Search results for: multiple choice objectives

Authors: Jihye Jeon

Abstract:

This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: Multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon.

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Authors: R.Balamurugan, S.Subramanian

Abstract:

This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems.

Keywords: Multiple fuels, power economic dispatch, selfadaptivedifferential evolution and valve-point effects.

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Authors: Bijaya Krushna Mangaraj, Deepak Kumar Das

Abstract:

Sustainability in rural production system can only be achieved if it can suitably satisfy the local requirement as well as the outside demand with the changing time. With the increased pressure from the food sector in a globalised world, the agrarian economy needs to re-organise its cultivable land system to be compatible with new management practices as well as the multiple needs of various stakeholders and the changing resource scenario. An attempt has been made to transform this problem into a multi-objective decisionmaking problem considering various objectives, resource constraints and conditional constraints. An interactive fuzzy multi-objective programming approach has been used for such a purpose taking a case study in Indian context to demonstrate the validity of the method.

Keywords: Land re-organisation, Crop planning, Multiobjective Decision-Making, Fuzzy Goal Programming.

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Authors: Ivan C. Mustakerov, Daniela I. Borissova

Abstract:

The paper proposes an approach for design of modular systems based on original technique for modeling and formulation of combinatorial optimization problems. The proposed approach is described on the example of personal computer configuration design. It takes into account the existing compatibility restrictions between the modules and can be extended and modified to reflect different functional and users- requirements. The developed design modeling technique is used to formulate single objective nonlinear mixedinteger optimization tasks. The practical applicability of the developed approach is numerically tested on the basis of real modules data. Solutions of the formulated optimization tasks define the optimal configuration of the system that satisfies all compatibility restrictions and user requirements.

Keywords: Constrained discrete combinatorial choice, modular systems design, optimization problem, PC configuration.

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Authors: C. Ardil

Abstract:

In this paper, composite programming is discussed for aircraft evaluation and selection problem using the multiple criteria decision analysis method. The decision criteria and aircraft alternatives were identified from the literature review. The importance of criteria weights was determined by the standard deviation method. The proposed model is applied to a practical decision problem for evaluating and selecting advanced jet trainer and light attack aircraft. The proposed technique gives robust and efficient results in modeling multiple criteria decisions. As a result of composite programming analysis, Hürjet, an advanced jet trainer and light attack aircraft alternative (a3), was chosen as the most suitable aircraft candidate.  

Keywords: composite programming, additive weighted model, multiplicative weighted model, multiple criteria decision making analysis, MCDMA, aircraft selection, advanced jet trainer and light attack aircraft, M-346, FA-50, Hürjet

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Authors: Rania Minkara, Jean-Pierre Dubois

Abstract:

The major problem that wireless communication systems undergo is multipath fading caused by scattering of the transmitted signal. However, we can treat multipath propagation as multiple channels between the transmitter and receiver to improve the signal-to-scattering-noise ratio. While using Single Input Multiple Output (SIMO) systems, the diversity receivers extract multiple signal branches or copies of the same signal received from different channels and apply gain combining schemes such as Root Mean Square Gain Combining (RMSGC). RMSGC asymptotically yields an identical performance to that of the theoretically optimal Maximum Ratio Combining (MRC) for values of mean Signal-to- Noise-Ratio (SNR) above a certain threshold value without the need for SNR estimation. This paper introduces an improvement of RMSGC using two different issues. We found that post-detection and de-noising the received signals improve the performance of RMSGC and lower the threshold SNR.

Keywords: Bit error rate, de-noising, pre-detection, root-meansquare gain combining, single-input multiple-output channels.

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Authors: Charalampos Saridakis, Stelios Tsafarakis

Abstract:

Although environmental concern is on the rise across Europe, current market data indicate that adoption rates of environmentally friendly vehicles remain extremely low. Against this background, the aim of this paper is to a) assess preferences of European consumers for clean-fuel cars and their characteristics and b) design car lines that optimize the combination of fuel types among models in the line-up. In this direction, the authors introduce a new evolutionary mechanism and implement it to stated-preference data derived from a large-scale choice-based conjoint experiment that measures consumer preferences for various factors affecting clean-fuel vehicle (CFV) adoption. The proposed two-step methodology provides interesting insights into how new and existing fuel-types can be combined in a car line that maximizes customer satisfaction.

