A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe

Decision making with Dempster-Shafer belief structure and the OWAWA operator

[EN] A new decision making model that uses the weighted average and the ordered weighted averaging (OWA) operator in the Dempster-Shafer belief structure is presented. Thus, we are able to represent the decision making problem considering objective and subjective information and the attitudinal character of the decision maker. For doing so, we use the ordered weighted averaging ¿ weighted average (OWAWA) operator. It is an aggregation operator that unifies the weighted average and the OWA in the same formulation. This approach is generalized by using quasi-arithmetic means and group decision making techniques. An application of the new approach in a group decision making problem concerning political management of a country is also developed.We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Spanish Ministry of Education under project JC2009-00189 , the University of Barcelona (099311) and the European Commission (PIEFGA-2011-300062) is gratefully acknowledgedMerigó, JM.; Engemann, KJ.; Palacios Marqués, D. (2013). Decision making with Dempster-Shafer belief structure and the OWAWA operator. Technological and Economic Development of Economy. 19(sup 1):S100-S118. https://doi.org/10.3846/20294913.2013.869517SS100S11819sup 1Antuchevičienė, J., Zavadskas, E. K., & Zakarevičius, A. (2010). MULTIPLE CRITERIA CONSTRUCTION MANAGEMENT DECISIONS CONSIDERING RELATIONS BETWEEN CRITERIA / DAUGIATIKSLIAI STATYBOS VALDYMO SPRENDIMAI ATSIŽVELGIANT Į RODIKLIŲ TARPUSAVIO PRIKLAUSOMYBĘ. Technological and Economic Development of Economy, 16(1), 109-125. doi:10.3846/tede.2010.07Brauers, W. K. M., & Zavadskas, E. K. (2010). PROJECT MANAGEMENT BY MULTIMOORA AS AN INSTRUMENT FOR TRANSITION ECONOMIES / PROJEKTŲ VADYBA SU MULTIMOORA KAIP PRIEMONĖ PEREINAMOJO LAIKOTARPIO ŪKIAMS. Technological and Economic Development of Economy, 16(1), 5-24. doi:10.3846/tede.2010.01Dempster, A. P. (1967). Upper and Lower Probabilities Induced by a Multivalued Mapping. The Annals of Mathematical Statistics, 38(2), 325-339. doi:10.1214/aoms/1177698950ENGEMANN, K. J., MILLER, H. E., & YAGER, R. R. (1996). DECISION MAKING WITH BELIEF STRUCTURES: AN APPLICATION IN RISK MANAGEMENT. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 04(01), 1-25. doi:10.1142/s0218488596000020ENGEMANN, K. J., FILEV, D. P., & YAGER, R. R. (1996). MODELLING DECISION MAKING USING IMMEDIATE PROBABILITIES. International Journal of General Systems, 24(3), 281-294. doi:10.1080/03081079608945123Engemann, K. J., & Miller, H. E. (2009). Critical infrastructure and smart technology risk modelling using computational intelligence. International Journal of Business Continuity and Risk Management, 1(1), 91. doi:10.1504/ijbcrm.2009.028953Fodor, J., Marichal, J.-L., & Roubens, M. (1995). Characterization of the ordered weighted averaging operators. IEEE Transactions on Fuzzy Systems, 3(2), 236-240. doi:10.1109/91.388176Han, Z., & Liu, P. (2011). A FUZZY MULTI-ATTRIBUTE DECISION-MAKING METHOD UNDER RISK WITH UNKNOWN ATTRIBUTE WEIGHTS / NERAIŠKUSIS MAŽESNĖS RIZIKOS DAUGIATIKSLIS SPRENDIMŲ PRIĖMIMO METODAS SU NEŽINOMAIS PRISKIRIAMAIS REIKŠMINGUMAIS. Technological and Economic Development of Economy, 17(2), 246-258. doi:10.3846/20294913.2011.580575Keršulienė, V., Zavadskas, E. K., & Turskis, Z. (2010). SELECTION OF RATIONAL DISPUTE RESOLUTION METHOD BY APPLYING NEW STEP‐WISE WEIGHT ASSESSMENT RATIO ANALYSIS (SWARA). Journal of Business Economics and Management, 11(2), 243-258. doi:10.3846/jbem.2010.12Liu, P. (2009). MULTI‐ATTRIBUTE