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The Solution Equivalence to General Models for the RIM Quantifier Problem

Department of Mathematics, Myongji University, Yongin 449-728, Kyunggido, Korea
Symmetry 2019, 11(4), 455; https://doi.org/10.3390/sym11040455
Received: 3 March 2019 / Revised: 25 March 2019 / Accepted: 28 March 2019 / Published: 1 April 2019
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ)
Hong investigated the relationship between the minimax disparity minimum variance regular increasing monotone (RIM) quantifier problems. He also proved the equivalence of their solutions to minimum variance and minimax disparity RIM quantifier problems. Hong investigated the relationship between the minimax ratio and maximum entropy RIM quantifier problems and proved the equivalence of their solutions to the maximum entropy and minimax ratio RIM quantifier problems. Liu proposed a general RIM quantifier determination model and proved it analytically by using the optimal control technique. He also gave the equivalence of solutions to the minimax problem for the RIM quantifier. Recently, Hong proposed a modified model for the general minimax RIM quantifier problem and provided correct formulation of the result of Liu. Thus, we examine the general minimum model for the RIM quantifier problem when the generating functions are Lebesgue integrable under the more general assumption of the RIM quantifier operator. We also provide a solution equivalent relationship between the general maximum model and the general minimax model for RIM quantifier problems, which is the corrected and generalized version of the equivalence of solutions to the general maximum model and the general minimax model for RIM quantifier problems of Liu’s result. View Full-Text
Keywords: OWA operator; RIM quantifier; maximum entropy; minimax ratio; generating function; minimal variability; minimax disparity; solution equivalence OWA operator; RIM quantifier; maximum entropy; minimax ratio; generating function; minimal variability; minimax disparity; solution equivalence
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Hong, D.H. The Solution Equivalence to General Models for the RIM Quantifier Problem. Symmetry 2019, 11, 455.

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