### Browsing by Author "Saati, S."

Now showing 1 - 20 of 21

###### Results Per Page

###### Sort Options

Item Metadata only An Application of Fuzzy Numbers Ranking in Performance Analysis(2009) Hatami-Marbini, A.; Saati, S.; Makui, A.Show more Data Envelopment Analysis (DEA) is a mathematical optimization technique that measures the relative efficiency of Decision Making Units (DMUs) with multiple input-output. In traditional DEA models, the data of different DMUs are assumed to be measured by precise values. But, in many real applications there are some imprecise data which represented by fuzzy numbers. In this study, an application of ranking fuzzy numbers is introduced and CCR model with fuzzy inputs and outputs in DEA is extended to propose an innovative version of fuzzy DEA (FDEA). In fact, we transform a fuzzy DEA model to a conventional crisp model by applying ranking fuzzy numbers method. Three numerical examples including an application to bank branches assessment at capital city of Iran are finally applied using the proposed fuzzy CCR model to show its applications and the differences from the other fuzzy DEA models.Show more Item Metadata only An application of fuzzy TOPSIS method in an SWOT analysis(2009) Hatami-Marbini, A.; Saati, S.Show more Analysis of strengths, weaknesses, opportunities and threats (SWOT) is a method to formulate the strategy. Although the SWOT analysis successfully provides the key factors of the problem, it has some drawbacks in selecting appropriate strategy for the evaluation and final decision steps. During recent years, some multiple criteria decision making (MCDM) techniques such as analytic hierarchy process (AHP) and analytic network process (ANP) remove some of these deficiencies, but the nature of these decision usually is very complex and using crisp data is not suitable. In this paper, linguistic variable represented with fuzzy numbers are used to assess the ratings and weights. Then, a MCDM model based on fuzzy sets theory is proposed to handle the strategy selection problem with imprecise data. According to the concept of the TOPSIS in multiple-criteria group decision making (MCGDM) problem, an index of closeness coefficient (CC) is defined to determine the ranking order of all strategies by calculating the distance to the both fuzzy ideal solution and fuzzy anti-ideal solution based on approach of ordering of the fuzzy numbers simultaneously. Finally, an example is given to highlight the procedure of the proposed method.Show more Item Metadata only A common set of weight approach using an ideal decision making unit in data envelopment analysis(AIMS, 2012-08) Saati, S.; Hatami-Marbini, A.; Agrell, P. J.; Tavana, M.Show more Data envelopment analysis (DEA) is a common non-parametric frontier analysis method. The multiplier framework of DEA allows flexibility in the selection of endogenous input and output weights of decision making units (DMUs) as to cautiously measure their efficiency. The calculation of DEA scores requires the solution of one linear program per DMU and generates an individual set of endogenous weights (multipliers) for each performance dimension. Given the large number of DMUs in real applications, the computational and conceptual complexities are considerable with weights that are potentially zero-valued or incommensurable across units. In this paper, we propose a two-phase algorithm to address these two problems. In the first step, we define an ideal DMU (IDMU) which is a hypothetical DMU consuming the least inputs to secure the most outputs. In the second step, we use the IDMU in a LP model with a small number of constraints to determine a common set of weights (CSW). In the final step of the process, we calculate the efficiency of the DMUs with the obtained CSW. The proposed model is applied to a numerical example and to a case study using panel data from 286 Danish district heating plants to illustrate the applicability of the proposed method.Show more Item Metadata only A data envelopment analysis model with discretionary and non-discretionary factors in fuzzy environments(Inderscience, 2011) Saati, S.; Hatami-Marbini, A.; Tavana, M.Show more Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision-making units (DMUs) that use multiple inputs to produce multiple outputs. The standard DEA models assume that all inputs and outputs are crisp and can be changed at the discretion of management. While crisp input and output data are fundamentally indispensable in the standard DEA evaluation process, input and output data in real-world problems are often imprecise or ambiguous. In addition, real-world problems may also include non-discretionary factors that are beyond the control of a DMU's management. Fuzzy logic and fuzzy sets are widely used to represent ambiguous, uncertain or imprecise data in DEA by formalising the inaccuracies inherent in human decision-making. In this paper, we show that considering bounded factors in DEA models results in a disregard to the concept of relative efficiency since the efficiency of the DMUs are calculated by comparing the DMUs with their lower and/or upper bounds. In addition, we present a fuzzy DEA model with discretionary and non discretionary factors in both the input and output-oriented CCR models. A numerical example is used to demonstrate the applicability and the efficacy of the proposed models.Show more Item Metadata only Data envelopment analysis with fuzzy parameters: An interactive approach(IGI, 2013) Hatami-Marbini, A.; Saati, S.; Tavana, M.Show more Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. In the conventional DEA, all the data assume the form of specific numerical values. