946 research outputs found

    Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach

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    [EN] Fuzzy analytic hierarchy process (FAHP) methodologies have witnessed a growing development from the late 1980s until now, and countless FAHP based applications have been published in many fields including economics, finance, environment or engineering. In this context, the FAHP methodologies have been generally restricted to fuzzy numbers with linear type of membership functions (triangular numbers-TN-and trapezoidal numbers-TrN). This paper proposes an extended FAHP model (E-FAHP) where pairwise fuzzy comparison matrices are represented by a special type of fuzzy numbers referred to as (m,n)-trapezoidal numbers (TrN (m,n)) with nonlinear membership functions. It is then demonstrated that there are a significant number of FAHP approaches that can be reduced to the proposed E-FAHP structure. A comparative analysis of E-FAHP and Mikhailov's model is illustrated with a case study showing that E-FAHP includes linear and nonlinear fuzzy numbers.Reig-Mullor, J.; Pla Santamaría, D.; Garcia-Bernabeu, A. (2020). Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach. Mathematics. 8(11):1-14. https://doi.org/10.3390/math8112014S114811Chai, J., Liu, J. N. K., & Ngai, E. W. T. (2013). Application of decision-making techniques in supplier selection: A systematic review of literature. Expert Systems with Applications, 40(10), 3872-3885. doi:10.1016/j.eswa.2012.12.040Tavana, M., Zareinejad, M., Di Caprio, D., & Kaviani, M. A. (2016). An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics. Applied Soft Computing, 40, 544-557. doi:10.1016/j.asoc.2015.12.005Medasani, S., Kim, J., & Krishnapuram, R. (1998). An overview of membership function generation techniques for pattern recognition. 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A web-based decision support system for multi-criteria inventory classification using fuzzy AHP methodology. Expert Systems with Applications, 35(3), 1367-1378. doi:10.1016/j.eswa.2007.08.041Isaai, M. T., Kanani, A., Tootoonchi, M., & Afzali, H. R. (2011). Intelligent timetable evaluation using fuzzy AHP. Expert Systems with Applications, 38(4), 3718-3723. doi:10.1016/j.eswa.2010.09.030Büyüközkan, G., & Güleryüz, S. (2016). A new integrated intuitionistic fuzzy group decision making approach for product development partner selection. Computers & Industrial Engineering, 102, 383-395. doi:10.1016/j.cie.2016.05.038Zheng, G., Zhu, N., Tian, Z., Chen, Y., & Sun, B. (2012). Application of a trapezoidal fuzzy AHP method for work safety evaluation and early warning rating of hot and humid environments. Safety Science, 50(2), 228-239. doi:10.1016/j.ssci.2011.08.042Calabrese, A., Costa, R., & Menichini, T. (2013). Using Fuzzy AHP to manage Intellectual Capital assets: An application to the ICT service industry. Expert Systems with Applications, 40(9), 3747-3755. doi:10.1016/j.eswa.2012.12.081Ishizaka, A., & Nguyen, N. H. (2013). Calibrated fuzzy AHP for current bank account selection. Expert Systems with Applications, 40(9), 3775-3783. doi:10.1016/j.eswa.2012.12.089Somsuk, N., & Laosirihongthong, T. (2014). A fuzzy AHP to prioritize enabling factors for strategic management of university business incubators: Resource-based view. Technological Forecasting and Social Change, 85, 198-210. doi:10.1016/j.techfore.2013.08.007Chan, H. K., Wang, X., & Raffoni, A. (2014). An integrated approach for green design: Life-cycle, fuzzy AHP and environmental management accounting. The British Accounting Review, 46(4), 344-360. doi:10.1016/j.bar.2014.10.004Tan, R. R., Aviso, K. B., Huelgas, A. P., & Promentilla, M. A. B. (2014). Fuzzy AHP approach to selection problems in process engineering involving quantitative and qualitative aspects. Process Safety and Environmental Protection, 92(5), 467-475. doi:10.1016/j.psep.2013.11.005Rezaei, J., Fahim, P. B. M., & Tavasszy, L. (2014). Supplier selection in the airline retail industry using a funnel methodology: Conjunctive screening method and fuzzy AHP. Expert Systems with Applications, 41(18), 8165-8179. doi:10.1016/j.eswa.2014.07.005Song, Z., Zhu, H., Jia, G., & He, C. (2014). Comprehensive evaluation on self-ignition risks of coal stockpiles using fuzzy AHP approaches. Journal of Loss Prevention in the Process Industries, 32, 78-94. doi:10.1016/j.jlp.2014.08.002Dong, M., Li, S., & Zhang, H. (2015). Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP. Expert Systems with Applications, 42(21), 7846-7857. doi:10.1016/j.eswa.2015.06.007Mangla, S. K., Kumar, P., & Barua, M. K. (2015). Risk analysis in green supply chain using fuzzy AHP approach: A case study. Resources, Conservation and Recycling, 104, 375-390. doi:10.1016/j.resconrec.2015.01.001Mosadeghi, R., Warnken, J., Tomlinson, R., & Mirfenderesk, H. (2015). Comparison of Fuzzy-AHP and AHP in a spatial multi-criteria decision making model for urban land-use planning. Computers, Environment and Urban Systems, 49, 54-65. doi:10.1016/j.compenvurbsys.2014.10.001Lupo, T. (2016). A fuzzy framework to evaluate service quality in the healthcare industry: An empirical case of public hospital service evaluation in Sicily. Applied Soft Computing, 40, 468-478. doi:10.1016/j.asoc.2015.12.010Tuljak-Suban, D., & Bajec, P. (2018). The Influence of Defuzzification Methods to Decision Support Systems Based on Fuzzy AHP with Scattered Comparison Matrix: Application to 3PLP Selection as a Case Study. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 26(03), 475-491. doi:10.1142/s021848851850023xAkbar, M. A., Shameem, M., Mahmood, S., Alsanad, A., & Gumaei, A. (2020). Prioritization based Taxonomy of Cloud-based Outsource Software Development Challenges: Fuzzy AHP analysis. Applied Soft Computing, 95, 106557. doi:10.1016/j.asoc.2020.106557Jung, H. (2011). A fuzzy AHP–GP approach for integrated production-planning considering manufacturing partners. Expert Systems with Applications, 38(5), 5833-5840. doi:10.1016/j.eswa.2010.11.039Shaw, K., Shankar, R., Yadav, S. S., & Thakur, L. S. (2012). Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming for developing low carbon supply chain. Expert Systems with Applications, 39(9), 8182-8192. doi:10.1016/j.eswa.2012.01.149Abdullah, L., & Zulkifli, N. (2015). Integration of fuzzy AHP and interval type-2 fuzzy DEMATEL: An application to human resource management. Expert Systems with Applications, 42(9), 4397-4409. doi:10.1016/j.eswa.2015.01.021Akkaya, G., Turanoğlu, B., & Öztaş, S. (2015). An integrated fuzzy AHP and fuzzy MOORA approach to the problem of industrial engineering sector choosing. Expert Systems with Applications, 42(24), 9565-9573. doi:10.1016/j.eswa.2015.07.061Kutlu, A. C., & Ekmekçioğlu, M. (2012). Fuzzy failure modes and effects analysis by using fuzzy TOPSIS-based fuzzy AHP. Expert Systems with Applications, 39(1), 61-67. doi:10.1016/j.eswa.2011.06.044Büyüközkan, G., & Çifçi, G. (2012). A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry. Expert Systems with Applications, 39(3), 