A two-step fusion process for multi-criteria decision applied to natural hazards in mountains

Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using multi-disciplinary quantitative or qualitative approaches. Expertise is considered as a decision process based on imperfect information coming from more or less reliable and conflicting sources. A methodology mixing the Analytic Hierarchy Process (AHP), a multi-criteria aid-decision method, and information fusion using Belief Function Theory is described. Fuzzy Sets and Possibilities theories allow to transform quantitative and qualitative criteria into a common frame of discernment for decision in Dempster-Shafer Theory (DST ) and Dezert-Smarandache Theory (DSmT) contexts. Main issues consist in basic belief assignments elicitation, conflict identification and management, fusion rule choices, results validation but also in specific needs to make a difference between importance and reliability and uncertainty in the fusion process

AHP and uncertainty theories for decision making using the ER-MCDA methodology

International audienceIn this paper, we present the ER-MCDA methodology for multi-criteria decision-making based on imperfect information coming from more or less reliable and conflicting sources. The Analytic Hierarchy Process (AHP), Fuzzy Sets, Possibility and Belief Functions theories are combined to take a decision based on imprecise and uncertain evaluations of quantitative, qualitative criteria. Classical aggregation of criteria is replaced by a two-step fusion process using advanced fusion rules based on the Dezert-Smarandache Theory (DSmT) that allows to make a difference between importance, reliability and uncertainty of information sources and contents

A group decision-making methodology with incomplete individual beliefs applied to e-Democracy

We consider the situation where there are several alternatives for investing a quantity of money to achieve a set of objectives. The choice of which alternative to apply depends on how citizens and political representatives perceive that such objectives should be achieved. All citizens with the right to vote can express their preferences in the decision-making process. These preferences may be incomplete. Political representatives represent the citizens who have not taken part in the decision-making process. The weight corresponding to political representatives depends on the number of citizens that have intervened in the decision-making process. The methodology we propose needs the participants to specify for each alternative how they rate the different attributes and the relative importance of attributes. On the basis of this information an expected utility interval is output for each alternative. To do this, an evidential reasoning approach is applied. This approach improves the insightfulness and rationality of the decision-making process using a belief decision matrix for problem modeling and the Dempster?Shafer theory of evidence for attribute aggregation. Finally, we propose using the distances of each expected utility interval from the maximum and the minimum utilities to rank the alternative set. The basic idea is that an alternative is ranked first if its distance to the maximum utility is the smallest, and its distance to the minimum utility is the greatest. If only one of these conditions is satisfied, a distance ratio is then used

Characterisation of the consistent completion of AHP comparison matrices using graph theory

