Fitting generated aggregation operators to empirical data

This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.<br /

Representation of Aggregation Knowledge in OLAP Systems

Decision support systems are mainly based on multidimensional modeling. Using On-Line Analytical Processing (OLAP) tools, decision makers navigate through and analyze multidimensional data. Typically, users need to analyze data at different aggregation levels, using OLAP operators such as roll-up and drill-down. Roll-up operators decrease the details of the measure, aggregating it along the dimension hierarchy. Conversely, drill-down operators increase the details of the measure. As a consequence, dimensions hierarchies play a central role in knowledge representation. More precisely, since aggregation hierarchies are widely used to support data aggregation, aggregation knowledge should be adequately represented in conceptual multidimensional models, and mapped in subsequent logical and physical models. However, current conceptual multidimensional models poorly represent aggregation knowledge, which (1) has a complex structure and dynamics and (2) is highly contextual. In order to account for the characteristics of this knowledge, we propose to represent it with objects and rules. Static aggregation knowledge is represented using UML class diagrams, while rules, which represent the dynamics (i.e. how aggregation may be performed depending on context), are represented using the Production Rule Representation (PRR) language. The latter allows us to incorporate dynamic aggregation knowledge. We argue that this representation of aggregation knowledge allows an early modeling of user requirements in a decision support system project. In order to illustrate the applicability and benefits of our approach, we exemplify the production rules and present an application scenario

Fuzzy Integral Driven Ensemble Classification using A Priori Fuzzy Measures

Aggregation operators are mathematical functions that enable the fusion of information from multiple sources. Fuzzy Integrals (FIs) are widely used aggregation operators, which combine information in respect to a Fuzzy Measure (FM) which captures the worth of both the individual sources and all their possible combinations. However, FIs suffer from the potential drawback of not fusing information according to the intuitively interpretable FM, leading to non-intuitive results. The latter is particularly relevant when a FM has been defined using external information (e.g. experts). In order to address this and provide an alternative to the FI, the Recursive Average (RAV) aggregation operator was recently proposed which enables intuitive data fusion in respect to a given FM. With an alternative fusion operator in place, in this paper, we define the concept of ‘A Priori’ FMs which are generated based on external information (e.g. classification accuracy) and thus provide an alternative to the traditional approaches of learning or manually specifying FMs. We proceed to develop one specific instance of such an a priori FM to support the decision level fusion step in ensemble classification. We evaluate the resulting approach by contrasting the performance of the ensemble classifiers for different FMs, including the recently introduced Uriz and the Sugeno lambda-measure; as well as by employing both the Choquet FI and the RAV as possible fusion operators. Results are presented for 20 datasets from machine learning repositories and contextualised to the wider literature by comparing them to state-of-the-art ensemble classifiers such as Adaboost, Bagging, Random Forest and Majority Voting

Insights and Characterization of l1-norm Based Sparsity Learning of a Lexicographically Encoded Capacity Vector for the Choquet Integral

This thesis aims to simultaneously minimize function error and model complexity for data fusion via the Choquet integral (CI). The CI is a generator function, i.e., it is parametric and yields a wealth of aggregation operators based on the specifics of the underlying fuzzy measure. It is often the case that we desire to learn a fusion from data and the goal is to have the smallest possible sum of squared error between the trained model and a set of labels. However, we also desire to learn as “simple’’ of solutions as possible. Herein, L1-norm regularization of a lexicographically encoded capacity vector relative to the CI is explored. The impact of regularization is explored in terms of what capacities and aggregation operators it induces under different common and extreme scenarios. Synthetic experiments are provided in order to illustrate the propositions and concepts put forth

Water Policies and Conflict Resolution of Public Participation Decision-Making Processes Using Prioritized Ordered Weighted Averaging (OWA) Operators

