Bonferroni Means with the Adequacy Coefficient and the Index of Maximum and Minimum Level
The aim of the paper is to develop new aggregation operators using Bonferroni means, OWA operators and some distance and norms measures. We introduce the BON-OWAAC and BON-OWAIMAM operators. We are able to include adequacy coefficient and the maximum and
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partment of Business Administration, Faculty of Business Administration, Antonio Nariño University, 7 Avenue, 21-84, 150001 Tunja, Colombia [email protected] 2 Department of Management Control and Information Systems, School of Economic and Business, University of Chile, Av. Diagonal Paraguay, 257, 8330015 Santiago, Chile
Abstract. The aim of the paper is to develop new aggregation operators using Bonferroni means, OWA operators and some distance and norms measures. We introduce the BON-OWAAC and BON-OWAIMAM operators. We are able to include adequacy coefficient and the maximum and minimum level in the same formulation with Bonferroni means and OWA operator. The main advantages on using these operators are that they allow considering continuous aggregations, multiple-comparison between each argument and distance measures in the same formulation. The numerical sample is focused on an entrepreneurial example in the sport industry in Colombia. Keywords: Bonferroni means
OWA operators Distance measures
1 Introduction In the literature, there are a wide range of methods that allows aggregating information [1–6], which allow obtaining representative values of the aggregated information. One of the most popular models used is the ordered weighted averaging OWA operator [1], from which has developed a great deal of extension in combination with others mathematical models. One of these models are selection indices [3]. These are called ordered weighted averaging distance (OWAD) [3, 7], ordered weighted averaging adequacy coefficient (OWAAC) operator and ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator [8, 9] and allow aggregating information through the comparison between two elements in order to get a representative value. Likewise, a new aggregation operator is proposed by using Bonferroni means (BM) [10], which allows making multiple-comparison between input arguments and capturing its interrelationship. Yager [11] combined OWA operator with BM proposing a new aggregation operator called BON-OWA and suggested a generalization of this operator. This new aggregation operator aroused the curiosity of the scientific community so that multiple authors study and develop new models based on it [12–19]. © Springer International Publishing Switzerland 2016 R. León et al. (Eds.): MS 2016, LNBIP 254, pp. 155–166, 2016. DOI: 10.1007/978-3-319-40506-3_16
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F. Blanco-Mesa and J.M. Merigó
The aim of this paper is to develop new mathematical application based on Bonferroni means, OWA operator and some distance measure. This application consists in that BM in combination with OWAIMAN and OWAAC operator. The main advantage of this proposition is that it allows considering continuous aggregations, multiplecomparison between each argument and distance measures in the same formulation. The structure of this paper is as follows: In Sect. 2, basic concepts Bonferroni means, OWA operators and distance measures are briefly reviewed and new proposition is presented. In Sect. 3, new method based on ade
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