DECISION‐MAKING METHOD RESEARCH BASED ON INTERVAL VAGUE SET AND TOPSIS METHOD. Technological and Economic Development of Economy, 15(3), 453-463. doi:10.3846/1392-8619.2009.15.453-463Liu, P. (2011). A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Systems with Applications, 38(1), 1053-1060. doi:10.1016/j.eswa.2010.07.144Merigó, J. M. (2011). A unified model between the weighted average and the induced OWA operator. Expert Systems with Applications, 38(9), 11560-11572. doi:10.1016/j.eswa.2011.03.034Merigó, J. M. (2012). The probabilistic weighted average and its application in multiperson decision making. International Journal of Intelligent Systems, 27(5), 457-476. doi:10.1002/int.21531Merigó, J. M., & Casanovas, M. (2009). Induced aggregation operators in decision making with the Dempster-Shafer belief structure. International Journal of Intelligent Systems, 24(8), 934-954. doi:10.1002/int.20368Merigó, J. M., & Casanovas, M. (2010). The uncertain induced quasi-arithmetic OWA operator. International Journal of Intelligent Systems, 26(1), 1-24. doi:10.1002/int.20444MERIGÓ, J. M., & CASANOVAS, M. (2011). THE UNCERTAIN GENERALIZED OWA OPERATOR AND ITS APPLICATION TO FINANCIAL DECISION MAKING. International Journal of Information Technology & Decision Making, 10(02), 211-230. doi:10.1142/s0219622011004300MERIGÓ, J. M., CASANOVAS, M., & MARTÍNEZ, L. (2010). LINGUISTIC AGGREGATION OPERATORS FOR LINGUISTIC DECISION MAKING BASED ON THE DEMPSTER-SHAFER THEORY OF EVIDENCE. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18(03), 287-304. doi:10.1142/s0218488510006544MERIGO, J., & GILLAFUENTE, A. (2009). The induced generalized OWA operator. Information Sciences, 179(6), 729-741. doi:10.1016/j.ins.2008.11.013Merigó, J. M., & Gil-Lafuente, A. M. (2010). New decision-making techniques and their application in the selection of financial products. Information Sciences, 180(11), 2085-2094. doi:10.1016/j.ins.2010.01.028Merigó, J. M., & Wei, G. (2011). PROBABILISTIC AGGREGATION OPERATORS AND THEIR APPLICATION IN UNCERTAIN MULTI-PERSON DECISION-MAKING / TIKIMYBINIAI SUMAVIMO OPERATORIAI IR JŲ TAIKYMAS PRIIMANT GRUPINIUS SPRENDIMUS NEAPIBRĖŽTOJE APLINKOJE. Technological and Economic Development of Economy, 17(2), 335-351. doi:10.3846/20294913.2011.584961Podvezko, V. (2009). Application of AHP technique. Journal of Business Economics and Management, 10(2), 181-189. doi:10.3846/1611-1699.2009.10.181-189Reformat, M., & Yager, R. R. (2007). Building ensemble classifiers using belief functions and OWA operators. Soft Computing, 12(6), 543-558. doi:10.1007/s00500-007-0227-2Srivastava, R. P., & Mock, T. J. (Eds.). (2002). Belief Functions in Business Decisions. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-7908-1798-0Torra, V. (1997). The weighted OWA operator. International Journal of Intelligent Systems, 12(2), 153-166. doi:10.1002/(sici)1098-111x(199702)12:23.0.co;2-pWei, G.-W. (2011). Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making. Computers & Industrial Engineering, 61(1), 32-38. doi:10.1016/j.cie.2011.02.007Wei, G., Zhao, X., & Lin, R. (2010). Some Induced Aggregating Operators with Fuzzy Number Intuitionistic Fuzzy Information and their Applications to Group Decision Making. International Journal of Computational Intelligence Systems, 3(1), 84-95. doi:10.1080/18756891.2010.9727679Xu, Z. (2005). An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20(8), 843-865. doi:10.1002/int.20097Xu, Z. (2009). A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making. Group Decision and Negotiation, 19(1), 57-76. doi:10.1007/s10726-009-9164-zXu, Z. S., & Da, Q. L. (2003). An