Search results for: weighted interval.

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: S. C. Arora, Ritu Kathuria

Abstract:

A slant weighted Toeplitz operator Aφ is an operator on L2(β) defined as Aφ = WMφ where Mφ is the weighted multiplication operator and W is an operator on L2(β) given by We2n = βn β2n en, {en}n∈Z being the orthonormal basis. In this paper, we generalise Aφ to the k-th order slant weighted Toeplitz operator Uφ and study its properties.

Keywords: Slant weighted Toeplitz operator, weighted multiplicationoperator.

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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: 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: José M. Merigó, Pilar López-Jurado, M.Carmen Gracia, Montserrat Casanovas

Abstract:

We present a method for the selection of students in interdisciplinary studies based on the hybrid averaging operator. We assume that the available information given in the problem is uncertain so it is necessary to use interval numbers. Therefore, we suggest a new type of hybrid aggregation called uncertain induced generalized hybrid averaging (UIGHA) operator. It is an aggregation operator that considers the weighted average (WA) and the ordered weighted averaging (OWA) operator in the same formulation. Therefore, we are able to consider the degree of optimism of the decision maker and grades of importance in the same approach. By using interval numbers, we are able to represent the information considering the best and worst possible results so the decision maker gets a more complete view of the decision problem. We develop an illustrative example of the proposed scheme in the selection of students in interdisciplinary studies. We see that with the use of the UIGHA operator we get a more complete representation of the selection problem. Then, the decision maker is able to consider a wide range of alternatives depending on his interests. We also show other potential applications that could be used by using the UIGHA operator in educational problems about selection of different types of resources such as students, professors, etc.

Keywords: Decision making, Selection of students, Uncertainty, Aggregation operators.

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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: Amnah E. Shammahy

Abstract:

In this paper, we study the boundedness and compactness of the weighted composition operator W_u,φ, which is induced by an holomorphic function u and holomorphic self-map φ, acting between the N_K-space and the Bers-type space H^∞_α on the unit disk.

Keywords: Weighted composition operators, NK-space, Bers-type space.

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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: Jing Liu

Abstract:

In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent weighted geometric(HFDWG) operators based on different weight vectors, and the most prominent characteristic of these operators is that the associated weights only depend on the aggregated hesitant fuzzy numbers and can relieve the influence of unfair hesitant fuzzy numbers on the aggregated results by assigning low weights to those “false” and “biased” ones. Some examples are given to illustrated the efficiency of the proposed operators.

Keywords: Hesitant fuzzy numbers, hesitant fuzzy dependent weighted averaging(HFDWA) operators, hesitant fuzzy dependent weighted geometric(HFDWG) operators.

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Authors: Shouzhen Zeng

Abstract:

We present a new intuitionistic fuzzy aggregation operator called the intuitionistic fuzzy ordered weighted averaging-weighted average (IFOWAWA) operator. The main advantage of the IFOWAWA operator is that it unifies the OWA operator with the WA in the same formulation considering the degree of importance that each concept has in the aggregation. Moreover, it is able to deal with an uncertain environment that can be assessed with intuitionistic fuzzy numbers. We study some of its main properties and we see that it has a lot of particular cases such as the intuitionistic fuzzy weighted average (IFWA) and the intuitionistic fuzzy OWA (IFOWA) operator. Finally, we study the applicability of the new approach on a financial decision making problem concerning the selection of financial strategies.

Keywords: Intuitionistic fuzzy numbers, Weighted average, OWA operator, Financial decision making

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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: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Ming-Hui Lee, Tsung-Chien Chen, Tsu-Ping Yu, Horng-Yuan Jang

Abstract:

The innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux of the multilayer materials as presented in this paper. The feasibility of this method can be verified by adopting the temperature measurement experiment. The experiment modular may be designed by using the copper sample which is stacked up 4 aluminum samples with different thicknesses. Furthermore, the bottoms of copper samples are heated by applying the standard heat source, and the temperatures on the tops of aluminum are measured by using the thermocouples. The temperature measurements are then regarded as the inputs into the presented method to estimate the heat flux in the bottoms of copper samples. The influence on the estimation caused by the temperature measurement of the sample with different thickness, the processing noise covariance Q, the weighting factor γ , the sampling time interval Δt , and the space discrete interval Δx , will be investigated by utilizing the experiment verification. The results show that this method is efficient and robust to estimate the unknown time-varying heat input of the multilayer materials.

