Search results for: generalized information criteria

Authors: Rana Rimawi, Ayman Baklizi

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Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: M. Y. Bakeir

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Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

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Authors: Oren Shtayermman

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The current investigation expended on research among parents caring for a child who is diagnosed with an autism spectrum disorder (ASD). An online web survey was used to collect data from 253 parents caring for a child with a diagnosis of ASD. Both parents reported on elevated levels of parental stress associated with caring for the child on the spectrum. In addition, lower levels of marital satisfaction were found in both parents. About 13% of the parents in the sample met the diagnostic criteria for Major Depressive Disorder and About 15% of the parents met the diagnostic criteria for Generalized Anxiety Disorder. Although the majority of the sample was females (94%) significant differences were found between males and females in relation to meeting the diagnostic criteria for Major Depressive Disorder and for Generalized Anxiety Disorder. Higher levels of stress were associated with higher number of Generalized Anxiety Disorder symptoms and higher number of Major Depressive Disorder symptoms. Findings from this study indicate how vulnerable parents and especially females are in relation to caring to a child diagnosed with ASD. Educational Objectives: At the conclusion of the paper, the readers should be able to: -Identify levels of stress and marital satisfaction among parents caring for a child diagnosed with autism spectrum disorder, -Recognize the impact of stress on the development of mental health issues, -Name the two most common mood and anxiety related disorders associated with caring for a child diagnosed with an autism spectrum disorder.

Keywords: autism, stress, parents, children

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Authors: Muqaddas Javed, Muhammad Hanif

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The generalized multivariate ratio and regression type estimators for population mean are suggested under multi-phase stratified systematic sampling (MPSSS) using multi auxiliary information. Estimators are developed under the two different situations of availability of auxiliary information. The expressions of bias and mean square error (MSE) are developed. Special cases of suggested estimators are also discussed and simulation study is conducted to observe the performance of estimators.

Keywords: generalized estimators, multi-phase sampling, stratified random sampling, systematic sampling

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Authors: Menghzheng Yao

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Generalized social trust among Chinese has been declining in the past few decades, making the search for its causes necessary. Drawing on the symbolic interaction theory and the 2012 Chinese General Social Survey data, this research investigated the impact of people’s socialization preferences and frequencies on their perceptions of generalized social trust in China. This research also took a preliminary step towards understanding the spatial differences of the generalized social trust using the ArcGIS software. The results show that respondents who interacted with their neighbors more frequently were more likely to have higher levels of perceptions of generalized social trust. Several demographics were also significantly related to perception of generalized social trust. Elderly and better educated Chinese and people with higher self-perceived social status were associated with greater levels of generalized social trust perception, while urban dwellers and religious respondents expressed lower levels of such perception. Implications for future research and policy are discussed.

Keywords: China, generalized social trust, symbolic interaction, ArcGIS

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Authors: Li-Zhi Liao

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The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported.

Keywords: central path, convex programming, generalized central path, interior point method

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Authors: Rada Somkhuean, Sa-aat Niwitpong, Suparat Niwitpong

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This paper presents the generalized p-values for testing the difference between two future population means when the variances are unknown, in both cases for when the variances are equal and unequal. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Keywords: generalized p-value, two future population means, upper bound, variances

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Authors: Mehmet Yörükoğlu, Serhat Aydın

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Since the discovery of the manuscript, mechanical methods for storing, transferring and using the information have evolved into digital methods over the time. In this process, libraries that are the center of the information have also become digitized and become accessible from anywhere and at any time in the world by taking on a structure that has no physical boundaries. In this context, some criteria for information obtained from digital libraries have become more important for users. This paper evaluates the user criteria from different perspectives that make a digital library more useful. The Step-Wise Weight Assessment Ratio Analysis-Weighted Aggregated Sum Product Assessment (SWARA-WASPAS) method is used with flexibility and easy calculation steps for the evaluation of digital library criteria. Three different digital libraries are evaluated by information technology experts according to five conflicting main criteria, ‘interface design’, ‘effects on users’, ‘services’, ‘user engagement’ and ‘context’. Finally, alternatives are ranked in descending order.