overview of operators for aggregating information. International Journal of Intelligent Systems, 18(9), 953-969. doi:10.1002/int.10127Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183-190. doi:10.1109/21.87068YAGER, R. R. (1992). DECISION MAKING UNDER DEMPSTER-SHAFER UNCERTAINTIES. International Journal of General Systems, 20(3), 233-245. doi:10.1080/03081079208945033Yager, R. R. (1993). Families of OWA operators. Fuzzy Sets and Systems, 59(2), 125-148. doi:10.1016/0165-0114(93)90194-mYager, R. R. (1998). Including importances in OWA aggregations using fuzzy systems modeling. IEEE Transactions on Fuzzy Systems, 6(2), 286-294. doi:10.1109/91.669028Yager, R. R. (2004). Generalized OWA Aggregation Operators. Fuzzy Optimization and Decision Making, 3(1), 93-107. doi:10.1023/b:fodm.0000013074.68765.97Yager, R. R., Engemann, K. J., & Filev, D. P. (1995). On the concept of immediate probabilities. International Journal of Intelligent Systems, 10(4), 373-397. doi:10.1002/int.4550100403Yager, R. R., & Kacprzyk, J. (Eds.). (1997). The Ordered Weighted Averaging Operators. doi:10.1007/978-1-4615-6123-1Yager, R. R., Kacprzyk, J., & Beliakov, G. (Eds.). (2011). Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-642-17910-5Yager, R. R., & Liu, L. (Eds.). (2008). Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-44792-4Zavadskas, E. K., & Turskis, Z. (2011). MULTIPLE CRITERIA DECISION MAKING (MCDM) METHODS IN ECONOMICS: AN OVERVIEW / DAUGIATIKSLIAI SPRENDIMŲ PRIĖMIMO METODAI EKONOMIKOJE: APŽVALGA. Technological and Economic Development of Economy, 17(2), 397-427. doi:10.3846/20294913.2011.593291Zavadskas, E. K., Vilutienė, T., Turskis, Z., & Tamosaitienė, J. (2010). CONTRACTOR SELECTION FOR CONSTRUCTION WORKS BY APPLYING SAW‐G AND TOPSIS GREY TECHNIQUES. Journal of Business Economics and Management, 11(1), 34-55. doi:10.3846/jbem.2010.03Zeng, S., & Su, W. (2011). Intuitionistic fuzzy ordered weighted distance operator. Knowledge-Based Systems, 24(8), 1224-1232. doi:10.1016/j.knosys.2011.05.013Zhang, X., & Liu, P. (2010). METHOD FOR AGGREGATING TRIANGULAR FUZZY INTUITIONISTIC FUZZY INFORMATION AND ITS APPLICATION TO DECISION MAKING / NUMANOMŲ NEAPIBRĖŽTŲJŲ AIBIŲ TEORIJA IR JOS TAIKYMAS PRIIMANT SPRENDIMUS. Technological and Economic Development of Economy, 16(2), 280-290. doi:10.3846/tede.2010.18Zhao, H., Xu, Z., Ni, M., & Liu, S. (2010). Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 25(1), 1-30. doi:10.1002/int.20386Zhou, L.-G., & Chen, H. (2010). Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. International Journal of Intelligent Systems, n/a-n/a. doi:10.1002/int.20419Zhou, L.-G., & Chen, H.-Y. (2011). Continuous generalized OWA operator and its application to decision making. Fuzzy Sets and Systems, 168(1), 18-34. doi:10.1016/j.fss.2010.05.009Zhou, L., & Chen, H. (2012). A generalization of the power aggregation operators for linguistic environment and its application in group decision making. Knowledge-Based Systems, 26, 216-224. doi:10.1016/j.knosys.2011.08.004Zhou, L., Chen, H., & Liu, J. (2011). Generalized Multiple Averaging Operators and their Applications to Group Decision Making. Group Decision and Negotiation, 22(2), 331-358. doi:10.1007/s10726-011-9267-1Zhou, L., Chen, H., & Liu, J. (2012). Generalized power aggregation operators and their applications in group decision making. Computers & Industrial Engineering, 62(4), 989-999. doi:10.1016/j.cie.2011.12.025Zhou, L.-G., Chen, H.-Y., Merigó, J. M., & Gil-Lafuente, A. M. (2012). Uncertain generalized aggregation operators. Expert Systems with Applications, 39(1), 1105-1117. doi:10.1016/j.eswa.2011.07.11

