Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements. The probabilistic hesitant fuzzy preference relations can more effectively express the hesitant preference information of decision makers. But in the existing research, all of them are based on discrete PROBABILITY distribution. In order to give decision maker more evaluation space, continuous PROBABILITY distribution is necessary to be considered. Therefore, in this paper, the continuous PROBABILITY-INTERVAL valued fuzzy set is defined and its PROBABILITY is represented by a PROBABILITY density function. A method of converting probabilistic hesitant fuzzy set into continuous PROBABILITY-INTERVAL valued fuzzy set is developed to transform discrete data into continuous data. Then, the continuous PROBABILITY-INTERVAL valued fuzzy preference relations is presented. In order to consider the consistency of continuous PROBABILITY-INTERVAL valued fuzzy preference relations, the multiplication consistent expected preference relations is proposed. The individual consistency index and group consensus index are also presented to determine the consistency level. And then, an algorithm is introduced for checking and improving the individual consistency level and group consensus level. Finally, a numerical example is shown to the effectiveness of proposed algorithm, the comparative analysis is given with the existing methods to show the superiority of this algorithm.

Background & Aims: Different scoring systems are used in order to assess the functional quality of intensive care units (ICU) and to predict the required costs and facilities of intensive cares. Variety of scoring systems has been explained that each has advantages and disadvantages. In this study Simplified Acute Physiology Score-III (SAPS-III) and Mortality PROBABILITY Model-III (MPM-III) were compared. Materials & Methods: The current cross-sectional study was conducted on 240 non-traumatic patients admitted at ICU of Al-Zahra Hospital in 2016-17. Patients' information including demographics, mean of systolic, diastolic and arterial pressure, pulse rate, respiratory rate, temperature, Glasgow Coma Scale(GCS), WBC, hematocrit, bilirubin, creatinine, arterial blood gas, and the presence of underlying diseases was gathered from the records for measurement of MPM-III and SAPS-III scores and then they were compared. Results: This study was conducted on 240 non-traumatic patients. Discrimination of MPM-III in cutoff point of 0. 17 was 0. 83(P<0. 001; 95%CI: 0. 765-0. 898), sensitivity and specificity of this test in prediction of non-traumatic mortality was 82% and 73%, respectively. Discrimination of SAPS-III in cut-off of 48. 5 was 0. 78(P<0. 001; 95%CI: 0. 72-0. 84), while its sensitivity and specificity was 83% and 70%, respectively. Duration of ICU hospitalization (P=0. 028 and 0. 002) and duration of intubation (P=0. 001 and <0. 001) had direct association with mortality based on both scoring systems while total duration of hospitalization was only significant in SAPSIII (P=0. 002). Conclusion: Comparison of SAPS-III and MPM-III in non-traumatic patients presented a higher discrimination ability for MPM-III. In addition, findings showed that mortality in MPM-III was in association with duration of ICU admission and intubation while for SAPS-III, in addition to previous factors, total duration of hospitalization was associated as well.

Background: Intensive care unit (ICU) is among the most important hospital wards. Variety of scoring systems for evaluation of patients' status and prediction of hospitalization outcomes in ICU has been raised that each has strong and weak points; assessment of these characteristics tends to promote new scoring systems. The current study compared scoring systems of Mortality PROBABILITY Model-III (MPM-III) and Simplified Acute Physiology Score-III (SAPS-III) in trauma patients in ICU. Methods: This randomized cross-sectional study was conducted on 200 patients admitted in ICU because of trauma in years 2016-17. Patients' information including demographics, mean of systolic, diastolic, and arterial blood pressure, pulse, respiratory rate, temperature, Glasgow coma scale (GCS), arterial gas analysis, white blood cell (WBC) counts, hematocrit, bilirubin, creatinine, type of admission, and presence of underlying diseases were extracted from records; MPM-III and SAPS-III were measured for these patients and compared. Findings: MPM-III scoring system had discrimination of 0. 935 [95% confidence INTERVAL (95%CI): 0. 89-0. 97; P < 0. 001) in cut-off point of 0. 13, and its sensitivity and specificity was 87% and 84%, respectively. For SAPS-III system, in cut-off point of 0. 13, the discrimination was 0. 77 (95%CI: 0. 69-0. 85; P < 0. 001), with the sensitivity of 80% and specificity of 68%. Based on both MPM-III and SAPS-III systems, mortality was in correlation with duration of ICU admission (P = 0. 001 for both systems) and duration of intubation (P < 0. 001 for both systems), while only for SAPS-III, total duration of hospitalization was in correlation with mortality (P < 0. 001). Conclusion: MPM-III scoring system was superior to SAPS-III regarding discrimination power in trauma patients. In addition, based on both systems, mortality rate was in direct association with days of ICU admission and intubation duration.

Despite modern scientific knowledge and computational power in hydrology, the key to properly addressing hydrologic uncertainty remains a critical and challenging one. Here, we applied lumped HBV hydrological model to describe the uncertainty in runoff prediction in Chehl-Chay watershed in Golestan province. We applied a new framework for uncertainty analysis that is rooted on ideas from predicting model residual uncertainty. The uncertainty calculated by local Errors and Clustering (EEC) is compared with estimates from two non parametric methods (quantile regression (QR) and random forest (RF)) and a parametric method (GLUE). Firstly, the model parameters were optimized by Shuffled Complex Evolution approach and model residuals of test data were computed. Fuzzy clustering in EEC is carried out by the fuzzy c-means method and employs four clusters, predictive discharges, observed discharges, rainfall values and residuals in study basin. The results of this case study show that the uncertainty estimates obtained by EES which is trained by SVM gives wider uncertainty band and RF gives narrower uncertainty band. The best overall uncertainty estimates according to the PICP, MPI and ARIL indices were obtained with QR and then EEC. In comparison with non-parametric, with respct to all indices nonparametric methods had better performance than GLUE method.

Since the binomial distribution is discrete‎, ‎finding accurate confidence INTERVALs for its parameters is not easily achievable‎. ‎Many approximate confidence INTERVALs have been suggested for the binomial distribution's ratio parameter thus far‎. ‎As we know‎, ‎these confidence INTERVALs have not been compared based on the maximum coverage probabilities‎. ‎This article aims to evaluate six widely used confidence INTERVALs for the binomial distribution's ratio parameter‎, ‎focusing on their accurate maximum coverage probabilities criterion.

This presentation outlines from a quantitative point of view, the relationships between PROBABILITY theory, possibility theory, and generalized uncertainty theory, and the role that fuzzy set theory plays in the context of these theories. Fuzzy sets, possibility, and PROBABILITY entities are de…ned in terms of a function. In each case, these three functions map the real numbers to the INTERVAL [0, 1]. However, each of these functions are de…ned with di¤ erent properties. There are generalizations associated with these three theories that lead to INTERVALs (sets of connected real numbers bounded by two points) and INTERVAL functions (sets of functions that are bounded by known upper and lower functions). An INTERVAL or INTERVAL function encodes the fact that it is unknown which of the points or functions is the point or function in questions, that is, the numerical value or real-valued function is unknown, it is uncertain. For generalizations given by pairs of numbers or functions, a case is made for a particular type of generalized uncertainty theory, INTERVAL-valued PROBABILITY measures, as a way to unify the generalizations of PROBABILITY, possibility theory, as well as other generalized PROBABILITY theories via fuzzy INTERVALs and fuzzy INTERVAL functions. This presentation brings a new understanding of quantitative fuzzy set theory, possibility theory, PROBABILITY theory, and generalized uncertainty and gleans from existing research with the intent to organize and further clarify existing approaches.