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. Previous methods have not considered the preferences of the decision makers (DMs) in the evaluation process. This paper proposes an interactive evaluation process for measuring the relative efficiencies of a set of DMUs in fuzzy DEA with consideration of the DMs’ preferences. The authors construct a linear programming (LP) model with fuzzy parameters and calculate the fuzzy efficiency of the DMUs for different a levels. Then, the DM identifies his or her most preferred fuzzy goal for each DMU under consideration. A modified Yager index is used to develop a ranking order of the DMUs. This study allows the DMs to use their preferences or value judgments when evaluating the performance of the DMUs.Show more Item Metadata only Data envelopment analysis with fuzzy parameters: An interactive approach(IGI, 2011) Hatami-Marbini, A.; Saati, S.; Tavana, M.Show more Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. In the conventional DEA, all the data assume the form of specific numerical values. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. Previous methods have not considered the preferences of the decision makers (DMs) in the evaluation process. This paper proposes an interactive evaluation process for measuring the relative efficiencies of a set of DMUs in fuzzy DEA with consideration of the DMs’ preferences. The authors construct a linear programming (LP) model with fuzzy parameters and calculate the fuzzy efficiency of the DMUs for different a levels. Then, the DM identifies his or her most preferred fuzzy goal for each DMU under consideration. A modified Yager index is used to develop a ranking order of the DMUs. This study allows the DMs to use their preferences or value judgments when evaluating the performance of the DMUs.Show more Item Metadata only Data envelopment analysis: An efficient duo linear programming approach(2011) Saati, S.; Hatami-Marbini, A.; Tavana, M.Show more Data envelopment analysis (DEA) is a powerful mathematical method that utilises linear programming (LP) to determine the relative efficiencies of a set of functionally similar decision-making units (DMUs). Evaluating the efficiency of DMUs continues to be a difficult problem to solve, especially when the multiplicity of inputs and outputs associated with these units is considered. Problems related to computational complexities arise when there are a relatively large number of redundant variables and constraints in the problem. In this paper, we propose a three-step algorithm to reduce the computational complexities and costs in the multiplier DEA problems. In the first step, we identify some of the inefficient DMUs through input?output comparisons. In the second step, we specify the efficient DMUs by solving a LP model. In the third step, we use the results derived from the second step and another LP model to obtain the efficiency of the inefficient DMUs. We also present a numerical example to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.Show more Item Open Access Efficiency analysis in two-stage structures using fuzzy data envelopment analysis.(Springer, 2018-05-03) Hatami-Marbini, A.; Saati, S.; Sajadi, S. M.Show more Two-stage data envelopment analysis (TsDEA) models evaluate the performance of a set of production systems in which each system includes two operational stages. Taking into account the internal structures is commonly found in many situations such as seller-buyer supply chain, health care provision and environmental management. Contrary to conventional DEA models as a black-box structure, TsDEA provides further insight into sources of inefficiencies and a more informative basis for multi-stage evaluation. In addition, ignoring the qualitative and imprecise data leads to distorted evaluations, both for the subunits and the system efficiency. We present the fuzzy input and output oriented TsDEA models to calculate the global and pure technical efficiencies of a system and sub-processes when some data are fuzzy. To this end, we propose a possibilistic programming problem and then convert it into a deterministic interval programming problem using the α-level based method. The proposed method preserves the link between two stages in the sense that the total efficiency of the system is equal to the product of the efficiencies derived from two stages. In addition to the study of technical efficiency, this research includes two further contributions to ancillary literature; firstly, we minutely discuss the efficiency decompositions to indicate the sources of inefficiency and secondly, we present a method for ranking the efficient units in a fuzzy environment. An empirical illustration is also utilised to show the applicability of the proposed technique.Show more Item Open Access Efficiency Evaluation in Two-stage Data Envelopment Analysis under a Fuzzy Environment: A Common-Weights Approach(Elsevier, 2018-08-02) Hatami-Marbini, A.; Saati, S.Show more Data envelopment analysis (DEA) has been genuinely known as an impeccable technique for efficiency measurement. In practice, since many production systems such as broadcasting companies, banking and R&D activities include two processes connected in series, we have need of utilizing two-stage DEA models to identify the sources of inefficiency and explore in turn appropriate options for improving performance. The lack of the ability to generate the actual weights is not only an ongoing challenge in traditional DEA models, it can have serious repercussion for the contemporary DEA models (e.g., two-stage DEA). This paper presents a common-weights method for two-stage structures that allows us to consider equality of opportunity in a fuzzy environment when evaluating the system efficiency and the component process efficiencies. The proposed approach first seeks upper bounds on factor weights and then determines a set of common weights by a single linear programming problem. We illustrate the approach with a data set taken from the literature.Show more Item Metadata only Efficiency measurement in fuzzy additive data envelopment analysis(Inderscience, 2012) Hatami-Marbini, A.; Tavana, M.; Emrouznejad, A.; Saati, S.Show more Performance evaluation in conventional data envelopment analysis (DEA) requires crisp numerical values. However, the observed values of the input and output data in real-world problems are often imprecise or vague. These imprecise and vague data can be represented by linguistic terms characterised by fuzzy numbers in DEA to reflect the decision-makers’ intuition and subjective judgements. This paper extends the conventional DEA models to a fuzzy framework by proposing a new fuzzy additive DEA model for evaluating the efficiency of a set of decision-making units (DMUs) with fuzzy inputs and outputs. The contribution of this paper is threefold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA, (2) we propose a new fuzzy additive DEA model derived from the α -level approach and (3) we demonstrate the practical aspects of our model with two numerical examples and show its comparability with five different fuzzy DEA methods in the literature.Show more Item Metadata only An extension of LINMAP method for group decision making under fuzzy environment(IEEE, 2013) Hatami-Marbini, A.; Kangi, F.; Saati, S.Show more The linear programming technique for multidimensional analysis of preference (LINMAP) as a multi-attribute decision-making (MADM) technique has a capability of determining the weights of attributes as well as providing a ranking order of alternatives through a linear programming model. The conventional LINMAP method used the precise and deterministic data while in reality fuzziness and impreciseness in data are inherent. Linguistic terms that can be characterized by fuzzy numbers are ideal means for handling ambiguity and impreciseness. This study presents a fuzzy decision-making framework to deal with ambiguous data in LINMAP model.Show more Item Metadata only A fuzzy data envelopment analysis for clustering operating units with imprecise data(World Scientific, 2013) Saati, S.; Hatami-Marbini, A.; Tavana, M.; Agrell, P. J.Show more Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiency of peer operating units that employ multiple inputs to produce multiple outputs. Several DEA methods have been proposed for clustering operating units. However, to the best of our knowledge, the existing methods in the literature do not simultaneously consider the priority between the clusters (classes) and the priority between the operating units in each cluster. Moreover, while crisp input and output data are indispensable in traditional DEA, real-world production processes may involve imprecise or ambiguous input and output data. Fuzzy set theory has been widely used to formalize and represent the impreciseness and ambiguity inherent in human decision-making. In this paper, we propose a new fuzzy DEA method for clustering operating units in a fuzzy environment by considering the priority between the clusters and the priority between the operating units in each cluster simultaneously. A numerical example and a case study for the Jet Ski purchasing decision by the Florida Border Patrol are presented to illustrate the efficacy and the applicability of the proposed method.Show more Item Metadata only A fuzzy group linear programming technique for multidimensional analysis of preference(IOS Press Amsterdam, 2013) Hatami-Marbini, A.; Tavana, M.; Saati, S.; Kangi, F.Show more Although crisp data are fundamentally indispensable in the conventional linear programming technique for multidimensional analysis of preference (LINMAP), the observed values in the real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized by linguistic terms which are fuzzy in nature. LINMAP has been widely used to solve multi-attribute decision making (MADM) problems. This paper extends the conventional LINMAP model to a fuzzy group decision making framework using trapezoidal fuzzy numbers. The ranking approach is used to transform the fuzzy model into a crisp model. The fuzzy LINMAP method proposed in this paper is a simple and effective tool for tackling the uncertainty and imprecision associated with the group MADM problems. A case study in fast food industry is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures.Show more Item Metadata only A fuzzy linear programming model with fuzzy parameters and decision variables(Inderscience, 2015) Saati, S.; Tavana, M.; Hatami-Marbini, A.; Hajiakhondi, E.Show more Linear programming (LP) is an optimisation technique most widely used for optimal allocation of limited resources amongst competing activities. Precise data are fundamentally indispensable in standard LP problems. However, the observed values of the data in real-world problems are often imprecise or vague. Fuzzy set theory has been extensively used to represent ambiguous, uncertain or imprecise data in LP by formalising the inaccuracies inherent in human decision-making. We propose a new method for solving fuzzy LP (FLP) problems in which the right-hand side parameters and the decision variables are represented by fuzzy numbers. A new fuzzy ranking model and a new supplementary variable are utilised in the proposed FLP method to obtain the fuzzy and crisp optimal solutions by solving one LP