Keywords: digital library, multi criteria decision making, SWARA-WASPAS method

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Authors: Noora Al-Shanfari, M. Mazharul Islam

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The cumulative incidence function (CIF) is a fundamental approach for analyzing survival data in the presence of competing risks, which estimates the marginal probability for each competing event. Parametric modeling of CIF has the advantage of fitting various shapes of CIF and estimates the impact of covariates with maximum efficiency. To calculate the total CIF's covariate influence using a parametric model., it is essential to parametrize the baseline of the CIF. As the CIF is an improper function by nature, it is necessary to utilize an improper distribution when applying parametric models. The Gompertz distribution, which is an improper distribution, is limited in its applicability as it only accounts for monotone hazard shapes. The generalized Gompertz distribution, however, can adapt to a wider range of hazard shapes, including unimodal, bathtub, and monotonic increasing or decreasing hazard shapes. In this paper, the generalized Gompertz distribution is used to parametrize the baseline of the CIF, and the parameters of the proposed model are estimated using the maximum likelihood approach. The proposed model is compared with the existing Gompertz model using the Akaike information criterion. Appropriate statistical test procedures and model-fitting criteria will be used to test the adequacy of the model. Both models are applied to the ‘colon’ dataset, which is available in the “biostat3” package in R.

Keywords: competing risks, cumulative incidence function, improper distribution, parametric modeling, survival analysis

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Authors: A. K. Sethi, R. N. Patra, B. Nayak

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In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: bulk viscosity, lyra geometry, generalized chaplygin gas, cosmology

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Authors: M. H. M. Rashid

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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge transform

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Authors: H. Moalla, A. Frikha

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Multi-criteria decision aid methods consider decision problems where numerous alternatives are evaluated on several criteria. These methods are used to deal with perfect information. However, in practice, it is obvious that this information requirement is too much strict. In fact, the imperfect data provided by more or less reliable decision makers usually affect decision results since any decision is closely linked to the quality and availability of information. In this paper, a PROMETHEE-BELIEF approach is proposed to help multi-criteria decisions based on incomplete information. This approach solves problems with incomplete decision matrix and unknown weights within PROMETHEE method. On the base of belief function theory, our approach first determines the distributions of belief masses based on PROMETHEE’s net flows and then calculates weights. Subsequently, it aggregates the distribution masses associated to each criterion using Murphy’s modified combination rule in order to infer a global belief structure. The final action ranking is obtained via pignistic probability transformation. A case study of real-world application concerning the location of a waste treatment center from healthcare activities with infectious risk in the center of Tunisia is studied to illustrate the detailed process of the BELIEF-PROMETHEE approach.

Keywords: belief function theory, incomplete information, multiple criteria analysis, PROMETHEE method

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Authors: Eric Mensah, Carlos Mensah

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The road maintenance backlogs created as a result of deferred maintenance especially in developing countries has caused considerable deterioration of many road assets. This is usually due to difficulties encountered in selecting and prioritising maintainable roads based on objective criteria rather than some political or other less important criteria. In order to ensure judicious use of limited resources for road maintenance, five factors were identified as the most important criteria for road management within the study area. This was based on the judgements of 40 experts. The results were further used to develop weightings using the Multi-Criteria Decision Process (MCDP) to analyse and select road alternatives according to maintenance goal. Using Geographical Information Systems (GIS), maintainable roads were grouped using the Jenk’s natural breaks to allow for further prioritised in order of importance for display on a dashboard of maps, charts, and tables. This reduces the problems of subjective maintenance and road selections, thereby reducing wastage of resources and easing the maintenance process through an object organised spatial decision support system.

Keywords: decision support, geographical information systems, multi-criteria decision process, weighted sum

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Authors: Fatemeh Mohammadi Aghjeh Mashhad

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In this paper, we give several ways for computing generalized local homology modules by using Gorenstein flat resolutions. Also, we find some bounds for vanishing of generalized local homology modules.

Keywords: a-adic completion functor, generalized local homology modules, Gorenstein flat modules

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Authors: Ahmad Termimi Ab Ghani, Kojiro Higuchi

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In this paper, we present some results of simultaneous infinite games. We mainly work with generalized reachability games and Buechi games. These games are two-player concurrent games where each player chooses simultaneously their moves at each step. Our goal is to give simple expressions of values for each game. Moreover, we are interested in the question of what type of optimal (ε-optimal) strategy exists for both players depending on the type of games. We first show the determinacy (optimal value) and optimal (ε-optimal) strategies in generalized reachability games. We provide a simple expressions of value of this game and prove the existence of memoryless randomized ε-optimal strategy for Player I in any generalized reachability games. We then observe games with more complex objectives, games with Buechi objectives. We present how to compute an ε-optimal strategies and approximate a value of game in some way. Specifically, the results of generalized reachability games are used to show the value of Buechi games can be approximated as values of some generalized reachability games.

Keywords: optimal Strategies, generalized reachability games, Buechi games

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Authors: A. S. Issa, S. K. Q. AL-Omari

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In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Boehmian, Fourier integral, Fourier type integral, generalized quotient

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Authors: Juan M. Rodriguez-Diaz

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The precision of parameter estimators in the Gaussian linear model is traditionally accounted by the variance-covariance matrix of the asymptotic distribution. However, this measure can underestimate the true variance, specially for small samples. Traditionally, optimal design theory pays attention to this variance through its relationship with the model's information matrix. For this reason it seems convenient, at least in some cases, adapt the optimality criteria in order to get the best designs for the actual variance structure, otherwise the loss in efficiency of the designs obtained with the traditional approach may be very important.