Keywords: Multilayer Materials, Input Estimation Method, IHCP, Heat Flux.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: Miin-Shen Yang, Yee-Shan Pan

Abstract:

Although there have been many researches in cluster analysis to consider on feature weights, little effort is made on sample weights. Recently, Yu et al. (2011) considered a probability distribution over a data set to represent its sample weights and then proposed sample-weighted clustering algorithms. In this paper, we give a sample-weighted version of generalized fuzzy clustering regularization (GFCR), called the sample-weighted GFCR (SW-GFCR). Some experiments are considered. These experimental results and comparisons demonstrate that the proposed SW-GFCR is more effective than the most clustering algorithms.

Keywords: Clustering; fuzzy c-means, fuzzy clustering, sample weights, regularization.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

Different types of aggregation operators such as the ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and the normalized Hamming distance are studied. We introduce the use of the OWA operator in generalized distances such as the quasiarithmetic distance. We will call these new distance aggregation the ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator. We develop a general overview of this type of generalization and study some of their main properties such as the distinction between descending and ascending orders. We also consider different families of Quasi-OWAD operators such as the Minkowski ordered weighted averaging distance (MOWAD) operator, the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized quasi-arithmetic distance, etc.

Keywords: Aggregation operators, Distance measures, Quasi- OWA operator.

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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: S.Aranganayagi, K.Thangavel

Abstract:

K-Modes is an extension of K-Means clustering algorithm, developed to cluster the categorical data, where the mean is replaced by the mode. The similarity measure proposed by Huang is the simple matching or mismatching measure. Weight of attribute values contribute much in clustering; thus in this paper we propose a new weighted dissimilarity measure for K-Modes, based on the ratio of frequency of attribute values in the cluster and in the data set. The new weighted measure is experimented with the data sets obtained from the UCI data repository. The results are compared with K-Modes and K-representative, which show that the new measure generates clusters with high purity.

Keywords: Clustering, categorical data, K-Modes, weighted dissimilarity measure

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Authors: Petra Heribanová, Jaroslav Polec, Michal Martinovič

Abstract:

In this paper we propose a new content-weighted method for full reference (FR) video quality control using a region of interest (ROI) and wherein two-component weighted metrics for Deaf People Video Communication. In our approach, an image is partitioned into region of interest and into region "dry-as-dust", then region of interest is partitioned into two parts: edges and background (smooth regions), while the another methods (metrics) combined and weighted three or more parts as edges, edges errors, texture, smooth regions, blur, block distance etc. as we proposed. Using another idea that different image regions from deaf people video communication have different perceptual significance relative to quality. Intensity edges certainly contain considerable image information and are perceptually significant.

Keywords: Video quality assessment, weighted MSE.

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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: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Maximum Weighted Independent Set (MWIS) problem is a classic graph optimization NP-hard problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the MWIS problem is to find a vertex set S V whose total weight is maximum subject to no two vertices in S are adjacent. This paper presents a novel approach to approximate the MWIS of a graph using minimum weighted vertex cover of the graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the proposed algorithm can yield better solutions than other existing algorithms found in the literature for solving the MWIS.

Keywords: weighted independent set, vertex cover, vertex support, heuristic, NP - hard problem.

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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: Dr. L. Arockiam, A. Aloysius

Abstract:

In general, class complexity is measured based on any one of these factors such as Line of Codes (LOC), Functional points (FP), Number of Methods (NOM), Number of Attributes (NOA) and so on. There are several new techniques, methods and metrics with the different factors that are to be developed by the researchers for calculating the complexity of the class in Object Oriented (OO) software. Earlier, Arockiam et.al has proposed a new complexity measure namely Extended Weighted Class Complexity (EWCC) which is an extension of Weighted Class Complexity which is proposed by Mishra et.al. EWCC is the sum of cognitive weights of attributes and methods of the class and that of the classes derived. In EWCC, a cognitive weight of each attribute is considered to be 1. The main problem in EWCC metric is that, every attribute holds the same value but in general, cognitive load in understanding the different types of attributes cannot be the same. So here, we are proposing a new metric namely Attribute Weighted Class Complexity (AWCC). In AWCC, the cognitive weights have to be assigned for the attributes which are derived from the effort needed to understand their data types. The proposed metric has been proved to be a better measure of complexity of class with attributes through the case studies and experiments

Keywords: Software Complexity, Attribute Weighted Class Complexity, Weighted Class Complexity, Data Type

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study some of their main properties. We also analyze a wide range of particular cases found in this generalization such as the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized Minkowski distance, etc. Finally, we give an illustrative example of the new approach where we can see the different results obtained by using different aggregation operators.

Keywords: Aggregation operators, Minkowski distance, OWA operators, Selection of strategies.

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

Abstract:

Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: Non-Linear Wilcoxon, robust estimation, Variogram estimation.

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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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