Keywords: Clean-fuel vehicles, product line design, conjoint analysis, choice experiment, differential evolution.

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Authors: Yatin Wadhawan, Clifford Neuman, Anas Al Majali

Abstract:

In this paper, we evaluate the resilience of the smart grid system in the presence of multiple cyber-physical attacks on its distinct functional components. We discuss attack-defense scenarios and their effect on smart grid resilience. Through contingency simulations in the Network and PowerWorld Simulator, we analyze multiple cyber-physical attacks that propagate from the cyber domain to power systems and discuss how such attacks destabilize the underlying power grid. The analysis of such simulations helps system administrators develop more resilient systems and improves the response of the system in the presence of cyber-physical attacks.

Keywords: Smart grid, resilience, gas pipeline, cyber-physical attack, security.

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Authors: Do-Jin Jang, Sung-Ah Kim

Abstract:

A kinetic façade responds to user requirements and environmental conditions.  In designing a kinetic façade, kinetic patterns play a key role in determining its performance. This paper proposes a biomimetic method for the multi-objective optimization for kinetic façade design. The autonomous decentralized control system is combined with flocking algorithm. The flocking agents are autonomously reacting to sensor values and bring about kinetic patterns changing over time. A series of experiments were conducted to verify the potential and limitations of the flocking based decentralized control. As a result, it could show the highest performance balancing multiple objectives such as solar radiation and openness among the comparison group.

Keywords: Biomimicry, flocking algorithm, autonomous decentralized control, multi-objective optimization.

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Authors: Shigeaki Sakurai, Ryohei Orihara

Abstract:

This paper proposes a new method for analyzing textual data. The method deals with items of textual data, where each item is described based on various viewpoints. The method acquires 2- class classification models of the viewpoints by applying an inductive learning method to items with multiple viewpoints. The method infers whether the viewpoints are assigned to the new items or not by using the models. The method extracts expressions from the new items classified into the viewpoints and extracts characteristic expressions corresponding to the viewpoints by comparing the frequency of expressions among the viewpoints. This paper also applies the method to questionnaire data given by guests at a hotel and verifies its effect through numerical experiments.

Keywords: Text mining, Multiple viewpoints, Differential analysis, Questionnaire data

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Authors: C. Ardil

Abstract:

Uncertainty set theory is a generalization of fuzzy set theory and intuitionistic fuzzy set theory. It serves as an effective tool for dealing with inconsistent, imprecise, and vague information. The technique for order preference by similarity to ideal solution (TOPSIS) method is a multiple-attribute method used to identify solutions from a finite set of alternatives. It simultaneously minimizes the distance from an ideal point and maximizes the distance from a nadir point. In this paper, an extension of the TOPSIS method for multiple attribute group decision-making (MAGDM) based on uncertainty sets is presented. In uncertainty decision analysis, decision-makers express information about attribute values and weights using uncertainty numbers to select the best stealth combat aircraft.

Keywords: Uncertainty set, stealth combat aircraft selection multiple criteria decision-making analysis, MCDM, uncertainty decision analysis, TOPSIS

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Authors: Arash Derakhshanmehr

Abstract:

Nowadays, efficiency, effectiveness and economy are regarded as the main objectives of managers and the secret of the continuity of an organization in competing economy. In such competing settings, it is essential that the management of an organization has not been neglected and been obliged to identify quickly the opportunities for improving the operation of organization and remove the shortcomings of their managed system in order to use the opportunities for development. Operational auditing is a useful tool for system adjustment and leading an organization toward its objectives. Operational auditing is indeed a viewpoint which identifies the causes of insufficiencies, weaknesses and deficiencies of system and plans to eliminate them. Operational auditing is useful in the effectiveness and optimization of executive managers- decisions and increasing the efficiency and economy of their performance in the future and prevents the waste and incorrect use of resources. Evidence shows that operational auditing is used at a limited level in Iran. This matter raises some questions like the following ones in the minds. Why do a limited number of corporations use operational auditing? Which factors can guarantee its full implementation? What obstacles are there in its implementation? The purpose of this article is to determine executive objectives, the operation domain of operational auditing, the components of operational auditing and the executive obstacles to operational auditing in Iran.

Keywords: Operational Auditing, Iran

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Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

Abstract:

Multimodal biometric systems integrate the data presented by multiple biometric sources, hence offering a better performance than the systems based on a single biometric modality. Although the coupling of biometric systems can be done at different levels, the fusion at the scores level is the most common since it has been proven effective than the rest of the fusion levels. However, the scores from different modalities are generally heterogeneous. A step of normalizing the scores is needed to transform these scores into a common domain before combining them. In this paper, we study the performance of several normalization techniques with various fusion methods in a context relating to the merger of three unimodal systems based on the face, the palmprint and the fingerprint. We also propose a new adaptive normalization method that takes into account the distribution of client scores and impostor scores. Experiments conducted on a database of 100 people show that the performances of a multimodal system depend on the choice of the normalization method and the fusion technique. The proposed normalization method has given the best results.

Keywords: Multibiometrics, Fusion, Score level, Score normalization, Adaptive normalization.

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Authors: Frantisek Jezek, Jan Sedlacek

Abstract:

This paper is concerned with the role strategic management plays in higher education and the methods it entails. Using the University of West Bohemia and the Czech Republic as examples, the paper describes the methods used in furthering strategic objectives within institutions and their different parts (faculties, institutes). The nature of the demands faced by the university dictates the need for a strategic framework which defines the basic objectives and parameters of tertiary education and research in a local, regional and national context. Sharing strategies with a wider range of actors (universities, cities, regions, the practical sphere) is key to laying the foundations for more efficient cooperation.

Keywords: Strategy, strategic plan, university, university environment.

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

Abstract:

The paper describes an approach for defining of k-best night vision devices based on multi-criteria mixed-integer optimization modeling. The parameters of night vision devices are considered as criteria that have to be optimized. Using different user preferences for the relative importance between parameters different choice of k-best devices can be defined. An ideal device with all of its parameters at their optimum is used to determine how far the particular device from the ideal one is. A procedure for evaluation of deviation between ideal solution and k-best solutions is presented. The applicability of the proposed approach is numerically illustrated using real night vision devices data. The proposed approach contributes to quality of decisions about choice of night vision devices by making the decision making process more certain, rational and efficient. 

Keywords: K-best devices, mixed-integer model, multi-criteria problem, night vision devices.

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Authors: J.W. Xiang, M. Liang

Abstract:

This paper presents a method to detect multiple cracks based on frequency information. When a structure is subjected to dynamic or static loads, cracks may develop and the modal frequencies of the cracked structure may change. To detect cracks in a structure, we construct a high precision wavelet finite element (EF) model of a certain structure using the B-spline wavelet on the interval (BSWI). Cracks can be modeled by rotational springs and added to the FE model. The crack detection database will be obtained by solving that model. Then the crack locations and depths can be determined based on the frequency information from the database. The performance of the proposed method has been numerically verified by a rotor example.

Keywords: Rotor, frequency measurement, multiple cracks, wavelet finite element method, identification.

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Authors: Jin-Bao Zhao, Wei Deng

Abstract:

This paper aims at developing a multilevel fuzzy decision support model for urban rail transit planning schemes in China under the background that China is presently experiencing an unprecedented construction of urban rail transit. In this study, an appropriate model using multilevel fuzzy comprehensive evaluation method is developed. In the decision process, the followings are considered as the influential objectives: traveler attraction, environment protection, project feasibility and operation. In addition, consistent matrix analysis method is used to determine the weights between objectives and the weights between the objectives- sub-indictors, which reduces the work caused by repeated establishment of the decision matrix on the basis of ensuring the consistency of decision matrix. The application results show that multilevel fuzzy decision model can perfectly deal with the multivariable and multilevel decision process, which is particularly useful in the resolution of multilevel decision-making problem of urban rail transit planning schemes.

Keywords: Urban rail transit, planning schemes, multilevel fuzzy decision support model, consistent matrix analysis

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Authors: Shu-Chiao Yang, Jong-Jiann Shieh

Abstract:

A Simultaneous Multithreading (SMT) Processor is capable of executing instructions from multiple threads in the same cycle. SMT in fact was introduced as a powerful architecture to superscalar to increase the throughput of the processor. Simultaneous Multithreading is a technique that permits multiple instructions from multiple independent applications or threads to compete limited resources each cycle. While the fetch unit has been identified as one of the major bottlenecks of SMT architecture, several fetch schemes were proposed by prior works to enhance the fetching efficiency and overall performance. In this paper, we propose a novel fetch policy called queue situation identifier (QSI) which counts some kind of long latency instructions of each thread each cycle then properly selects which threads to fetch next cycle. Simulation results show that in best case our fetch policy can achieve 30% on speedup and also can reduce the data cache level 1 miss rate.

Keywords: SMT, QSI, DL1 miss rate.

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Authors: Mitsuhiro Taniyama, Yuu Hidaka, Masato Arai, Satoshi Kai, Hiromi Igawa, Hiroshi Yajima, Ryoichi Sasaki

Abstract:

Along with the progress of our information society, various risks are becoming increasingly common, causing multiple social problems. For this reason, risk communications for establishing consensus among stakeholders who have different priorities have become important. However, it is not always easy for the decision makers to agree on measures to reduce risks based on opposing concepts, such as security, privacy and cost. Therefore, we previously developed and proposed the “Multiple Risk Communicator" (MRC) with the following functions: (1) modeling the support role of the risk specialist, (2) an optimization engine, and (3) displaying the computed results. In this paper, MRC program version 1.0 is applied to the personal information leakage problem. The application process and validation of the results are discussed.

Keywords: Decision Making, Personal Information Leakage Problem, Risk Communication, Risk Management

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Authors: Mohd Shahriman B. Mohd Yunus, Mohd Hanif B. Jamaludin, Norain Bt. Bahror

Abstract:

The performance of an embedded grounding system is very important for the safe operation of electrical appliances and human beings. In principle, a safe grounding system has two objectives, which are to dissipate fault current without exceeding any operating and equipment limits and to ensure there is no risk of electric shock to humans in the vicinity of earthed facilities. The case studies in this paper present the calculating grounding resistance for multiple configurations of vertical and horizontally by using a simple and accurate formula. From the analytic calculated results, observed good/empirical relationship between the grounding resistance and length of the embedded grounding configurations. Moreover, the configurations of vertical and horizontal observed effectiveness of grounding resistance and good agreement on the reduction of grounding resistance values especially for vertical configuration.

Keywords: Grounding system, grounding resistance, soil resistivity, electrode geometry, configurations.

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Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: Approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median.

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Authors: Young-Seok Choi

Abstract:

We present a refined multiscale Shannon entropy for analyzing electroencephalogram (EEG), which reflects the underlying dynamics of EEG over multiple scales. The rationale behind this method is that neurological signals such as EEG possess distinct dynamics over different spectral modes. To deal with the nonlinear and nonstationary nature of EEG, the recently developed empirical mode decomposition (EMD) is incorporated, allowing a decomposition of EEG into its inherent spectral components, referred to as intrinsic mode functions (IMFs). By calculating the Shannon entropy of IMFs in a time-dependent manner and summing them over adaptive multiple scales, it results in an adaptive subscale entropy measure of EEG. Simulation and experimental results show that the proposed entropy properly reveals the dynamical changes over multiple scales.

Keywords: EEG, subscale entropy, Empirical mode decomposition, Intrinsic mode function.

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Authors: C. Ardil

Abstract:

This paper considers a comparative analysis of multiple criteria decision making analysis methods for strategic, tactical, and operational decisions in military fighter aircraft selection for the air force fleet planning. The evaluation criteria governing the decision analysis process are determined from the literature for the three existing military combat aircraft. Military fighter aircraft selection problem is structured using "preference analysis for reference ideal solution (PARIS)” approach in multiple criteria decision analysis (MCDMA). Systematic comparisons were made with existing MCDMA methods (PARIS, and TOPSIS) to verify the stability and accuracy of the results obtained. The proposed integrated MCDMA systematic approach is expected to address the issues encountered in the aircraft selection process. The comparative analysis results show that the proposed method is an effective and accurate tool that can help analysts make better strategic, tactical, and operational decisions.