2341-2354. doi:10.1016/j.eswa.2011.08.061Taylan, O., Bafail, A. O., Abdulaal, R. M. S., & Kabli, M. R. (2014). Construction projects selection and risk assessment by fuzzy AHP and fuzzy TOPSIS methodologies. Applied Soft Computing, 17, 105-116. doi:10.1016/j.asoc.2014.01.003Patil, S. K., & Kant, R. (2014). A fuzzy AHP-TOPSIS framework for ranking the solutions of Knowledge Management adoption in Supply Chain to overcome its barriers. Expert Systems with Applications, 41(2), 679-693. doi:10.1016/j.eswa.2013.07.093Sun, L., Ma, J., Zhang, Y., Dong, H., & Hussain, F. K. (2016). Cloud-FuSeR: Fuzzy ontology and MCDM based cloud service selection. Future Generation Computer Systems, 57, 42-55. doi:10.1016/j.future.2015.11.025Ar, I. M., Erol, I., Peker, I., Ozdemir, A. I., Medeni, T. D., & Medeni, I. T. (2020). Evaluating the feasibility of blockchain in logistics operations: A decision framework. Expert Systems with Applications, 158, 113543. doi:10.1016/j.eswa.2020.113543Yalcin, N., Bayrakdaroglu, A., & Kahraman, C. (2012). Application of fuzzy multi-criteria decision making methods for financial performance evaluation of Turkish manufacturing industries. Expert Systems with Applications, 39(1), 350-364. doi:10.1016/j.eswa.2011.07.024Chang, S.-C., Tsai, P.-H., & Chang, S.-C. (2015). A hybrid fuzzy model for selecting and evaluating the e-book business model: A case study on Taiwan e-book firms. Applied Soft Computing, 34, 194-204. doi:10.1016/j.asoc.2015.05.011Li, N., & Zhao, H. (2016). Performance evaluation of eco-industrial thermal power plants by using fuzzy GRA-VIKOR and combination weighting techniques. Journal of Cleaner Production, 135, 169-183. doi:10.1016/j.jclepro.2016.06.113Mandic, K., Delibasic, B., Knezevic, S., & Benkovic, S. (2014). Analysis of the financial parameters of Serbian banks through the application of the fuzzy AHP and TOPSIS methods. Economic Modelling, 43, 30-37. doi:10.1016/j.econmod.2014.07.036Li, Y., Liu, X., & Chen, Y. (2012). Supplier selection using axiomatic fuzzy set and TOPSIS methodology in supply chain management. Fuzzy Optimization and Decision Making, 11(2), 147-176. doi:10.1007/s10700-012-9117-xKaya, Ö., Alemdar, K. D., & Çodur, M. Y. (2020). A novel two stage approach for electric taxis charging station site selection. Sustainable Cities and Society, 62, 102396. doi:10.1016/j.scs.2020.102396Chen, J.-F., Hsieh, H.-N., & Do, Q. H. (2015). Evaluating teaching performance based on fuzzy AHP and comprehensive evaluation approach. Applied Soft Computing, 28, 100-108. doi:10.1016/j.asoc.2014.11.050Javanbarg, M. B., Scawthorn, C., Kiyono, J., & Shahbodaghkhan, B. (2012). Fuzzy AHP-based multicriteria decision making systems using particle swarm optimization. Expert Systems with Applications, 39(1), 960-966. doi:10.1016/j.eswa.2011.07.095Che, Z. H., Wang, H. S., & Chuang, C.-L. (2010). A fuzzy AHP and DEA approach for making bank loan decisions for small and medium enterprises in Taiwan. Expert Systems with Applications, 37(10), 7189-7199. doi:10.1016/j.eswa.2010.04.010Krejčí, J. (2015). Additively reciprocal fuzzy pairwise comparison matrices and multiplicative fuzzy priorities. Soft Computing, 21(12), 3177-3192. doi:10.1007/s00500-015-2000-2Xu, Z., & Liao, H. (2014). Intuitionistic Fuzzy Analytic Hierarchy Process. IEEE Transactions on Fuzzy Systems, 22(4), 749-761. doi:10.1109/tfuzz.2013.2272585Mikhailov, L. (2000). A fuzzy programming method for deriving priorities in the analytic hierarchy process. Journal of the Operational Research Society, 51(3), 341-349. doi:10.1057/palgrave.jors.260089

    Multi-Criteria Decision-Making Methods Application in Supply Chain Management: A Systematic Literature Review

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    Over the last decade, a large number of research papers, certified courses, professional development programs and scientific conferences have addressed supply chain management (SCM), thereby attesting to its significance and importance. SCM is a multi-criteria decision-making (MCDM) problem because throughout its process, different criteria related to each supply chain (SC) activity and their associated sub-criteria must be considered. Often, these criteria are conflicting in nature. For their part, MCDM methods have also attracted significant attention among researchers and practitioners in the field of SCM. The aim of this chapter is to conduct a systematic literature review of published articles in the application of MCDM methods in SCM decisions at the strategic, tactical and operational levels. This chapter considers major SC activities such as supplier selection, manufacturing, warehousing and logistics. A total of 140 published articles (from 2005 to 2017) were studied and categorized, and gaps in the literature were identified. This chapter is useful for academic researchers, decision makers and experts to whom it will provide a better understanding of the application of MCDM methods in SCM, at various levels of the decision-making process, and establish guidelines for selecting an appropriate MCDM method for managing SC activities

    Sustainable and agile manufacturing outsourcing partner selection: a literature review

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    [EN] Outsourcing to third party to manage non-core activities helps the firm to focus on core activities. Manufacturing firms are outsourcing product development, manufacturing, logistics, customer care etc. to enhance production capacity and flexibility, and to reduce operational costs, which in turn can improve profitability and competitive advantage of the enterprise. Sustainability in operations and supply chain is gaining momentum due to increased global environmental concern, pressures from consumers and communities, and enforced regulations. Volatile and uncertain business environment necessitates the adoption of agility and flexibility to effectively manage manufacturing and supply chain. Globalisation has made the market very competitive and hence manufacturing firms are adopting manufacturing outsourcing to third parties. Selecting a sustainable and agile manufacturing outsourcing partner (MPS) is crucial as it will improve sustainability, efficiency, and effectiveness of the supply chain and competitive advantage to the firm. Detailed literature review on sustainable and agile manufacturing outsourcing partner selection has been carried out from EBSCO data base and Goggle scholar. Selection criteria used are classified into agile, operational, economic, environmental and social. The techniques use are mostly multi criteria decision making methods (MCDM) while few have adopted programming techniques. Discussion, implication and the scope of future work is also provided.Akhtar, M. (2022). Sustainable and agile manufacturing outsourcing partner selection: a literature review. International Journal of Production Management and Engineering. 10(2):143-158. https://doi.org/10.4995/ijpme.2022.1680714315810

    Logistics service providers (LSPs) evaluation and selection: Literature review and framework development

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    Purpose – The purpose of this paper is to provide an insight to the outsourcing decision-making through investigating if the old evaluation/selection criteria and methods still fit with current business priorities or not and, therefore, to identify the appropriate criteria and methods to develop a new selection framework. Since the economic recession of 2008, logistics outsourcing decisions have become more prominent to avoid high fixed costs and heavy investment requirements and to achieve competitive advantages. Design/methodology/approach – This is a focused literature review prepared after analyzing 56 articles related to the logistics service provider (LSP) evaluation and selection methods and criteria during 2008-2013. The academic articles are analyzed based on research focus/area, evaluation and selection methodology/methods and evaluation and selection criteria. Then reviewed result is compared with previous literature studies for the periods (1991-2008) to identify any possible shifts. Findings – The review reveals that: several problems in current LSPs literature have been identified; the reviewed papers can be categorized into seven groups, the usage and importance of evaluation and selection criteria fluctuate during different periods; 12 crucial criteria have been identified, increasing the importance of specific selection methods and the integrated models and fuzzy logic in logistics literature. Then, a comprehensive LSPs’ evaluation and selection framework has been developed. Originality/value – To the best of our knowledge, this is the first focused logistics outsourcing study that reviews the 2008-2013 period in detail, comparing results with previous literature studies, identifies current LSPs literature problems/gaps, new trends and shifts in the way that LSPs are evaluated and selected, identifies crucial selection criteria and proposes a new holistic LSPs evaluation and selection framework. In addition, it identifies important issues for future research. Keywords Supplier or partner selection, Evaluation and selection methods and criteria, Logistics outsourcing, Logistics service provider, LSP framewor