Fuzzy decision making in complex frameworks with generalized aggregation operators

[EN] This article presents a new aggregation system applied to fuzzy decision making. The fuzzy generalized unified aggregation operator (FGUAO) is a system that integrates many operators by adding a new aggregation process that considers the relevance that each operator has in the analysis. It also deals with an uncertain environment where the information is studied with fuzzy numbers. A wide range of particular cases and properties are studied. This approach is further extended by using quasi-arithmetic means. The paper ends studying the applicability in decision making problems regarding the European Union decisions. For doing so, the work uses a multi-person aggregation process obtaining the multi-person - FGUAO operator. An example concerning the fixation of the interest rate by the European Central Bank is presented. (C) 2018 Elsevier B.V. All rights reserved.We would like to thank the associate editor and the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Chilean Government through the Fondecyt Regular program (project number 1160286), the University of Chile, the project PIEF-GA-2011-300062 of the European Commission and the Distinguished Scientist Fellowship Program of the King Saud University (Saudi Arabia), is gratefully acknowledged.Merigó -Lindahl, JM.; Gil-Lafuente, AM.; Yu, D.; Llopis Albert, C. (2018). Fuzzy decision making in complex frameworks with generalized aggregation operators. Applied Soft Computing. 68:314-321. https://doi.org/10.1016/j.asoc.2018.04.002S3143216

Decisión making with induced aggregation operators and the adequacy coefficient

We present a method for decision making by using induced aggregation operators. This method is very useful for business decision making problems such as product management, investment selection and strategic management. We introduce a new aggregation operator that uses the induced ordered weighted averaging (IOWA) operator and the weighted average in the adequacy coefficient. We callit the induced ordered weighted averaging weighted averaging adequacy coefficient (IOWAWAAC) operator. The main advantage is that it is able to deal with complex attitudinal characters in the aggregation process. Thus, we are able to give a better representation of the problem considering the complex environment that affects the decisions. Moreover, it is able to provide a unified framework between the OWA and the weighted average. We generalize it by using generalized aggregation operators, obtaining the induced generalized OWAWAAC (IGOWAWAAC) operator . We study some of the main properties of this approach. We end the paper with a numerical example of the new approach in a group decision making problem in strategic managemen

OWA operators in the calculation of the average green-house gases emissions

This study proposes, through weighted averages and ordered weighted averaging operators, a new aggregation system for the investigation of average gases emissions. We present the ordered weighted averaging operators gases emissions, the induced ordered weighted averaging operators gases emissions, the weighted ordered weighted averaging operators gases emissions and the induced probabilistic weighted ordered weighted averaging operators gases emissions. These operators represent a new way of analyzing the average gases emissions of different variables like countries or regions. The work presents further generalizations by using generalized and quasi-arithmetic means. The article also presents an illustrative example with respect to the calculations of the average gases emissions in the European region

Expertons and uncertain averaging operators versus correlational approaches: A case study on corporate social responsibility and effectiveness

The purpose of this paper is to explore the relationship between corporate social responsibility (CSR), work-life balance (WLB) and effectiveness by comparing a correlational approach, expertons method and uncertain averaging operators (uncertain average [UA], uncertain weighted average [UWA], uncertain probabilistic aggregation [UPA] and uncertain probabilistic weighted averaging [UPWA])

The ordered weighted average inflation

This paper introduces the ordered weighted average inflation (OWAI). The OWAI operator aggregates the information of a set of inflations and provides a range of scenarios from the minimum and the maximum inflation. The advantage of this approach is that it can provide a flexible inflation formula that can be adapted to the specific characteristics of the enterprise, region, state or country (...

OWA-based aggregation operations in multi-expert MCDM model

This paper presents an analysis of multi-expert multi-criteria decision making (ME-MCDM) model based on the ordered weighted averaging (OWA) operators. Two methods of modeling the majority opinion are studied as to aggregate the experts' judgments, in which based on the induced OWA operators. Then, an overview of OWA with the inclusion of different degrees of importance is provided for aggregating the criteria. An alternative OWA operator with a new weighting method is proposed which termed as alternative OWAWA (AOWAWA) operator. Some extensions of ME-MCDM model with respect to two-stage aggregation processes are developed based on the classical and alternative schemes. A comparison of results of different decision schemes then is conducted. Moreover, with respect to the alternative scheme, a further comparison is given for different techniques in integrating the degrees of importance. A numerical example in the selection of investment strategy is used as to exemplify the model and for the analysis purpose

Aggregation operators in group decision making: Identifying citation classics via H-classics

To analyze the past, present and future of a particular research field, classic papers are usually studied because they identify the highly cited papers being a relevant reference point in that specific research area. As a result of the possible mapping between high quality research and high citation counts, highly cited papers are very interesting. The objective of this study is to use the H-classics method, which is based on the popular h-index, to identify and analyze the highly cited documents published about aggregation operators in the research area of group decision making. According to the H-classics method, this research area is represented by 87 citation classics, which have been published from 1988 to 2014. Authors, affiliations (universities/institutions and countries), journals, books and conferences, and the topics covered by these 87 highly cited papers are studied.The authors would like to thank FEDER financial support from the Projects TIN2013-40658-P and TIN2016- 75850-P