Search results for: Interval Number

Authors: Susovan Chakrabortty, Madhumangal Pal, Prasun Kumar Nayak

Abstract:

A manufacturing inventory model with shortages with carrying cost, shortage cost, setup cost and demand quantity as imprecise numbers, instead of real numbers, namely interval number is considered here. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. A common algorithm for the optimum production quantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) is developed which works well on interval number optimization under consideration. Finally, the designed algorithm is illustrated with numerical example.

Keywords: EOQ, Inventory, Interval Number, Demand, Production, Simulation

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Authors: K. Ganesan

Abstract:

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.

Keywords: Interval arithmetic, Interval matrix, linear equations.

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Authors: Tarasankar Pramanik, Sukumar Mondal, Madhumangal Pal

Abstract:

In an interval graph G = (V,E) the distance between two vertices u, v is de£ned as the smallest number of edges in a path joining u and v. The eccentricity of a vertex v is the maximum among distances from all other vertices of V . The diameter (δ) and radius (ρ) of the graph G is respectively the maximum and minimum among all the eccentricities of G. The center of the graph G is the set C(G) of vertices with eccentricity ρ. In this context our aim is to establish the relation ρ = δ 2  for an interval graph and to determine the center of it.

Keywords: Interval graph, interval tree, radius, center.

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Authors: Hidehiko Okada

Abstract:

The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks. 

Keywords: Evolutionary algorithms, differential evolution, neural network, neuroevolution, interval arithmetic.

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Authors: Michal Cerny

Abstract:

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

Keywords: Linear regression, interval-censored data, computational complexity.

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Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: Uniquely restricted matching, interval graph, design and analysis of algorithms, matching, induced matching, witness counting.

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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithms, swarm intelligence, particle swarm optimization, neural network, interval arithmetic.

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Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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Authors: Arsham Borumand Saeid

Abstract:

In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

Keywords: BG-algebra, fuzzy BG-subalgebra, interval-valued fuzzy set, interval-valued fuzzy BG-subalgebra.

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Authors: Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

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Authors: V.Rezaie, M.Khanmohammady

Abstract:

An original DEA model is to evaluate each DMU optimistically, but the interval DEA Model proposed in this paper has been formulated to obtain an efficiency interval consisting of Evaluations from both the optimistic and the pessimistic view points. DMUs are improved so that their lower bounds become so large as to attain the maximum Value one. The points obtained by this method are called ideal points. Ideal PPS is calculated by ideal of efficiency DMUs. The purpose of this paper is to rank DMUs by this ideal PPS. Finally we extend the efficiency interval of a DMU under variable RTS technology.

Keywords: Data envelopment analysis (DEA), Decision makingunit (DMU), Interval DEA, Ideal points, Ideal PPS, Return to scale(RTS).

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Authors: Yiannis G. Smirlis

Abstract:

The classification and the prediction of efficiencies in Data Envelopment Analysis (DEA) is an important issue, especially in large scale problems or when new units frequently enter the under-assessment set. In this paper, we contribute to the subject by proposing a grid structure based on interval segmentations of the range of values for the inputs and outputs. Such intervals combined, define hyper-rectangles that partition the space of the problem. This structure, exploited by Interval DEA models and a dominance relation, acts as a DEA pre-processor, enabling the classification and prediction of efficiency scores, without applying any DEA models.

Keywords: Data envelopment analysis, interval DEA, efficiency classification, efficiency prediction.

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Authors: Chen-Chien Hsu, Chun-Hui Gao

Abstract:

In this paper, a PSO-based approach is proposed to derive a digital controller for redesigned digital systems having an interval plant based on resemblance of the extremal gain/phase margins. By combining the interval plant and a controller as an interval system, extremal GM/PM associated with the loop transfer function can be obtained. The design problem is then formulated as an optimization problem of an aggregated error function revealing the deviation on the extremal GM/PM between the redesigned digital system and its continuous counterpart, and subsequently optimized by a proposed PSO to obtain an optimal set of parameters for the digital controller. Computer simulations have shown that frequency responses of the redesigned digital system having an interval plant bare a better resemblance to its continuous-time counter part by the incorporation of a PSO-derived digital controller in comparison to those obtained using existing open-loop discretization methods.

Keywords: Digital redesign, Extremal systems, Particle swarm optimization, Uncertain interval systems

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Authors: Arunee Wongkha, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

Keywords: The inverse of a normal mean, confidence interval, generalized confidence intervals, known coefficient of variation.

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Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Suparat Niwitpong

Abstract:

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

Keywords: Confidence interval, generalized confidence interval, the closed form method of variance estimation, variance.