    VIKOR Technique:A Systematic Review of the State of the Art Literature on Methodologies and Applications

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    The main objective of this paper is to present a systematic review of the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method in several application areas such as sustainability and renewable energy. This study reviewed a total of 176 papers, published in 2004 to 2015, from 83 high-ranking journals; most of which were related to Operational Research, Management Sciences, decision making, sustainability and renewable energy and were extracted from the “Web of Science and Scopus” databases. Papers were classified into 15 main application areas. Furthermore, papers were categorized based on the nationalities of authors, dates of publications, techniques and methods, type of studies, the names of the journals and studies purposes. The results of this study indicated that more papers on VIKOR technique were published in 2013 than in any other year. In addition, 13 papers were published about sustainability and renewable energy fields. Furthermore, VIKOR and fuzzy VIKOR methods, had the first rank in use. Additionally, the Journal of Expert Systems with Applications was the most significant journal in this study, with 27 publications on the topic. Finally, Taiwan had the first rank from 22 nationalities which used VIKOR technique

    The state of the art development of AHP (1979-2017): A literature review with a social network analysis

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    Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979?1990, 1991?2001 and 2002?2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

    Application of fuzzy TOPSIS framework for selecting complex project in a case company

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    Purpose This study aims to propose a method known as the fuzzy technique for order preference by similarity to ideal solution (fuzzy TOPSIS) for complex project selection in organizations. To fulfill study objectives, the factors responsible for making a project complex are collected through literature review, which is then analyzed by fuzzy TOPSIS, based on three decision-makers’ opinions. Design/methodology/approach The selection of complex projects is a multi-criteria decision-making (MCDM) process for global organizations. Traditional procedures for selecting complex projects are not adequate due to the limitations of linguistic assessment. To crossover such limitation, this study proposes the fuzzy MCDM method to select complex projects in organizations. Findings A large-scale engine manufacturing company, engaged in the energy business, is studied to validate the suitability of the fuzzy TOPSIS method and rank eight projects of the case company based on project complexity. Out of these eight projects, the closeness coefficient of the most complex project is found to be 0.817 and that of the least complex project is found to be 0.274. Finally, study outcomes are concluded in the conclusion section, along with study limitations and future works. Research limitations/implications The outcomes from this research may not be generalized sufficiently due to the subjectivity of the interviewers. The study outcomes support project managers to optimize their project selection processes, especially to select complex projects. The presented methodology can be used extensively used by the project planners/managers to find the driving factors related to project complexity. Originality/value The presented study deliberately explained how complex projects in an organization could be select efficiently. This selection methodology supports top management to maintain their proposed projects with optimum resource allocations and maximum productivity.© 2021, Ahm Shamsuzzoha, Sujan Piya and Mohammad Shamsuzzaman. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) license. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this license may be seen at http://creativecommons.org/licences/by/4.0/legalcodefi=vertaisarvioitu|en=peerReviewed

    The state of the art development of AHP (1979-2017): a literature review with a social network analysis

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    Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979–1990, 1991–2001 and 2002–2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

    Analysis of Decision Support Systems of Industrial Relevance: Application Potential of Fuzzy and Grey Set Theories