Keywords: correlated observations, information matrix, optimality criteria, variance-covariance matrix

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Authors: Andrea Schnabl, Mario Bernhart

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The controlling instrument of an internal cost allocation (IT chargeback) is commonly used to make IT costs transparent and controllable. Information Technology (IT) became, especially for information industries, a central competitive factor. Consequently, the focus is not on minimizing IT costs but on the strategic aligned application of IT. Hence, an internal IT cost allocation should be designed to enhance the business-IT alignment (strategic alignment of IT) in order to support the effective application of IT from a company’s point of view. To identify design criteria for an internal cost allocation to support business alignment a case study analysis at a typical medium-sized firm in information industry is performed. Documents, Key Performance Indicators, and cost accounting data over a period of 10 years are analyzed and interviews are performed. The derived design criteria are evaluated by 6 heads of IT departments from 6 different companies, which have an internal IT cost allocation at use. By applying these design criteria an internal cost allocation serves not only for cost controlling but also as an instrument in strategic IT management.

Keywords: accounting for IT services, Business IT Alignment, internal cost allocation, IT controlling, IT governance, strategic IT management

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Christoph Köster

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Supplier selection is one of the key challenges in supply chain management and can be considered a multi-criteria decision-making (MCDM) problem. In the 1960s, it evolved from considering only economic criteria, such as price, quality, and performance, to including environmental and social criteria nowadays. Although receiving considerable attention from scholars and practitioners over the past decades, existing research has not considered governance criteria so far. This is, however, surprising, as ESG (environmental, social, and governance) criteria have gained considerable attention. In order to complement ESG criteria in the supplier selection process, this study investigates German DAX and MDAX companies and evaluates the impact of governance criteria along their supplier selection process. Moreover, it proposes a set of criteria for the respective process steps. Specifically, eleven criteria for the first process step and five criteria for the second process step are identified. This paper contributes to a better understanding of the supplier selection process by elucidating the relevance of governance criteria in the supplier selection process and providing a set of empirically developed governance criteria. These results can be applied by practitioners to complement the criteria set in the supplier selection process and thus balance economic, environmental, social, and governance targets.

Keywords: ESG, governance, sustainable supplier selection, sustainability

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Marianna Bolla

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The aim of this paper is to compare spectral, discrepancy, and degree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized (multiclass) quasirandomness of Lovasz–Sos (2008), they can be regarded as generalized quasirandom properties akin to the equivalent quasirandom properties of the seminal Chung-Graham-Wilson paper (1989) in the one-class scenario. Since these properties are valid for deterministic graph sequences, irrespective of stochastic models, the partial implications also justify for low-dimensional embedding of large-scale graphs and for discrepancy minimizing spectral clustering.

Keywords: generalized random graphs, multiway discrepancy, normalized modularity spectra, spectral clustering

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Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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Authors: Mahtab Baghaei, Seyed Mahmoud Tabatabaei

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Aim & Background: Electrical stimulation of transcranial direct current is considered one of the treatment methods for mental disorders. The aim of this study was to evaluate the effectiveness of transcranial electrical stimulation on the delta, theta, alpha, beta and systolic and diastolic blood pressure in patients with generalized anxiety disorder. Materials and Methods: The present study was a double-blind intervention with a pre-test and post-test design on people with generalized anxiety disorder in Tabriz in 1400. In this study, 30 patients with generalized anxiety disorder were selected by purposive sampling method based on the criteria specified in DSM-5 and randomly divided into an experimental group (n = 15) and a control group (n = 15). The experimental group received two sessions of 30 minutes of electrical stimulation of transcranial direct current with an intensity of 2 mA in the area of the lateral dorsal prefrontal cortex, and the control group also received artificial stimulation. Results: The results showed that transcranial electrical stimulation reduces delta and theta waves and increases beta and alpha brain waves in the experimental group. On the other hand, this method also showed a significant decrease in systolic and diastolic blood pressure in these patients (p <0.01). Conclusion: The results show that transcranial electrical stimulation has a statistically significant effect on brain waves and blood pressure, and this non-invasive method can be used as one of the treatment methods in people with generalized anxiety disorder.

