n-K-Increasing Aggregation Functions
Author:
Mesiar Radko12, Kolesárová Anna1, Šeliga Adam1ORCID, Halaš Radomír2ORCID
Affiliation:
1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia 2. Department of Algebra and Geometry, Faculty of Science, Palacký Univeristy Olomouc, 771 46 Olomouc, Czech Republic
Abstract
We introduce and discuss the concept of n-ary K-increasing fusion functions and n-ary K-increasing aggregation functions, K being a subset of the index set {1,…,n} indicating in which variables a considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each n-ary K-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of n-ary K-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary K-increasing aggregation functions, including fuzzy implication and complication functions, among others.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference28 articles.
1. Beliakov, G., Pradera, A., and Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners, Springer. 2. Calvo, T., Mayor, G., and Mesiar, R. (2002). Aggregation Operators, Physica-Verlag. 3. Grabisch, M., Marichal, J.-L., Mesiar, R., and Pap, E. (2009). Aggregation Functions, Cambridge University Press. 4. Ehrgott, M., Greco, S., and Figueira, J.R. (2016). Trends in Multiple Criteria Decision Analysis, Springer. 5. Keeney, R.L., and Raiffa, H. (1976). Decision Making with Multiple Objectives Preferences and Value Tradeoffs, Wiley.
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