[EN] There is a growing interest in environmental policies about how to implement public participation engagement in the context of water resources management. This paper presents a robust methodology, based on ordered weighted averaging (OWA) operators, to conflict resolution decision-making problems under uncertain environments due to both information and stakeholders' preferences. The methodology allows integrating heterogeneous interests of the general public and stakeholders on account of their different degree of acceptance or preference and level of influence or power regarding the measures and policies to be adopted, and also of their level of involvement (i.e., information supply, consultation and active involvement). These considerations lead to different environmental and socio-economic outcomes, and levels of stakeholders' satisfaction. The methodology establishes a prioritization relationship over the stakeholders. The individual stakeholders' preferences are aggregated through their associated weights, which depend on the satisfaction of the higher priority decision maker. The methodology ranks the optimal management strategies to maximize the stakeholders' satisfaction. It has been successfully applied to a real case study, providing greater fairness, transparency, social equity and consensus among actors. Furthermore, it provides support to environmental policies, such as the EU Water Framework Directive (WFD), improving integrated water management while covering a wide range of objectives, management alternatives and stakeholders.Llopis Albert, C.; Merigó-Lindahl, JM.; Liao, H.; Xu, Y.; Grima-Olmedo, J.; Grima-Olmedo, C. (2018). Water Policies and Conflict Resolution of Public Participation Decision-Making Processes Using Prioritized Ordered Weighted Averaging (OWA) Operators. Water Resources Management. 32(2):497-510. https://doi.org/10.1007/s11269-017-1823-2S497510322Amin GR, Sadeghi H (2010) Application of prioritized aggregation operators in preference voting. Int J Intell Syst 25(10):1027–1034Chen TY (2014) A prioritized aggregation operator-based approach to multiple criteria decision making using interval-valued intuitionistic fuzzy sets: A comparative perspective. Inf Sci 281:97–112Chen LH, Xu ZS (2014) A prioritized aggregation operator based on the OWA operator and prioritized measures. J Intell Fuzzy Syst 27:1297–1307Chen LH, Xu ZS, Yu XH (2014a) Prioritized measure-guided aggregation operators. IEEE Trans Fuzzy Syst 22:1127–1138Chen LH, Xu ZS, Yu XH (2014b) Weakly prioritized measure aggregation in prioritized multicriteria decision making. Int J Intell Syst 29:439–461CHJ (2016). Júcar river basin authority http://www.chj.es/CHS (2016). Segura river basin authority http://www.chsegura.es/Dong JY, Wan SP (2016) A new method for prioritized multi-criteria group decision making with triangular intuitionistic fuzzy numbers. J Intell Fuzzy Syst 30:1719–1733EC (2000). Directive 2000/60/EC of the European Parliament and of the Council of October 23 2000 Establishing a Framework for Community Action in the Field of Water Policy. Official Journal of the European Communities, L327/1eL327/72 22.12.2000Jackson S, Tan P-L, Nolan S (2012) Tools to enhance public participation and confidence in the development of the Howard East aquifer water plan, Northern Territory. J Hydrol 474:22–28Jin FF, Ni ZW, Chen HY (2016) Note on “Hesitant fuzzy prioritized operators and their application to multiple attribute decision making”. Knowl-Based Syst 96:115–119Kentel E, Aral MM (2007) Fuzzy Multiobjective Decision-Making Approach for Groundwater Resources Management. J Hydrol Eng 12(2):206–217. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:2(206).Kirchherr J, Charles KJ, Walton MJ (2016) Multi-causal pathways of public opposition to dam project in Asia: A fuzzy set qualitative comparative analysis (fsQCA). Glob Environ Chang 41:33–45. https://doi.org/10.1016/j.gloenvcha.2016.08.001Llopis-Albert C, Pulido-Velazquez D (2015) Using MODFLOW code to approach transient hydraulic head with a sharp-interface solution. Hydrol Process 29(8):2052–2064. https://doi.org/10.1002/hyp.10354Llopis-Albert C, Palacios-Marqués D, Soto-Acosta P (2015) Decision-making and stakeholders constructive participation in environmental projects. J Bus Res 68:1641–1644. https://doi.org/10.1016/j.jbusres.2015.02.010Llopis-Albert C, Merigó JM, Xu Y, Huchang L (2017) Improving regional climate projections by prioritized aggregation via ordered weighted averaging operators. Environ Eng Sci. https://doi.org/10.1089/ees.2016.0546Maia R (2017) The WFD Implementation in the European Member States. Water Resour Manag 31(10):3043–3060. https://doi.org/10.1007/s11269-017-1723-5Malczewski J, Chapman