of diastolic blood pressure in men and high-density lipoprotein in women are more important in CHD than other risk factors.

Concepts: Statistics, Atherosclerosis, Risk, Decision theory, Decision making software, Probability, Analytic Hierarchy Process, Arithmetical hierarchy


As an important composition component of river ecosystems, river habitats must undergo quality assessment to potentially provide scientific basis for river ecological restoration. Substrate composition, habitat complexity, bank erosion degree, river meandering degree, human activity intensity, vegetation buffer width, water quality, and water condition were determined as indicators for river habitat assessment. The comprehensive habitat quality index (CHQI) was established for the Wei River Basin. In addition, the indicator values were determined on the basis of a field investigation at 12 national hydrological stations distributed across the Wei, Jing, and Beiluo Rivers. The analytic hierarchy process was used to determine the indicator weights and thus distinguish the relative importance of the assessment indicator system. Results indicated that the average CHQIs for the Wei, Jing, and Beiluo Rivers were 0.417, 0.508, and 0.304, respectively. The river habitat quality for the three rivers was well. As for the whole river basin, the river habitat quality for 25% of the cross section was very well, the other 25% was well, and the 50% remaining was in critical state. The river habitat quality of the Jing River was better than that of the Wei and Beiluo Rivers.

Concepts: Water, Hierarchy, Hydrology, Drainage basin, Analytical hierarchy, Analytic set, Geomorphology, Arithmetical hierarchy


To explore the difference of cumulative incidence rate of coal workers' pneumoconiosis (CWP) among four large state-owned coal enterprises in northern China, we created an index system for evaluating the quality of comprehensive measures against CWP and applied the system to evaluate and compare the measures of the four coal enterprises.

Concepts: Hierarchy, Computer program, Analytic Hierarchy Process, Analytical hierarchy, Analytic set, Arithmetical hierarchy, Descriptive set theory, Projective hierarchy


This paper presents a new approach to prioritize “Large-scale Data” of patients with chronic heart diseases by using body sensors and communication technology during disasters and peak seasons. An evaluation matrix is used for emergency evaluation and large-scale data scoring of patients with chronic heart diseases in telemedicine environment. However, one major problem in the emergency evaluation of these patients is establishing a reasonable threshold for patients with the most and least critical conditions. This threshold can be used to detect the highest and lowest priority levels when all the scores of patients are identical during disasters and peak seasons. A practical study was performed on 500 patients with chronic heart diseases and different symptoms, and their emergency levels were evaluated based on four main measurements: electrocardiogram, oxygen saturation sensor, blood pressure monitoring, and non-sensory measurement tool, namely, text frame. Data alignment was conducted for the raw data and decision-making matrix by converting each extracted feature into an integer. This integer represents their state in the triage level based on medical guidelines to determine the features from different sources in a platform. The patients were then scored based on a decision matrix by using multi-criteria decision-making techniques, namely, integrated multi-layer for analytic hierarchy process (MLAHP) and technique for order performance by similarity to ideal solution (TOPSIS). For subjective validation, cardiologists were consulted to confirm the ranking results. For objective validation, mean ± standard deviation was computed to check the accuracy of the systematic ranking. This study provides scenarios and checklist benchmarking to evaluate the proposed and existing prioritization methods. Experimental results revealed the following. (1) The integration of TOPSIS and MLAHP effectively and systematically solved the patient settings on triage and prioritization problems. (2) In subjective validation, the first five patients assigned to the doctors were the most urgent cases that required the highest priority, whereas the last five patients were the least urgent cases and were given the lowest priority. In objective validation, scores significantly differed between the groups, indicating that the ranking results were identical. (3) For the first, second, and third scenarios, the proposed method exhibited an advantage over the benchmark method with percentages of 40%, 60%, and 100%, respectively. In conclusion, patients with the most and least urgent cases received the highest and lowest priority levels, respectively.

Concepts: Medicine, Decision theory, Decision making software, Scores, Standard deviation, Analytical hierarchy, Priority level, Arithmetical hierarchy


This study assesses vulnerability of groundwater to pollution in Beihai City, China, as a support of groundwater resource protection. The assessment result not only objectively reflects potential possibility of groundwater to contamination but also provides scientific basis for the planning and utilization of groundwater resources. This study optimizes the parameters consisting of natural factors and human factors upon the DRASTIC model and modifies the ratings of these parameters, based on the local environmental conditions for the study area. And a weight of each parameter is assigned by the analytic hierarchy process (AHP) to reduce the subjectivity of humans to vulnerability assessment. The resulting scientific ratings and weights of modified DRASTIC model (AHP-DRASTLE model) contribute to obtain the more realistic assessment of vulnerability of groundwater to contaminant. The comparison analysis validates the accuracy and rationality of the AHP-DRASTLE model and shows it suits the particularity of the study area. The new assessment method (AHP-DRASTLE model) can provide a guide for other scholars to assess the vulnerability of groundwater to contamination. The final vulnerability map for the AHP-DRASTLE model shows four classes: highest (2%), high (29%), low (55%), and lowest (14%). The vulnerability map serves as a guide for decision makers on groundwater resource protection and land use planning at the regional scale and that it is adapted to a specific area.

Concepts: Hierarchy, Decision theory, Decision making software, Analytic Hierarchy Process, Analytical hierarchy, C++, Analytic set, Arithmetical hierarchy