Keywords: transcranial direct current electrical stimulation, brain waves, systolic blood pressure, diastolic blood pressure

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Authors: Tomas Barnak, Libor Matejka

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The aim of this study is to create a standard application using multi-criteria evaluation in the field of forensic engineering. This situation can occur in the professional assessment in several cases such as when it is necessary to consider more criteria variant of the structural subsystems, more variants according to several criteria based on a court claim, which requires expert advice. A problematic situation arises when it is necessary to clearly determine the ranking of the options according to established criteria, and reduce subjective evaluation. For the procurement in the field of construction which is based on the prepared text of the law not only economic criteria but also technical, technological and environmental criteria will be determined. This fact substantially changes the style of evaluation of individual bids. For the above-mentioned needs of procurement, the unification of expert’s decisions and the use of multi-criteria assessment seem to be a reasonable option. In the case of experimental verification when using multi-criteria evaluation of alternatives construction subsystem the economic, technical, technological and environmental criteria will be compared. The core of the solution is to compare a selected number of set criteria, application methods and evaluation weighting based on the weighted values assigned to each of the criteria to use multi-criteria evaluation methods. The sequence of individual variations is determined by the evaluation of the importance of the values of corresponding criteria concerning expertise in the problematic of outside wall constructional subsystems.

Keywords: criteria, expertise, multi-criteria evaluation, outside wall subsystems

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Authors: Nurullah Ekmekci, Ömer Akkaya, Kazım Karaboğa, Mahmut Tekin

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Job selection is one of the most important decisions that affect their lives in the name of being more useful to themselves and the society. There are many criteria to consider in the job selection. The amount of criteria in the job selection makes it a multi-criteria decision-making (MCDM) problem. In this study; job selection has been discussed as multi-criteria decision-making problem and has been solved by Analytic Hierarchy Process (AHP), one of the multi-criteria decision making methods. A survey, contains 5 different job selection criteria (finding a job friendliness, salary status, job , social security, work in the community deems reputation and business of the degree of difficulty) within many job selection criteria and 4 different job alternative (being academician, working at the civil service, working at the private sector and working at in their own business), has been conducted to the students of Selcuk University Faculty of Economics and Administrative Sciences. As a result of pairwise comparisons, the highest weighted criteria in the job selection and the most coveted job preferences were identified.

Keywords: analytical hierarchy process, job selection, multi-criteria, decision making

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Authors: Ali M. Al-Shaery

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The purpose of this paper is to address the functions of sustainability dimensions in city information modelling and to present the required sustainability criteria that support establishing a sustainable planning framework for enhancing existing cities and developing future smart cities. The paper is divided into two sections. The first section is based on the examination of a wide and extensive array of cross-disciplinary literature in the last decade and a half to conceptualize the terms ‘sustainable’ and ‘smart city,' and map their associated criteria to city information modelling. The second section is based on analyzing two approaches relating to city information modelling, namely statistical and dynamic approaches, and their suitability in the development of cities’ action plans. The paper argues that the use of statistical approaches to embedding sustainability dimensions in city information modelling have limited value. Despite the popularity of such approaches in addressing other dimensions like utility and service management in development and action plans of the world cities, these approaches are unable to address the dynamics across various city sectors with regards to economic, environmental and social criteria. The paper suggests an integrative dynamic and cross-disciplinary planning approach to embedding sustainability dimensions in city information modelling frameworks. Such an approach will pave the way towards optimal planning and implementation of priority actions of projects and investments. The approach can be used to achieve three main goals: (1) better development and action plans for world cities (2) serve the development of an integrative dynamic and cross-disciplinary framework that incorporates economic, environmental and social sustainability criteria and (3) address areas that require further attention in the development of future sustainable and smart cities. The paper presents an innovative approach for city information modelling and a well-argued, balanced hierarchy of sustainability criteria that can contribute to an area of research which is still in its infancy in terms of development and management.

Keywords: information modelling, smart city, sustainable city, sustainability dimensions, sustainability criteria, city development planning

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Authors: Manideepa Saha, Jahnavi Chakrabarty

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Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

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Authors: Hamidrza Joodaki

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The most complex issue in urban land use planning is site selection that needs to assess the verity of elements and factors. Multi Criteria Decision Making (MCDM) methods are the best approach to deal with complex problems. In this paper, combination of the analytical hierarchy process (AHP) model and FUZZY logic was used as MCDM methods to select the best site for gas station in the 4th gas zone of Tehran. The first and the most important step in FUZZY-AHP model is selection of criteria and sub-criteria. Population, accessibility, proximity and natural disasters were considered as the main criteria in this study. After choosing the criteria, they were weighted based on AHP by EXPERT CHOICE software, and FUZZY logic was used to enhance accuracy and to approach the reality. After these steps, criteria layers were produced and weighted based on FUZZY-AHP model in GIS. Finally, through ARC GIS software, the layers were integrated and the 4th gas zone in TEHRAN was selected as the best site to locate gas station.

Keywords: multiple criteria decision making (MCDM), analytic hierarchy process (AHP), FUZZY logic, geographic information system (GIS)

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