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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Authors: S. Phanyaem

Abstract:

This paper presents the confidence intervals for the effect size base on bootstrap resampling method. The meta-analytic confidence interval for effect size is proposed that are easy to compute. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. The best confidence interval method will have a coverage probability close to 0.95. Simulation results have shown that our proposed confidence intervals perform well in terms of coverage probability and expected length.

Keywords: Effect size, confidence interval, Bootstrap Method.

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Authors: Khalil el Hindi

Abstract:

This paper presents a simple and effective method for approximate indexing of instances for instance based learning. The method uses an interval tree to determine a good starting search point for the nearest neighbor. The search stops when an early stopping criterion is met. The method proved to be very effective especially when only the first nearest neighbor is required.

Keywords: Instance based learning, interval trees, the knn algorithm, machine learning.

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Authors: Jeerapa Sappakitkamjorn, Sa-aat Niwitpong

Abstract:

In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.  

Keywords: Bounded parameters, coefficient of variation, confidence interval, Monte Carlo simulation.

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Authors: S. Khoshemehry, M. J. Pourvaghar

Abstract:

Inflammatory markers are known as the main predictors of cardiovascular diseases. This study aimed at determining the effect of 8 weeks of interval endurance training on hs-CRP level and some anthropometric parameters in overweight men. Following the call for participation in research project in Kashan, 73 volunteers participated in it and constituted the statistical population of the study. Then, 28 overweight young men from the age of 22 to 25 years old were randomly assigned into two groups of experimental and control group (n=14). Anthropometric and the blood sample was collected before and after the termination of the program for measuring hs-CRP. The interval endurance program was performed at 60 to 75% of maximum heart rate in 2 sessions per week for 8 weeks. Kolmogorov-Smirnov test was used to test whether two samples come from the same distribution and T-test was used to assess the difference of two groups which were statistically significant at the level of 0.05. The result indicated that there was a significant difference between the hs-RP, weight, BMI and W/H ratio of overweight men in posttest in the exercise group (P≤0.05) but not in the control group. Interval endurance training program causes decrease in hs-CRP level and anthropometric parameters.

Keywords: Interval endurance training program, hs-CRP, overweight, anthropometric.

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Authors: F. A. M. Elfaki, Amar Abobakar, M. Azram, M. Usman

Abstract:

This paper discusses regression analysis of partly interval-censored failure time data, which is occur in many fields including demographical, epidemiological, financial, medical and sociological studies. For the problem, we focus on the situation where the survival time of interest can be described by the additive hazards model in the present of partly interval-censored. A major advantage of the approach is its simplicity and it can be easily implemented by using R software. Simulation studies are conducted which indicate that the approach performs well for practical situations and comparable to the existing methods. The methodology is applied to a set of partly interval-censored failure time data arising from anti D in Rhesus D negative studies.

Keywords: Anti D in Rhesus D negative, Cox’s model, EM algorithm.

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Authors: Rizik Al-Sayyed, Colin Pattinson, Tony Dacre

Abstract:

This paper presents the findings of two experiments that were performed on the Redundancy in Wireless Connection Model (RiWC) using the 802.11b standard. The experiments were simulated using OPNET 11.5 Modeler software. The first was aimed at finding the maximum number of simultaneous Voice over Internet Protocol (VoIP) users the model would support under the G.711 and G.729 codec standards when the packetization interval was 10 milliseconds (ms). The second experiment examined the model?s VoIP user capacity using the G.729 codec standard along with background traffic using the same packetization interval as in the first experiment. To determine the capacity of the model under various experiments, we checked three metrics: jitter, delay and data loss. When background traffic was added, we checked the response time in addition to the previous three metrics. The findings of the first experiment indicated that the maximum number of simultaneous VoIP users the model was able to support was 5, which is consistent with recent research findings. When using the G.729 codec, the model was able to support up to 16 VoIP users; similar experiments in current literature have indicated a maximum of 7 users. The finding of the second experiment demonstrated that the maximum number of VoIP users the model was able to support was 12, with the existence of background traffic.

Keywords: WLAN, IEEE 802.11b, Codec, VoIP, OPNET, Background traffic, and QoS.

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Authors: Mário A. R. Talaia

Abstract:

As it is known, buoyancy and drag forces rule bubble's rise velocity in a liquid column. These forces are strongly dependent on fluid properties, gravity as well as equivalent's diameter. This study reports a set of bubble rising velocity experiments in a liquid column using water or glycerol. Several records of terminal velocity were obtained. The results show that bubble's rise terminal velocity is strongly dependent on dynamic viscosity effect. The data set allowed to have some terminal velocities data interval of 8.0 ? 32.9 cm/s with Reynolds number interval 1.3 -7490. The bubble's movement was recorded with a video camera. The main goal is to present an original set data and results that will be discussed based on two-phase flow's theory. It will also discussed, the prediction of terminal velocity of a single bubble in liquid, as well as the range of its applicability. In conclusion, this study presents general expressions for the determination of the terminal velocity of isolated gas bubbles of a Reynolds number range, when the fluid proprieties are known.