T, Flegel C, Walters D, Shrubsole D, Healy MA (2003) GIS - multicriteria evaluation with ordered weighted averaging (OWA): case study of developing watershed management strategies. Environ Plan A 35:1769–1784. https://doi.org/10.1068/a35156Merigó JM, Casanovas M (2011) The uncertain generalized owa operator and its application to financial decision making. Int J Inf Technol Decis Mak 10(2):211–230Merigó JM, Yager RR (2013) Generalized moving averages, distance measures and OWA operators. Int J Uncertain, Fuzziness Knowl-Based Syst 21(4):533–559Merigó JM, Palacios-Marqués D, Ribeiro-Navarrete B (2015) Aggregation systems for sales forecasting. J Bus Res 68:2299–2304Mesiar R, Stupnanová A, Yager RR (2015) Generalizations of OWA Operators. IEEE Trans Fuzzy Syst 23(6):2154–2162O’Hagan M (1988) Aggregating Template Rule Antecedents in Real-time Expert Systems with Fuzzy Set Logic. In: Proceedings of 22nd annual IEEE Asilomar Conference on Signals. IEEE and Maple Press, Pacific Grove, Systems and Computers, pp 681–689Rahmani MA, Zarghami M (2013) A new approach to combine climate change projections by ordered weighting averaging operator; applications to northwestern provinces of Iran. Glob Planet Chang 102:41–50Ran LG, Wei GW (2015) Uncertain prioritized operators and their application to multiple attribute group decision making. Technol Econ Dev Econ 21:118–139Ruiz-Villaverde, A., García-Rubio, M.A. (2017). Public Participation in European Water Management: from Theory to Practice. Water Resour Manag 31(8), 2479–2495. https://doi.org/10.1007/s11269-016-1355-1Sadiq R, Tesfamariam S (2007) Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices. Eur J Oper Res 182:1350–1368Sadiq R, Rodríguez MJ, Tesfamariam S (2010) Integrating indicators for performance assessment of small water utilities using ordered weighted averaging (OWA) operators. Expert Syst Appl 37:4881–4891Verma R, Sharma B (2016) Prioritized information fusion method for triangular fuzzy information and its application to multiple attribute decision making. Int J Uncertain, Fuzziness Knowl-Based Syst 24:265–290Wang HM, Xu YJ, Merigó JM (2014) Prioritized aggregation for non-homogeneous group decision making in water resource management. Econ Comput Econ Cybern Stud Res 48(1):247–258Wei GW (2012) Hesitant fuzzy prioritized operators. Knowl-Based Syst 31:176–182Wei CP, Tang XJ (2012) Generalized prioritized aggregation operators. Int J Intell Syst 27:578–589Xu ZS (2005) An Overview of Methods for Determining OWA Weights. Int J Intell Syst 20:843–865Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems. Man Cybern B 18(1988):183–190Yager RR (2008) Prioritized Aggregation Operators. Int J Approx Reason 48:263–274Yan H-B, Huynh V-N, Nakamori Y, Murai T (2011) On prioritized weighted aggregation in multi-criteria decision making. Expert Syst Appl 38(1):812–823Ye J (2014) Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multicriteria decision-making. Neural Comput & Applic 25:1447–1454Yu XH, Xu ZS, Liu SS (2013) Prioritized multi-criteria decision making based on preference relations. Comput Ind Eng 66:104–115Zadeh LA (1983) A Computational Approach to Fuzzy Quantifiers in Natural Languages. Comput Math Appl 9:149–184Zarghami M, Szidarovszky F (2009) Revising the OWA operator for multi criteria decision making problems under uncertainty. Eur J Oper Res 198:259–265Zarghami M, Ardakanian R, Memariani A, Szidarovszky F (2008) Extended OWA Operator for Group Decision Making on Water Resources Projects. J Water Resour Plan Manag 134(3):266–275. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:3(266)Zarghami M, Szidarovszky F, Ardakanian R (2009) Multi-attribute decision making on inter-basin water transfer projects. Transaction E. Ind Eng 16(1):73–80Zhao XF, Li QX, Wei GW (2014) Some prioritized aggregating operators with linguistic information and their application to multiple attribute group decision making. J Intell Fuzzy Syst 26:1619–1630Zhao N, Xu ZS, Ren ZL (2016) On typical hesitant fuzzy prioritized “or” operator in multi-attribute decision making. Int J Intell Syst 31:73–100Zhou LY, Lin R, Zhao XF, Wei GW (2013) Uncertain linguistic prioritized aggregation operators and their application to multiple attribute group decision making. Int J Uncertain, Fuzziness Knowl-Based Syst 21:603–627Zhou LG, Merigó JM, Chen HY, Liu JP (2016) The optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the COWGA operator. Inf Sci 328:250–26

Construction of aggregation operators with noble reinforcement

This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements. <br /

Pareto Optimality and Strategy Proofness in Group Argument Evaluation (Extended Version)

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences