**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**367

# Search results for: interval arithmetic.

##### 367 On Some Properties of Interval Matrices

**Authors:**
K. Ganesan

**Abstract:**

**Keywords:**
Interval arithmetic,
Interval matrix,
linear equations.

##### 366 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.

##### 365 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.

##### 364 Two Different Computing Methods of the Smith Arithmetic Determinant

**Authors:**
Xing-Jian Li,
Shen Qu

**Abstract:**

The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.

**Keywords:**
Elementary row transformation,
Euler function,
Matrix decomposition,
Smith arithmetic determinant.

##### 363 A Processor with Dynamically Reconfigurable Circuit for Floating-Point Arithmetic

**Authors:**
Yukinari Minagi ,
Akinori Kanasugi

**Abstract:**

**Keywords:**
dynamic reconfiguration,
floating-point arithmetic,
double precision,
FPGA

##### 362 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 CO_{2} 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.

##### 361 An Interval Type-2 Dual Fuzzy Polynomial Equations and Ranking Method of Fuzzy Numbers

**Authors:**
Nurhakimah Ab. Rahman,
Lazim Abdullah

**Abstract:**

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

**Keywords:**
Dual fuzzy polynomial equations,
Interval type-2,
Ranking method,
Value.

##### 360 A New Approach to Design an Efficient CIC Decimator Using Signed Digit Arithmetic

**Authors:**
Vishal Awasthi,
Krishna Raj

**Abstract:**

Any digital processing performed on a signal with larger nyquist interval requires more computation than signal processing performed on smaller nyquist interval. The sampling rate alteration generates the unwanted effects in the system such as spectral aliasing and spectral imaging during signal processing. Multirate-multistage implementation of digital filter can result a significant computational saving than single rate filter designed for sample rate conversion. In this paper, we presented an efficient cascaded integrator comb (CIC) decimation filter that perform fast down sampling using signed digit adder algorithm with compensated frequency droop that arises due to aliasing effect during the decimation process. This proposed compensated CIC decimation filter structure with a hybrid signed digit (HSD) fast adder provide an improved performance in terms of down sampling speed by 65.15% than ripple carry adder (RCA) and reduced area and power by 57.5% and 0.01 % than signed digit (SD) adder algorithms respectively.

**Keywords:**
Sampling rate conversion,
Multirate Filtering,
Compensation Theory,
Decimation filter,
CIC filter,
Redundant signed digit arithmetic,
Fast adders.

##### 359 A Dynamically Reconfigurable Arithmetic Circuit for Complex Number and Double Precision Number

**Authors:**
Haruo Shimada,
Akinori Kanasugi

**Abstract:**

**Keywords:**
arithmetic circuit,
complex number,
double precision,
dynamic reconfiguration

##### 358 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.

##### 357 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.

##### 356 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

**Authors:**
Swapnil Gupta,
C. Pandu Rangan

**Abstract:**

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

##### 355 EEG Correlates of Trait and Mathematical Anxiety during Lexical and Numerical Error-Recognition Tasks

**Authors:**
Alexander N. Savostyanov,
Tatiana A. Dolgorukova,
Elena A. Esipenko,
Mikhail S. Zaleshin,
Margherita Malanchini,
Anna V. Budakova,
Alexander E. Saprygin,
Tatiana A. Golovko,
Yulia V. Kovas

**Abstract:**

**Keywords:**
EEG,
brain activity,
lexical and numerical error-recognition
tasks,
mathematical and trait anxiety.

##### 354 A Reduced-Bit Multiplication Algorithm for Digital Arithmetic

**Authors:**
Harpreet Singh Dhillon,
Abhijit Mitra

**Abstract:**

A reduced-bit multiplication algorithm based on the ancient Vedic multiplication formulae is proposed in this paper. Both the Vedic multiplication formulae, Urdhva tiryakbhyam and Nikhilam, are first discussed in detail. Urdhva tiryakbhyam, being a general multiplication formula, is equally applicable to all cases of multiplication. It is applied to the digital arithmetic and is shown to yield a multiplier architecture which is very similar to the popular array multiplier. Due to its structure, it leads to a high carry propagation delay in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in the multiplication of large numbers as it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and is further optimized by use of some general arithmetic operations such as expansion and bit-shifting to take advantage of bit-reduction in multiplication. We illustrate the proposed algorithm by reducing a general 4x4-bit multiplication to a single 2 x 2-bit multiplication operation.