model. Moreover, we introduce an alternative model with deterministic variables and parameters derived from the proposed FLP model. Interestingly, the result of the alternative model is identical to the crisp solution of the proposed FLP model. We use a numerical example from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedure.Show more Item Metadata only Ideal and anti-Ideal decision making units: A fuzzy DEA approach(Springer, 2010) Hatami-Marbini, A.; Saati, S.; Makui, A.Show more In this paper, by introducing two virtual decision-making units (DMUs) called ideal DMU (IDMU) and anti-ideal DMU (ADMU) with fuzzy inputs-outputs, the efficiency evaluation of DMUs are done by fuzzy data envelopment analysis (FDEA). Therefore, we evaluate DMUs from the perspective of the best and worst possible relative efficiency. For each DMU two efficiencies are calculated while inputs and outputs are fuzzy. These two distinctive efficiencies are combined with the closeness coefficient (CC) index. The CC index is then used for an overall ranking of all DMUs. Finally, we compare the result of proposed fuzzy DEA model with León et al.’s (2003) results by representing a numerical example.Show more Item Metadata only An ideal-seeking fuzzy data envelopment analysis framework(Elsevier, 2010) Hatami-Marbini, A.; Saati, S.; Tavana, M.Show more Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.Show more Item Metadata only Improving the computational complexity and weights dispersion in fuzzy DEA(World Scientific Publishing Co, 2013) Saati, S.; Hatami-Marbini, A.Show more One of the prominent features of standard and fuzzy data envelopment analysis (DEA) is the representation of each of the participating decision making units (DMUs) in the best possible light. This causes two problems; first, the different set of factor weights with large number of zeros and second a large number of linear programming models to solve. In this paper, we propose an efficient method to address these two problems. In proposed method by solving just one linear programming a Common Set of Weights (CSW) is achieved in fuzzy DEA. Since resulted efficiencies by the proposed CSW are interval numbers rather than crisp values, it is more informative for decision maker. The proposed model is applied to a numerical example to demonstrate the concept.Show more Item Metadata only Positive and normative use of Fuzzy DEA-BCC models: A critical view on NATO enlargement(Wiley, 2013) Hatami-Marbini, A.; Tavana, M.; Saati, S.; Agrell, P. J.Show more Data envelopment analysis (DEA) is a widely used mathematical programming approach for comparing the input and output of a set of comparable decision-making units (DMUs) by evaluating their relative efficiency. The traditional DEA methods require accurate measurement of both the inputs and outputs. However, the real evaluation of the DMUs is often characterized by imprecision and uncertainty in data definitions and measurements. The development of fuzzy DEA (FDEA) with imprecise and ambiguous data has extended the scope of application for efficiency measurement. The purpose of this paper is to develop a fuzzy DEA framework with a BCC model for measuring crisp and interval efficiencies in fuzzy environments. We use an α-level approach to convert the fuzzy Banker, Charnes, and Cooper (BCC) (variable returns to scale) model into an interval programming model. Instead of comparing the equality (or inequality) of the two intervals, we define a variable in the interval to satisfy our constraints and maximize the efficiency value. We present a numerical example to show the similarities and differences between our solution and the solutions obtained from four fuzzy DEA methods in the literature. In addition, a case study for NATO enlargement is presented to illustrate the applicability of the proposed method.Show more Item Metadata only A robust optimization approach for imprecise data envelopment analysis(Elsevier, 2010) Shokouhi, A. H.; Hatami-Marbini, A.; Tavana, M.; Saati, S.Show more Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.Show more Item Metadata only Stability of RTS of efficient DMUs in DEA with fuzzy u0 under fuzzy data(m-hikari, 2009) Hatami-Marbini, A.; Saati, S.Show more An important property of production functions is the concept return to scale (RTS) as found in the literature. There are two common variations RTS in data envelopment analysis (DEA) used, constant return to scale (CRS) and variation return to scale (VRS). The envelopment surface in BCC model is VRS and this is the result of the presence of the convexity constraint in the dual model and, equivalently, the presence of new separate variable, usually called u0, is introduced in the primal model which makes it possible to determine whether operations were led in the areas of constant, increasing and decreasing. In conventional BCC model make an assumption that input-output data and are exact. While accurate measurement in many real applications due to either non-availability of sophisticated measurement tools or qualitative nature of the phenomena may not be possible, consequently, this information can be represented as fuzzy numbers or linguistic terms. In this paper the RTS of efficient decision making units (DMUs) are investigated in BCC model where fuzziness is considered in both inputs and outputs and variable u0. The proposed models provide the stability of fuzzy u0 as interval region, consequently analyst can easily examine the sensitivity of RTS of efficient DMUs. Using alpha-cut, an alternative approach is suggested to solve the obtained model. To illustrate the proposed method, a numerical example is solved.Show more