Granular computing and optimization model-based method for large-scale group decision-making and its application

In large-scale group decision-making process, some decision makers hesitate among several linguistic terms and cannot compare some alternatives, so they often express evaluation information with incomplete hesitant fuzzy linguistic preference relations. How to obtain suitable large-scale group decision-making results from incomplete preference information is an important and interesting issue to concern about. After analyzing the existing researches, we find that: i) the premise that complete preference relation is perfectly consistent is too strict, ii) deleting all incomplete linguistic preference relations that cannot be fully completed will lose valid assessment information, iii) semantics given by decision makers are greatly possible to be changed during the consistency improving process. In order to solve these issues, this work proposes a novel method based on Granular computing and optimization model for large-scale group decision-making, considering the original consistency of incomplete hesitant fuzzy linguistic preference relation and improving its consistency without changing semantics during the completion process. An illustrative example and simulation experiments demonstrate the rationality and advantages of the proposed method: i) semantics are not changed during the consistency improving process, ii) completion process does not significantly alter the inherent quality of information, iii) complete preference relations are globally consistent, iv) final large-scale group decision-making result is acquired by fusing complete preference relations with different weights

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed

Managing Incomplete Preference Relations in Decision Making: A Review and Future Trends

In decision making, situations where all experts are able to efficiently express their preferences over all the available options are the exception rather than the rule. Indeed, the above scenario requires all experts to possess a precise or sufficient level of knowledge of the whole problem to tackle, including the ability to discriminate the degree up to which some options are better than others. These assumptions can be seen unrealistic in many decision making situations, especially those involving a large number of alternatives to choose from and/or conflicting and dynamic sources of information. Some methodologies widely adopted in these situations are to discard or to rate more negatively those experts that provide preferences with missing values. However, incomplete information is not equivalent to low quality information, and consequently these methodologies could lead to biased or even bad solutions since useful information might not being taken properly into account in the decision process. Therefore, alternative approaches to manage incomplete preference relations that estimates the missing information in decision making are desirable and possible. This paper presents and analyses methods and processes developed on this area towards the estimation of missing preferences in decision making, and highlights some areas for future research

Consistency and Consensus Driven for Hesitant Fuzzy Linguistic Decision Making with Pairwise Comparisons

Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of decision making with HFLPR, the paper introduces an algorithm for group decision making with HFLPRs based on the acceptable consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing a procedure for consistency checking and inconsistency improving for HFLPR; (2) measuring the group consensus based on the similarity between the original individual HFLPRs and the overall perfect HFLPR, then establishing a procedure for consensus ensuring including the determination of decision-makers weights. The convergence and monotonicity of the proposed two procedures have been proved. Some experiments are furtherly performed to investigate the critical values of the defined HFLGCI, and comparative analyses are conducted to show the effectiveness of the proposed algorithm. A case concerning the performance evaluation of venture capital guiding funds is given to illustrate the availability of the proposed algorithm. As an application of our work, an online decision-making portal is finally provided for decision-makers to utilize the proposed algorithms to solve decision-making problems.Comment: Pulished by Expert Systems with Applications (ISSN: 0957-4174

Linking objective and subjective modeling in engineering design through arc-elastic dominance

Engineering design in mechanics is a complex activity taking into account both objective modeling processes derived from physical analysis and designers’ subjective reasoning. This paper introduces arc-elastic dominance as a suitable concept for ranking design solutions according to a combination of objective and subjective models. Objective models lead to the aggregation of information derived from physics, economics or eco-environmental analysis into a performance indicator. Subjective models result in a confidence indicator for the solutions’ feasibility. Arc-elastic dominant design solutions achieve an optimal compromise between gain in performance and degradation in confidence. Due to the definition of arc-elasticity, this compromise value is expressive and easy for designers to interpret despite the difference in the nature of the objective and subjective models. From the investigation of arc-elasticity mathematical properties, a filtering algorithm of Pareto-efficient solutions is proposed and illustrated through a design knowledge modeling framework. This framework notably takes into account Harrington’s desirability functions and Derringer’s aggregation method. It is carried out through the re-design of a geothermal air conditioning system

Predicting missing pairwise preferences from similarity features in group decision making

In group decision-making (GDM), fuzzy preference relations (FPRs) refer to pairwise preferences in the form of a matrix. Within the field of GDM, the problem of estimating missing values is of utmost importance, since many experts provide incomplete preferences. In this paper, we propose a new method called the entropy-based method for estimating the missing values in the FPR. We compared the accuracy of our algorithm for predicting the missing values with the best candidate algorithm from state of the art achievements. In the proposed entropy-based method, we took advantage of pairwise preferences to achieve good results by storing extra information compared to single rating scores, for example, a pairwise comparison of alternatives vs. the alternative’s score from one to five stars. The entropy-based method maps the prediction problem into a matrix factorization problem, and thus the solution for the matrix factorization can be expressed in the form of latent expert features and latent alternative features. Thus, the entropy-based method embeds alternatives and experts in the same latent feature space. By virtue of this embedding, another novelty of our approach is to use the similarity of experts, as well as the similarity between alternatives, to infer the missing values even when only minimal data are available for some alternatives from some experts. Note that current approaches may fail to provide any output in such cases. Apart from estimating missing values, another salient contribution of this paper is to use the proposed entropy-based method to rank the alternatives. It is worth mentioning that ranking alternatives have many possible applications in GDM, especially in group recommendation systems (GRS).Andalusian Government P20 00673 PID2019-103880RB-I00 MCIN/AEI/10.13039/50110001103

A systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version

Integer programming modeling on group decision making with incomplete hesitant fuzzy linguistic preference relations

© 2013 IEEE. Complementing missing information and priority vector are of significance important aspects in group decision making (GDM) with incomplete hesitant fuzzy linguistic preference relations (HFLPRs). In this paper, an integer programming model is developed based on additive consistency to estimate missing values of incomplete HFLPRs by using additive consistency. Once the missing values are complemented, a mixed 0-1 programming model is established to derive the priority vectors from complete HFLPRs, in which the underlying idea of the mixed 0-1 programming model is the probability sampling in statistics and minimum deviation between the priority vector and HFLPR. In addition, we also propose a new GDM approach for incomplete HFLPRs by integrating the integer programming model and the mixed 0-1 programming model. Finally, two case studies and comparative analysis detail the application of the proposed models

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