1,854 research outputs found
Right-left asymmetry of the eigenvector method: A simulation study
The eigenvalue method, suggested by the developer of the extensively used
Analytic Hierarchy Process methodology, exhibits right-left asymmetry: the
priorities derived from the right eigenvector do not necessarily coincide with
the priorities derived from the reciprocal left eigenvector. This paper offers
a comprehensive numerical experiment to compare the two eigenvector-based
weighting procedures and their reasonable alternative of the row geometric mean
with respect to four measures. The underlying pairwise comparison matrices are
constructed randomly with different dimensions and levels of inconsistency. The
disagreement between the two eigenvectors turns out to be not always a
monotonic function of these important characteristics of the matrix. The
ranking contradictions can affect alternatives with relatively distant
priorities. The row geometric mean is found to be almost at the midpoint
between the right and inverse left eigenvectors, making it a straightforward
compromise between them.Comment: 19 pages, 6 figure
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A review of fuzzy AHP methods for decision-making with subjective judgements
Analytic Hierarchy Process (AHP) is a broadly applied multi-criteria decision-making method to determine the weights of criteria and priorities of alternatives in a structured manner based on pairwise comparison. As subjective judgments during comparison might be imprecise, fuzzy sets have been combined with AHP. This is referred to as fuzzy AHP or FAHP. An increasing amount of papers are published which describe different ways to derive the weights/priorities from a fuzzy comparison matrix, but seldomly set out the relative benefits of each approach so that the choice of the approach seems arbitrary. A review of various fuzzy AHP techniques is required to guide both academic and industrial experts to choose suitable techniques for a specific practical context. This paper reviews the literature published since 2008 where fuzzy AHP is applied to decision-making problems in industry, particularly the various selection problems. The techniques are categorised by the four aspects of developing a fuzzy AHP model: (i) representation of the relative importance for pairwise comparison, (ii) aggregation of fuzzy sets for group decisions and weights/priorities, (iii) defuzzification of a fuzzy set to a crisp value for final comparison, and (iv) consistency measurement of the judgements. These techniques are discussed in terms of their underlying principles, origins, strengths and weakness. Summary tables and specification charts are provided to guide the selection of suitable techniques. Tips for building a fuzzy AHP model are also included and six open questions are posed for future work
Sensitivity Analysis Method to Address User Disparities in the Analytic Hierarchy Process
Decision makers often face complex problems, which can seldom be addressed well without the use of structured analytical models. Mathematical models have been developed to streamline and facilitate decision making activities, and among these, the Analytic Hierarchy Process (AHP) constitutes one of the most utilized multi-criteria decision analysis methods. While AHP has been thoroughly researched and applied, the method still shows limitations in terms of addressing user profile disparities. A novel sensitivity analysis method based on local partial derivatives is presented here to address these limitations. This new methodology informs AHP users of which pairwise comparisons most impact the derived weights and the ranking of alternatives. The method can also be applied to decision processes that require the aggregation of results obtained by several users, as it highlights which individuals most critically impact the aggregated group results while also enabling to focus on inputs that drive the final ordering of alternatives. An aerospace design and engineering example that requires group decision making is presented to demonstrate and validate the proposed methodology
Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach
[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 SantamarĂa, 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. International Journal of Approximate Reasoning, 19(3-4), 391-417. doi:10.1016/s0888-613x(98)10017-8Medaglia, A. L., Fang, S.-C., Nuttle, H. L. W., & Wilson, J. R. (2002). An efficient and flexible mechanism for constructing membership functions. European Journal of Operational Research, 139(1), 84-95. doi:10.1016/s0377-2217(01)00157-6Mikhailov, L. (2003). Deriving priorities from fuzzy pairwise comparison judgements. Fuzzy Sets and Systems, 134(3), 365-385. doi:10.1016/s0165-0114(02)00383-4Appadoo, S. S. (2014). Possibilistic Fuzzy Net Present Value Model and Application. Mathematical Problems in Engineering, 2014, 1-11. doi:10.1155/2014/865968Mikhailov, L., & Tsvetinov, P. (2004). Evaluation of services using a fuzzy analytic hierarchy process. Applied Soft Computing, 5(1), 23-33. doi:10.1016/j.asoc.2004.04.001Hepu Deng. (1999). Multicriteria analysis with fuzzy pairwise comparison. FUZZ-IEEE’99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315). doi:10.1109/fuzzy.1999.793038Van Laarhoven, P. J. M., & Pedrycz, W. (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 11(1-3), 229-241. doi:10.1016/s0165-0114(83)80082-7Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17(3), 233-247. doi:10.1016/0165-0114(85)90090-9Chang, D.-Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649-655. doi:10.1016/0377-2217(95)00300-2Enea, M., & Piazza, T. (2004). Project Selection by Constrained Fuzzy AHP. Fuzzy Optimization and Decision Making, 3(1), 39-62. doi:10.1023/b:fodm.0000013071.63614.3dKrejÄŤĂ, J., PavlaÄŤka, O., & Talašová, J. (2016). A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic. Fuzzy Optimization and Decision Making, 16(1), 89-110. doi:10.1007/s10700-016-9241-0Cakir, O., & Canbolat, M. S. (2008). 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.2010.09.030BĂĽyĂĽközkan, G., & GĂĽleryĂĽz, 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). 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Intelligent multimedia communication for enhanced medical e-collaboration in back pain treatment
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2004 SAGE PublicationsRemote, multimedia-based, collaboration in back pain treatment is an option which only recently has come to the attention of clinicians and IT providers. The take-up of such applications will inevitably depend on their ability to produce an acceptable level of service over congested and unreliable public networks. However, although the problem of multimedia application-level performance is closely linked to both the user perspective of the experience as well as to the service provided by the underlying network, it is rarely studied from an integrated viewpoint. To alleviate this problem, we propose an intelligent mechanism that integrates user-related requirements with the more technical characterization of quality of service, obtaining a priority order of low-level quality of service parameters, which would ensure that user-centred quality of perception is maintained at an optimum level. We show how our framework is capable of suggesting appropriately tailored transmission protocols, by incorporating user requirements in the remote delivery of e-health solutions
Towards secure judgments aggregation in AHP
In the decision making methods the common assumption is the honesty and
professionalism of experts. However, this is not the case when one or more
experts in the group decision making framework, such as the group analytic
hierarchy process (GAHP), try to manipulate results in their favor. The aim of
this paper is to introduce two heuristics in the GAHP setting allowing to
detect the manipulators and minimize their effect on the group consensus by
diminishing their weights. The first heuristic is based on the assumption that
manipulators will provide judgments which can be considered outliers with
respect to judgments of the rest of the experts in the group. Second heuristic
assumes that dishonest judgments are less consistent than average consistency
of the group. Both approaches are illustrated with numerical examples and
simulations.Comment: 32 page
A Pairwise Comparison Matrix Framework for Large-Scale Decision Making
abstract: A Pairwise Comparison Matrix (PCM) is used to compute for relative priorities of criteria or alternatives and are integral components of widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, a PCM suffers from several issues limiting its application to large-scale decision problems, specifically: (1) to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker (DM), (2) inconsistent and (3) imprecise preferences maybe obtained due to the limited cognitive power of DMs. This dissertation proposes a PCM Framework for Large-Scale Decisions to address these limitations in three phases as follows. The first phase proposes a binary integer program (BIP) to intelligently decompose a PCM into several mutually exclusive subsets using interdependence scores. As a result, the number of pairwise comparisons is reduced and the consistency of the PCM is improved. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets. This is done to derive the global weights of the elements from the original PCM. The proposed BIP is applied to both AHP and ANP methodologies. However, it is noted that the optimal number of subsets is provided subjectively by the DM and hence is subject to biases and judgement errors. The second phase proposes a trade-off PCM decomposition methodology to decompose a PCM into a number of optimally identified subsets. A BIP is proposed to balance the: (1) time savings by reducing pairwise comparisons, the level of PCM inconsistency, and (2) the accuracy of the weights. The proposed methodology is applied to the AHP to demonstrate its advantages and is compared to established methodologies. In the third phase, a beta distribution is proposed to generalize a wide variety of imprecise pairwise comparison distributions via a method of moments methodology. A Non-Linear Programming model is then developed that calculates PCM element weights which maximizes the preferences of the DM as well as minimizes the inconsistency simultaneously. Comparison experiments are conducted using datasets collected from literature to validate the proposed methodology.Dissertation/ThesisPh.D. Industrial Engineering 201
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