Keywords: Bubbles, terminal velocity, two phase-flow, vertical column.

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Authors: S. A. Gayvoronsky, T. A. Ezangina

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The robust control system objects with interval- undermined parameters is considers in this paper. Initial information about the system is its characteristic polynomial with interval coefficients. On the basis of coefficient estimations of quality indices and criterion of the maximum stability degree, the methods of synthesis of a robust regulator parametric is developed. The example of the robust stabilization system synthesis of the rope tension is given in this article.

Keywords: An interval polynomial, controller synthesis, analysis of quality factors, maximum degree of stability, robust degree of stability, robust oscillation, system accuracy.

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Authors: Liping Li, Changchun Liu, Ke Li, Chengyu Liu

Abstract:

Non-stationary trend in R-R interval series is considered as a main factor that could highly influence the evaluation of spectral analysis. It is suggested to remove trends in order to obtain reliable results. In this study, three detrending methods, the smoothness prior approach, the wavelet and the empirical mode decomposition, were compared on artificial R-R interval series with four types of simulated trends. The Lomb-Scargle periodogram was used for spectral analysis of R-R interval series. Results indicated that the wavelet method showed a better overall performance than the other two methods, and more time-saving, too. Therefore it was selected for spectral analysis of real R-R interval series of thirty-seven healthy subjects. Significant decreases (19.94±5.87% in the low frequency band and 18.97±5.78% in the ratio (p<0.001)) were found. Thus the wavelet method is recommended as an optimal choice for use.

Keywords: empirical mode decomposition, heart rate variability, signal detrending, smoothness priors, wavelet

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Authors: Tanuj Kumar, Rakesh Kumar Bajaj

Abstract:

In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.

Keywords: Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

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Authors: Sa-aat Niwitpong

Abstract:

Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic expressions of the coverage probability and the expected length of confidence interval for the normal mean when the whole parameter space is bounded. We also construct the confidence interval for the normal variance with restricted parameter for the first time and its coverage probability and expected length are also mathematically derived. As a result, one can use these criteria to assess the confidence interval for the normal mean and variance when the parameter space is restricted without the back up from simulation experiments.

Keywords: Confidence interval, coverage probability, expected length, restricted parameter space.

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Authors: P. T. Ahamed Seyd, V. I. Thajudin Ahamed, Jeevamma Jacob, Paul Joseph K

Abstract:

Diabetes mellitus (DM) is frequently characterized by autonomic nervous dysfunction. Analysis of heart rate variability (HRV) has become a popular noninvasive tool for assessing the activities of autonomic nervous system (ANS). In this paper, changes in ANS activity are quantified by means of frequency and time domain analysis of R-R interval variability. Electrocardiograms (ECG) of 16 patients suffering from DM and of 16 healthy volunteers were recorded. Frequency domain analysis of extracted normal to normal interval (NN interval) data indicates significant difference in very low frequency (VLF) power, low frequency (LF) power and high frequency (HF) power, between the DM patients and control group. Time domain measures, standard deviation of NN interval (SDNN), root mean square of successive NN interval differences (RMSSD), successive NN intervals differing more than 50 ms (NN50 Count), percentage value of NN50 count (pNN50), HRV triangular index and triangular interpolation of NN intervals (TINN) also show significant difference between the DM patients and control group.

Keywords: Autonomic nervous system, diabetes mellitus, frequency domain and time domain analysis, heart rate variability.

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Authors: Nurnadiah Z., Lazim A.

Abstract:

The design of weight is one of the important parts in fuzzy decision making, as it would have a deep effect on the evaluation results. Entropy is one of the weight measure based on objective evaluation. Non--probabilistic-type entropy measures for fuzzy set and interval type-2 fuzzy sets (IT2FS) have been developed and applied to weight measure. Since the entropy for (IT2FS) for decision making yet to be explored, this paper proposes a new objective weight method by using entropy weight method for multiple attribute decision making (MADM). This paper utilizes the nature of IT2FS concept in the evaluation process to assess the attribute weight based on the credibility of data. An example was presented to demonstrate the feasibility of the new method in decision making. The entropy measure of interval type-2 fuzzy sets yield flexible judgment and could be applied in decision making environment.

Keywords: Objective weight, entropy weight, multiple attributedecision making, type-2 fuzzy sets, interval type-2 fuzzy sets

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