Keywords: aircraft, military fighter aircraft selection, multiple criteria decision making, multiple criteria decision making analysis, mean weight, entropy weight, MCDMA, PARIS, TOPSIS, Saab Gripen, Dassault Rafale, Eurofighter Typhoon

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

Abstract:

Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE work parameters have fuzzy character. Hence consideration of fuzzy skewness and kurtosis coefficients is expedient. Investigation of the basic characteristics changes- dynamics of GTE work parameters allows drawing conclusion on necessity of the Fuzzy Statistical Analysis at preliminary identification of the engines' technical condition. Researches of correlation coefficients values- changes shows also on their fuzzy character. Therefore for models choice the application of the Fuzzy Correlation Analysis results is offered. At the information sufficiency is offered to use recurrent algorithm of aviation GTE technical condition identification (Hard Computing technology is used) on measurements of input and output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stageby- stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: S. Ali. Tajer, Babak H. Khalaj

Abstract:

This paper represents an investigation on how exploiting multiple transmit antennas by OFDM based wireless LAN subscribers can mitigate physical layer error rate. Then by comparing the Wireless LANs that utilize spatial diversity techniques with the conventional ones it will reveal how PHY and TCP throughputs behaviors are ameliorated. In the next step it will assess the same issues based on a cellular context operation which is mainly introduced as an innovated solution that beside a multi cell operation scenario benefits spatio-temporal signaling schemes as well. Presented simulations will shed light on the improved performance of the wide range and high quality wireless LAN services provided by the proposed approach.

Keywords: Multiple Input Multiple Output (MIMO), Orthogonal Frequency Division Multiplexing (OFDM), and WirelessLocal Area Network (WLAN).

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Authors: Xiang Zhang, David Rey, S. Travis Waller

Abstract:

Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: Parameter calibration, sequential quadratic programming, Stochastic User Equilibrium, traffic assignment, transportation planning.

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Authors: C. Ardil

Abstract:

Fuzzy set and intuitionistic fuzzy set are dealing with the imprecision and uncertainty inherent in a complex decision problem. However, sometimes these theories are not sufficient to model indeterminate and inconsistent information encountered in real-life problems. To overcome this insufficiency, the neutrosophic set, which is useful in practical applications, is proposed, triangular neutrosophic numbers and trapezoidal neutrosophic numbers are examined, their definitions and applications are discussed. In this study, a decision making algorithm is developed using neutrosophic set processes and an application is given in fighter aircraft selection as an example of a decision making problem. The estimation of the fighter aircraft selection with the neutrosophic multiple criteria decision analysis method is examined.  

Keywords: neutrosophic set, multiple criteria decision making analysis, fighter aircraft selection, MCDMA, neutrosophic numbers

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Authors: Feng Cheng Chang

Abstract:

A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000.

Keywords: Polynomial roots, greatest common divisor, Longhand polynomial division, Euclidean GCD Algorithm.

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Authors: C. Ardil

Abstract:

Multiple criteria decision making analysis (MCDMA) methods are applied to many real - life problems in different fields of engineering science and technology. The "preference analysis for reference ideal solution (PARIS)" method is proposed for an efficient MCDMA evaluation of decision problems. The multiple criteria aircraft evaluation approach is based on the integrated the mean weight, entropy weight, PARIS, and TOPSIS method, which eliminates the subjective importance weight assignment process. The evaluation criteria were identified from an extensive literature review of aircraft selection process. The aim of this study is to propose an efficient methodology for handling the aircraft selection process in which the proposed method solves effectively the MCDMA problem. A numerical example is presented to demonstrate the applicability and validity of the proposed MCDMA approach. 

Keywords: aircraft selection, aircraft, multiple criteria decision making, multiple criteria decision making analysis, mean weight, entropy weight, MCDMA, PARIS, TOPSIS, VIKOR, ELECTRE, PROMETHEE

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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