**Keywords:**
Multiplication,
algorithm,
Vedic mathematics,
digital
arithmetic,
reduced-bit.

##### 353 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.

##### 352 Membership Surface and Arithmetic Operations of Imprecise Matrix

**Authors:**
Dhruba Das

**Abstract:**

**Keywords:**
Imprecise number,
Imprecise vector,
Membership
surface,
Imprecise matrix.

##### 351 Solution of Interval-valued Manufacturing Inventory Models With Shortages

**Authors:**
Susovan Chakrabortty,
Madhumangal Pal,
Prasun Kumar Nayak

**Abstract:**

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

##### 350 Implementation and Analysis of Elliptic Curve Cryptosystems over Polynomial basis and ONB

**Authors:**
Yong-Je Choi,
Moo-Seop Kim,
Hang-Rok Lee,
Ho-Won Kim

**Abstract:**

**Keywords:**
Elliptic Curve Cryptosystem,
Crypto Algorithm,
Polynomial Basis,
Optimal Normal Basis,
Security.

##### 349 OWA Operators in Generalized Distances

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

**Abstract:**

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

##### 348 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.

##### 347 On Simple Confidence Intervals for the Normal Mean with Known Coefficient of Variation

**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.

##### 346 Ranking DMUs by Ideal PPS in Data Envelopment Analysis

**Authors:**
V.Rezaie,
M.Khanmohammady

**Abstract:**

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

##### 345 Classifying and Predicting Efficiencies Using Interval DEA Grid Setting

**Authors:**
Yiannis G. Smirlis

**Abstract:**

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

##### 344 Digital Redesign of Interval Systems via Particle Swarm Optimization

**Authors:**
Chen-Chien Hsu,
Chun-Hui Gao

**Abstract:**

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

##### 343 Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation

**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.

##### 342 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.

##### 341 Switching Rule for the Exponential Stability and Stabilization of Switched Linear Systems with Interval Time-varying Delays

**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.

##### 340 Approximate Confidence Interval for Effect Size Base on Bootstrap Resampling Method

**Authors:**
S. Phanyaem

**Abstract:**

**Keywords:**
Effect size,
confidence interval,
Bootstrap Method.

##### 339 An Algorithm Proposed for FIR Filter Coefficients Representation

**Authors:**
Mohamed Al Mahdi Eshtawie,
Masuri Bin Othman

**Abstract:**

Finite impulse response (FIR) filters have the advantage of linear phase, guaranteed stability, fewer finite precision errors, and efficient implementation. In contrast, they have a major disadvantage of high order need (more coefficients) than IIR counterpart with comparable performance. The high order demand imposes more hardware requirements, arithmetic operations, area usage, and power consumption when designing and fabricating the filter. Therefore, minimizing or reducing these parameters, is a major goal or target in digital filter design task. This paper presents an algorithm proposed for modifying values and the number of non-zero coefficients used to represent the FIR digital pulse shaping filter response. With this algorithm, the FIR filter frequency and phase response can be represented with a minimum number of non-zero coefficients. Therefore, reducing the arithmetic complexity needed to get the filter output. Consequently, the system characteristic i.e. power consumption, area usage, and processing time are also reduced. The proposed algorithm is more powerful when integrated with multiplierless algorithms such as distributed arithmetic (DA) in designing high order digital FIR filters. Here the DA usage eliminates the need for multipliers when implementing the multiply and accumulate unit (MAC) and the proposed algorithm will reduce the number of adders and addition operations needed through the minimization of the non-zero values coefficients to get the filter output.

**Keywords:**
Pulse shaping Filter,
Distributed Arithmetic,
Optimization algorithm.

##### 338 Autonomous Vehicle Navigation Using Harmonic Functions via Modified Arithmetic Mean Iterative Method

**Authors:**
Azali Saudi,
Jumat Sulaiman

**Abstract:**

**Keywords:**
Modified Arithmetic Mean method,
Harmonic
functions,
Laplace’s equation,
path planning.