[EN] Decision-making is frequently affected by uncertainty and/or incomplete information, which turn decision-making into a complex task. It is often the case that some of the actors involved in decision-making are not sufficiently familiar with all of the issues to make the appropriate decisions. In this paper, we are concerned about missing information. Specifically, we deal with the problem of consistently completing an analytic hierarchy process comparison matrix and make use of graph theory to characterize such a completion. The characterization includes the degree of freedom of the set of solutions and a linear manifold and, in particular, characterizes the uniqueness of the solution, a result already known in the literature, for which we provide a completely independent proof. Additionally, in the case of nonuniqueness, we reduce the problem to the solution of nonsingular linear systems. In addition to obtaining the priority vector, our investigation also focuses on building the complete pairwise comparison matrix, a crucial step in the necessary process (between synthetic consistency and personal judgement) with the experts. The performance of the obtained results is confirmed.Benítez López, J.; Carpitella, S.; Certa, A.; Izquierdo Sebastián, J. (2019). Characterisation of the consistent completion of AHP comparison matrices using graph theory. Journal of Multi-Criteria Decision Analysis. 26(1-2):3-15. https://doi.org/10.1002/mcda.1652S315261-2Benítez, J., Carrión, L., Izquierdo, J., & Pérez-García, R. (2014). Characterization of Consistent Completion of Reciprocal Comparison Matrices. Abstract and Applied Analysis, 2014, 1-12. doi:10.1155/2014/349729Benítez, J., Delgado-Galván, X., Gutiérrez, J. A., & Izquierdo, J. (2011). Balancing consistency and expert judgment in AHP. Mathematical and Computer Modelling, 54(7-8), 1785-1790. doi:10.1016/j.mcm.2010.12.023Benítez, J., Delgado-Galván, X., Izquierdo, J., & Pérez-García, R. (2011). Achieving matrix consistency in AHP through linearization. Applied Mathematical Modelling, 35(9), 4449-4457. doi:10.1016/j.apm.2011.03.013Benítez, J., Delgado-Galván, X., Izquierdo, J., & Pérez-García, R. (2015). Consistent completion of incomplete judgments in decision making using AHP. Journal of Computational and Applied Mathematics, 290, 412-422. doi:10.1016/j.cam.2015.05.023Benítez, J., Delgado-Galván, X., Izquierdo, J., & Pérez-García, R. (2012). Improving consistency in AHP decision-making processes. Applied Mathematics and Computation, 219(5), 2432-2441. doi:10.1016/j.amc.2012.08.079Benítez, J., Izquierdo, J., Pérez-García, R., & Ramos-Martínez, E. (2014). A simple formula to find the closest consistent matrix to a reciprocal matrix. Applied Mathematical Modelling, 38(15-16), 3968-3974. doi:10.1016/j.apm.2014.01.007Beynon, M., Curry, B., & Morgan, P. (2000). The Dempster–Shafer theory of evidence: an alternative approach to multicriteria decision modelling. Omega, 28(1), 37-50. doi:10.1016/s0305-0483(99)00033-xBozóki, S., Csató, L., & Temesi, J. (2016). An application of incomplete pairwise comparison matrices for ranking top tennis players. European Journal of Operational Research, 248(1), 211-218. doi:10.1016/j.ejor.2015.06.069Bozóki, S., Fülöp, J., & Rónyai, L. (2010). On optimal completion of incomplete pairwise comparison matrices. Mathematical and Computer Modelling, 52(1-2), 318-333. doi:10.1016/j.mcm.2010.02.047Certa, A., Enea, M., Galante, G. M., & La Fata, C. M. (2013). A Multistep Methodology for the Evaluation of Human Resources Using the Evidence Theory. International Journal of Intelligent Systems, 28(11), 1072-1088. doi:10.1002/int.21617Crawford, G., & Williams, C. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29(4), 387-405. doi:10.1016/0022-2496(85)90002-1Dong, 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.2015.06.007Ergu, D., Kou, G., Peng, Y., Li, F., & Shi, Y. (2014). Data Consistency in Emergency Management. International Journal of Computers Communications & Control, 7(3), 450. doi:10.15837/ijccc.2012.3.1386Ergu, D., Kou, G., Peng, Y., & Zhang, M. (2016). Estimating the missing values for the incomplete decision matrix and consistency optimization in emergency management. Applied Mathematical Modelling, 40(1), 254-267. doi:10.1016/j.apm.2015.04.047Floricel, S., Michela, J. L., & Piperca, S. (2016). Complexity, uncertainty-reduction strategies, and project performance. International Journal of Project Management, 34(7), 1360-1383. doi:10.1016/j.ijproman.2015.11.007Forman, E., & Peniwati, K. (1998). Aggregating individual judgments and priorities with the analytic hierarchy process. European Journal of Operational Research, 108(1), 165-169. doi:10.1016/s0377-2217(97)00244-0Guitouni, A., & Martel, J.-M. (1998). Tentative guidelines to help choosing an appropriate MCDA method. European Journal of Operational Research, 109(2), 501-521. doi:10.1016/s0377-2217(98)00073-3Harker, P. T. (1987). Alternative modes of questioning in the analytic hierarchy process. Mathematical Modelling, 9(3-5), 353-360. doi:10.1016/0270-0255(87)90492-1Ho, W. (2008). Integrated analytic hierarchy process and its applications – A literature review. European Journal of Operational Research, 186(1), 211-228. doi:10.1016/j.ejor.2007.01.004Homenda, W., Jastrzebska, A., & Pedrycz, W. (2016). Multicriteria decision making inspired by human cognitive processes. Applied Mathematics and Computation, 290, 392-411. doi:10.1016/j.amc.2016.05.041Hsu, W.