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    The present work articulates few case empirical studies on decision making in industrial context. Development of variety of Decision Support System (DSS) under uncertainty and vague information is attempted herein. The study emphases on five important decision making domains where effective decision making may surely enhance overall performance of the organization. The focused territories of this work are i) robot selection, ii) g-resilient supplier selection, iii) third party logistics (3PL) service provider selection, iv) assessment of supply chain’s g-resilient index and v) risk assessment in e-commerce exercises. Firstly, decision support systems in relation to robot selection are conceptualized through adaptation to fuzzy set theory in integration with TODIM and PROMETHEE approach, Grey set theory is also found useful in this regard; and is combined with TODIM approach to identify the best robot alternative. In this work, an attempt is also made to tackle subjective (qualitative) and objective (quantitative) evaluation information simultaneously, towards effective decision making. Supplier selection is a key strategic concern for the large-scale organizations. In view of this, a novel decision support framework is proposed to address g-resilient (green and resilient) supplier selection issues. Green capability of suppliers’ ensures the pollution free operation; while, resiliency deals with unexpected system disruptions. A comparative analysis of the results is also carried out by applying well-known decision making approaches like Fuzzy- TOPSIS and Fuzzy-VIKOR. In relation to 3PL service provider selection, this dissertation proposes a novel ‘Dominance- Based’ model in combination with grey set theory to deal with 3PL provider selection, considering linguistic preferences of the Decision-Makers (DMs). An empirical case study is articulated to demonstrate application potential of the proposed model. The results, obtained thereof, have been compared to that of grey-TOPSIS approach. Another part of this dissertation is to provide an integrated framework in order to assess gresilient (ecosilient) performance of the supply chain of a case automotive company. The overall g-resilient supply chain performance is determined by computing a unique ecosilient (g-resilient) index. The concepts of Fuzzy Performance Importance Index (FPII) along with Degree of Similarity (DOS) (obtained from fuzzy set theory) are applied to rank different gresilient criteria in accordance to their current status of performance. The study is further extended to analyze, and thereby, to mitigate various risk factors (risk sources) involved in e-commerce exercises. A total forty eight major e-commerce risks are recognized and evaluated in a decision making perspective by utilizing the knowledge acquired from the fuzzy set theory. Risk is evaluated as a product of two risk quantifying parameters viz. (i) Likelihood of occurrence and, (ii) Impact. Aforesaid two risk quantifying parameters are assessed in a subjective manner (linguistic human judgment), rather than exploring probabilistic approach of risk analysis. The ‘crisp risk extent’ corresponding to various risk factors are figured out through the proposed fuzzy risk analysis approach. The risk factor possessing high ‘crisp risk extent’ score is said be more critical for the current problem context (toward e-commerce success). Risks are now categorized into different levels of severity (adverse consequences) (i.e. negligible, minor, marginal, critical and catastrophic). Amongst forty eight risk sources, top five risk sources which are supposed to adversely affect the company’s e-commerce performance are recognized through such categorization. The overall risk extent is determined by aggregating individual risks (under ‘critical’ level of severity) using Fuzzy Inference System (FIS). Interpretive Structural Modeling (ISM) is then used to obtain structural relationship amongst aforementioned five risk sources. An appropriate action requirement plan is also suggested, to control and minimize risks associated with e-commerce exercises

    Permutation based decision making under fuzzy environment using Tabu search

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    One of the techniques, which are used for Multiple Criteria Decision Making (MCDM) is the permutation. In the classical form of permutation, it is assumed that weights and decision matrix components are crisp. However, when group decision making is under consideration and decision makers could not agree on a crisp value for weights and decision matrix components, fuzzy numbers should be used. In this article, the fuzzy permutation technique for MCDM problems has been explained. The main deficiency of permutation is its big computational time, so a Tabu Search (TS) based algorithm has been proposed to reduce the computational time. A numerical example has illustrated the proposed approach clearly. Then, some benchmark instances extracted from literature are solved by proposed TS. The analyses of the results show the proper performance of the proposed method
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