Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 151

Search results for: interval neutrosophic sets

151 Lithofacies Classification from Well Log Data Using Neural Networks, Interval Neutrosophic Sets and Quantification of Uncertainty

Authors: Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong

Abstract:

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

Keywords: Multiclass classification, feed-forward backpropagation neural network, interval neutrosophic sets, uncertainty.

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150 Entropy Measures on Neutrosophic Soft Sets and Its Application in Multi Attribute Decision Making

Authors: I. Arockiarani

Abstract:

The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.

Keywords: Entropy measure, Hausdorff distance, neutrosophic set, soft set.

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149 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

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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148 A New Objective Weight on Interval Type-2 Fuzzy Sets

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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147 Comparative Study of Intuitionistic and Generalized Neutrosophic Soft Sets

Authors: Debabrata Mandal

Abstract:

The aim of this paper is to define several operations such as Intersection, Union, OR, AND operations of intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Maji and compare these with intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Said et al via examples. At the end of the paper, a new concept - extension is introduced, which can be used to refine our choices in case of decision making.

Keywords: AND, OR, Union, Intersection, Extension, Decision making.

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146 Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

Authors: K. M. Alsager, N. O. Alshehri

Abstract:

In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: Single valued neutrosophic hesitant set, single valued neutrosophic hesitant relation, single valued neutrosophic hesitant fuzzy rough set, decision making method.

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145 A Family of Entropies on Interval-valued Intuitionistic Fuzzy Sets and Their Applications in Multiple Attribute Decision Making

Authors: Min Sun, Jing Liu

Abstract:

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFS. Firstly, we propose a family of entropies on IvIFS with a parameter λ ∈ [0, 1], which generalize two entropy measures defined independently by Zhang and Wei, for IvIFS, and then we prove that the new entropy is an increasing function with respect to the parameter λ. Furthermore, a new multiple attribute decision making (MADM) method using entropy-based attribute weights is proposed to deal with the decision making situations where the alternatives on attributes are expressed by IvIFS and the attribute weights information is unknown. Finally, a numerical example is given to illustrate the applications of the proposed method.

Keywords: Interval-valued intuitionistic fuzzy sets, intervalvalued intuitionistic fuzzy entropy, multiple attribute decision making

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144 On Some Properties of Interval Matrices

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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143 On Solution of Interval Valued Intuitionistic Fuzzy Assignment Problem Using Similarity Measure and Score Function

Authors: Gaurav Kumar, Rakesh Kumar Bajaj

Abstract:

The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), zpqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree Fpq instead of  and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.

Keywords: Assignment problem, Interval-valued Intuitionistic Fuzzy Sets, Similarity Measures, score function.

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142 Comparison of Two Interval Models for Interval-Valued Differential Evolution

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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141 The Diameter of an Interval Graph is Twice of its Radius

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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140 Using Interval Constrained Petri Nets for the Fuzzy Regulation of Quality: Case of Assembly Process Mechanics

Authors: Nabli L., Dhouibi H., Collart Dutilleul S., Craye E.

Abstract:

The indistinctness of the manufacturing processes makes that a parts cannot be realized in an absolutely exact way towards the specifications on the dimensions. It is thus necessary to assume that the effectively realized product has to belong in a very strict way to compatible intervals with a correct functioning of the parts. In this paper we present an approach based on mixing tow different characteristics theories, the fuzzy system and Petri net system. This tool has been proposed to model and control the quality in an assembly system. A robust command of a mechanical assembly process is presented as an application. This command will then have to maintain the specifications interval of parts in front of the variations. It also illustrates how the technique reacts when the product quality is high, medium, or low.

Keywords: Petri nets, production rate, performance evaluation, tolerant system, fuzzy sets.

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139 Some Results on Interval-Valued Fuzzy BG-Algebras

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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138 Classifying and Predicting Efficiencies Using Interval DEA Grid Setting

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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137 Regular Generalized Star Star closed sets in Bitopological Spaces

Authors: K. Kannan, D. Narasimhan, K. Chandrasekhara Rao, R. Ravikumar

Abstract:

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.

Keywords: τ1τ2-regular closed sets, τ1τ2-regular open sets, τ1τ2-regular generalized closed sets, τ1τ2-regular generalized star closed sets, τ1τ2-regular generalized star star closed sets.

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136 Solution of Interval-valued Manufacturing Inventory Models With Shortages

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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135 Comparing Interval Estimators for Reliability in a Dependent Set-up

Authors: Alessandro Barbiero

Abstract:

In this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these intervals are empirically checked through a simulation study. An application to real paired data is also provided.

Keywords: Approximate estimators, asymptotic theory, confidence interval, Monte Carlo simulations, stress-strength, variance estimation.

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134 Using Interval Trees for Approximate Indexing of Instances

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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133 Investigations on Some Operations of Soft Sets

Authors: Xun Ge, Songlin Yang

Abstract:

Soft set theory was initiated by Molodtsov in 1999. In the past years, this theory had been applied to many branches of mathematics, information science and computer science. In 2003, Maji et al. introduced some operations of soft sets and gave some operational rules. Recently, some of these operational rules are pointed out to be not true. Furthermore, Ali et al., in their paper, introduced and discussed some new operations of soft sets. In this paper, we further investigate these operational rules given by Maji et al. and Ali et al.. We obtain some sufficient-necessary conditions such that corresponding operational rules hold and give correct forms for some operational rules. These results will be help for us to use rightly operational rules of soft sets in research and application of soft set theory.