-K. K., Huang, S.-H. S., & Tseng, W.-J. (2016). Evaluating the risk of operational safety for dangerous goods in airfreights – A revised risk matrix based on fuzzy AHP. Transportation Research Part D: Transport and Environment, 48, 235-247. doi:10.1016/j.trd.2016.08.018Hua, Z., Gong, B., & Xu, X. (2008). A DS–AHP approach for multi-attribute decision making problem with incomplete information. Expert Systems with Applications, 34(3), 2221-2227. doi:10.1016/j.eswa.2007.02.021Karanik, M., Wanderer, L., Gomez-Ruiz, J. A., & Pelaez, J. I. (2016). Reconstruction methods for AHP pairwise matrices: How reliable are they? Applied Mathematics and Computation, 279, 103-124. doi:10.1016/j.amc.2016.01.008Kubler, S., Robert, J., Derigent, W., Voisin, A., & Le Traon, Y. (2016). A state-of the-art survey & testbed of fuzzy AHP (FAHP) applications. Expert Systems with Applications, 65, 398-422. doi:10.1016/j.eswa.2016.08.064Liu, S., Chan, F. T. S., & Ran, W. (2016). Decision making for the selection of cloud vendor: An improved approach under group decision-making with integrated weights and objective/subjective attributes. Expert Systems with Applications, 55, 37-47. doi:10.1016/j.eswa.2016.01.059Lolli, F., Ishizaka, A., Gamberini, R., & Rimini, B. (2017). A multicriteria framework for inventory classification and control with application to intermittent demand. Journal of Multi-Criteria Decision Analysis, 24(5-6), 275-285. doi:10.1002/mcda.1620Massanet, S., Vicente Riera, J., Torrens, J., & Herrera-Viedma, E. (2016). A model based on subjective linguistic preference relations for group decision making problems. Information Sciences, 355-356, 249-264. doi:10.1016/j.ins.2016.03.040Ortiz-Barrios, M. A., Aleman-Romero, B. A., Rebolledo-Rudas, J., Maldonado-Mestre, H., Montes-Villa, L., De Felice, F., & Petrillo, A. (2017). The analytic decision-making preference model to evaluate the disaster readiness in emergency departments: The A.D.T. model. Journal of Multi-Criteria Decision Analysis, 24(5-6), 204-226. doi:10.1002/mcda.1629Pandey, A., & Kumar, A. (2016). A note on ‘‘Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP”. Information Sciences, 346-347, 1-5. doi:10.1016/j.ins.2016.01.054Qazi, A., Quigley, J., Dickson, A., & Kirytopoulos, K. (2016). Project Complexity and Risk Management (ProCRiM): Towards modelling project complexity driven risk paths in construction projects. International Journal of Project Management, 34(7), 1183-1198. doi:10.1016/j.ijproman.2016.05.008Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281. doi:10.1016/0022-2496(77)90033-5Saaty, T. L. (2008). Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 102(2), 251-318. doi:10.1007/bf03191825Seiti, H., Tagipour, R., Hafezalkotob, A., & Asgari, F. (2017). Maintenance strategy selection with risky evaluations using RAHP. Journal of Multi-Criteria Decision Analysis, 24(5-6), 257-274. doi:10.1002/mcda.1618Shiraishi, S., Obata, T., & Daigo, M. (1998). PROPERTIES OF A POSITIVE RECIPROCAL MATRIX AND THEIR APPLICATION TO AHP. Journal of the Operations Research Society of Japan, 41(3), 404-414. doi:10.15807/jorsj.41.404Srdjevic, B., Srdjevic, Z., & Blagojevic, B. (2014). First-Level Transitivity Rule Method for Filling in Incomplete Pair-Wise Comparison Matrices in the Analytic Hierarchy Process. Applied Mathematics & Information Sciences, 8(2), 459-467. doi:10.12785/amis/080202Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of Operational Research, 169(1), 1-29. doi:10.1016/j.ejor.2004.04.028Van 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)80082-7van Uden , E. 2002 Estimating missing data in pairwise comparison matrices Texts in Operational and Systems Research in the Face to Challenge the XXI Century, Methods and Techniques in Information Analysis and Decision Making Academic Printing House WarsawVargas, L., De Felice, F., & Petrillo, A. (2017). Editorial journal of multicriteria decision analysis special issue on «Industrial and Manufacturing Engineering: Theory and Application using AHP/ANP». Journal of Multi-Criteria Decision Analysis, 24(5-6), 201-202. doi:10.1002/mcda.1632Wang, T.-C., & Chen, Y.-H. (2008). Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Information Sciences, 178(19), 3755-3765. doi:10.1016/j.ins.2008.05.028Wang, Z.-J., & Tong, X. (2016). Consistency analysis and group decision making based on triangular fuzzy additive reciprocal preference relations. Information Sciences, 361-362, 29-47. doi:10.1016/j.ins.2016.04.047Wang, H., & Xu, Z. (2016). Interactive algorithms for improving incomplete linguistic preference relations based on consistency measures. Applied Soft Computing, 42, 66-79. doi:10.1016/j.asoc.2015.09.058Weiss-Cohen, L., Konstantinidis, E., Speekenbrink, M., & Harvey, N. (2016). Incorporating conflicting descriptions into decisions from experience. Organizational Behavior and Human Decision Processes, 135, 55-69. doi:10.1016/j.obhdp.2016.05.005Xu, Y., Chen, L., Rodríguez, R. M., Herrera, F., & Wang, H. (2016). Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowledge-Based Systems, 99, 71-78. doi:10.1016/j.knosys.2016.01.047Zhang, H. (2016). Group decision making based on multiplicative consistent reciprocal preference relations. Fuzzy Sets and Systems, 282, 31-46. doi:10.1016/j.fss.2015.04.009Zhang, H. (2016). Group decision making based on incomplete multiplicative and fuzzy preference relations. Applied Soft Computing, 48, 735-744. doi:10.1016/j.asoc.2016.07.04