Keywords: Soft sets, union, intersection, complement.

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132 Confidence Intervals for the Difference of Two Normal Population Variances

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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131 Computational Aspects of Regression Analysis of Interval Data

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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130 3D Brain Tumor Segmentation Using Level-Sets Method and Meshes Simplification from Volumetric MR Images

Authors: K. Aloui, M. S. Naceur

Abstract:

The main objective of this paper is to provide an efficient tool for delineating brain tumors in three-dimensional magnetic resonance images. To achieve this goal, we use basically a level-sets approach to delineating three-dimensional brain tumors. Then we introduce a compression plan of 3D brain structures based for the meshes simplification, adapted for time to the specific needs of the telemedicine and to the capacities restricted by network communication. We present here the main stages of our system, and preliminary results which are very encouraging for clinical practice.

Keywords: Medical imaging, level-sets, compression, meshess implification, telemedicine.

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129 A Rough Sets Approach for Relevant Internet/Web Online Searching

Authors: Erika Martinez Ramirez, Rene V. Mayorga

Abstract:

The internet is constantly expanding. Identifying web links of interest from web browsers requires users to visit each of the links listed, individually until a satisfactory link is found, therefore those users need to evaluate a considerable amount of links before finding their link of interest; this can be tedious and even unproductive. By incorporating web assistance, web users could be benefited from reduced time searching on relevant websites. In this paper, a rough set approach is presented, which facilitates classification of unlimited available e-vocabulary, to assist web users in reducing search times looking for relevant web sites. This approach includes two methods for identifying relevance data on web links based on the priority and percentage of relevance. As a result of these methods, a list of web sites is generated in priority sequence with an emphasis of the search criteria.

Keywords: Web search, Web Mining, Rough Sets, Web Intelligence, Intelligent Portals, Relevance.

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128 Products in Early Development Phases: Ecological Classification and Evaluation Using an Interval Arithmetic Based Calculation Approach

Authors: Helen L. Hein, Joachim Schwarte

Abstract:

As a pillar of sustainable development, ecology has become an important milestone in research community, especially due to global challenges like climate change. The ecological performance of products can be scientifically conducted with life cycle assessments. In the construction sector, significant amounts of CO2 emissions are assigned to the energy used for building heating purposes. Therefore, sustainable construction materials for insulating purposes are substantial, whereby aerogels have been explored intensively in the last years due to their low thermal conductivity. Therefore, the WALL-ACE project aims to develop an aerogel-based thermal insulating plaster that would achieve minor thermal conductivities. But as in the early stage of development phases, a lot of information is still missing or not yet accessible, the ecological performance of innovative products bases increasingly on uncertain data that can lead to significant deviations in the results. To be able to predict realistically how meaningful the results are and how viable the developed products may be with regard to their corresponding respective market, these deviations however have to be considered. Therefore, a classification method is presented in this study, which may allow comparing the ecological performance of modern products with already established and competitive materials. In order to achieve this, an alternative calculation method was used that allows computing with lower and upper bounds to consider all possible values without precise data. The life cycle analysis of the considered products was conducted with an interval arithmetic based calculation method. The results lead to the conclusion that the interval solutions describing the possible environmental impacts are so wide that the result usability is limited. Nevertheless, a further optimization in reducing environmental impacts of aerogels seems to be needed to become more competitive in the future.

Keywords: Aerogel-based, insulating material, early develop¬ment phase, interval arithmetic.

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127 Particle Swarm Optimization with Interval-valued Genotypes and Its Application to Neuroevolution

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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126 A Contractor for the Symmetric Solution Set

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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125 Some Clopen Sets in the Uniform Topology on BCI-algebras

Authors: A. Hasankhani, H. Saadat, M. M. Zahedi

Abstract:

In this paper some properties of the uniformity topology on a BCI-algebras are discussed.

Keywords: (Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

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124 Automated Knowledge Engineering

Authors: Sandeep Chandana, Rene V. Mayorga, Christine W. Chan

Abstract:

This article outlines conceptualization and implementation of an intelligent system capable of extracting knowledge from databases. Use of hybridized features of both the Rough and Fuzzy Set theory render the developed system flexibility in dealing with discreet as well as continuous datasets. A raw data set provided to the system, is initially transformed in a computer legible format followed by pruning of the data set. The refined data set is then processed through various Rough Set operators which enable discovery of parameter relationships and interdependencies. The discovered knowledge is automatically transformed into a rule base expressed in Fuzzy terms. Two exemplary cancer repository datasets (for Breast and Lung Cancer) have been used to test and implement the proposed framework.

Keywords: Knowledge Extraction, Fuzzy Sets, Rough Sets, Neuro–Fuzzy Systems, Databases

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123 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

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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122 The Effects of Eight Weeks of Interval Endurance Training on hs-CRP Levels and Anthropometric Parameters in Overweight Men

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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