Multi-criteria decision making support tools for maintenance of marine machinery systems

PhD ThesisFor ship systems to remain reliable and safe they must be effectively maintained through a sound maintenance management system. The three major elements of maintenance management systems are; risk assessment, maintenance strategy selection and maintenance task interval determination. The implementation of these elements will generally determine the level of ship system safety and reliability. Reliability Centred Maintenance (RCM) is one method that can be used to optimise maintenance management systems. However the tools used within the framework of the RCM methodology have limitations which may compromise the efficiency of RCM in achieving the desired results. This research presents the development of tools to support the RCM methodology and improve its effectiveness in marine maintenance system applications. Each of the three elements of the maintenance management system has been considered in turn. With regard to risk assessment, two Multi-Criteria Decision Making techniques (MCDM); Vlsekriterijumska Optimizacija Ikompromisno Resenje, meaning: Multi-criteria Optimization and Compromise Solution (VIKOR) and Compromise Programming (CP) have been integrated into Failure Mode and Effects Analysis (FMEA) along with a novel averaging technique which allows the use of incomplete or imprecise failure data. Three hybrid MCDM techniques have then been compared for maintenance strategy selection; an integrated Delphi-Analytical Hierarchy Process (AHP) methodology, an integrated Delphi-AHP-PROMETHEE (Preference Ranking Organisation METHod for Enrichment Evaluation) methodology and an integrated Delphi-AHP-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) methodology. Maintenance task interval determination has been implemented using a MCDM framework integrating a delay time model to determine the optimum inspection interval and using the age replacement model for the scheduled replacement tasks. A case study based on a marine Diesel engine has been developed with input from experts in the field to demonstrate the effectiveness of the proposed methodologies.Tertiary Education Trust Fund (TETFUND), a scholarship body of the Federal Republic of Nigeria for providing the fund for this research. My gratitude also goes to Federal University of Petroleum Resource, Effurun, Nigeria for giving me the opportunity to be a beneficiary of the scholarship