The General Least Square Deviation OWA Operator Problem

Abstract

A crucial issue in applying the ordered weighted averaging (OWA) operator for decision making is the determination of the associated weights. This paper proposes a general least convex deviation model for OWA operators which attempts to obtain the desired OWA weight vector under a given orness level to minimize the least convex deviation after monotone convex function transformation of absolute deviation. The model includes the least square deviation (LSD) OWA operators model suggested by Wang, Luo and Liu in Computers & Industrial Engineering, 2007, as a special class. We completely prove this constrained optimization problem analytically. Using this result, we also give solution of LSD model suggested by Wang, Luo and Liu as a function of n and α completely. We reconsider two numerical examples that Wang, Luo and Liu, 2007 and Sang and Liu, Fuzzy Sets and Systems, 2014, showed and consider another different type of the model to illustrate our results.

The General Model for Least Convex Disparity RIM Quantifier Problems

“…where the generating functions are absolutely continuous. Hong and Han [10] recently proposed the general least convex deviation model with a given orness level, as follows:…”

“…One of the important topics in the theory of ordered weighted averaging (OWA) operators is the determination of the associated weights. Several authors have suggested a number of methods for obtaining associated weights in many areas, such as decision-making, approximate reasoning, expert systems, data mining, as well as fuzzy systems and control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Yager [15] proposed regular increasing monotone (RIM) quantifiers as a method for obtaining OWA weight vectors through fuzzy linguistic quantifiers.…”

“…Hong and Han [10] recently provided the following general model for the least squares deviation (LSD) method as an alternative approach to determine the OWA operator weights:…”

Type-1 OWA Operators in Aggregating Multiple Sources of Uncertain Information: Properties and Real-World Applications in Integrated Diagnosis

“…In domains where information fusion/integration or multi-factorial evaluation is needed, an aggregation process is necessary to combine multiple sources of infor-mation into a global result so that in the final decision, all the individual sources of information are taken into account [1]. For example, in medicine, diagnosis or measurement can rarely be decided based on an individual criterion.…”

Empirical Means on Pseudo-Orthogonal Groups

“…In general, smooth manifolds in function optimization serve to conveniently represent non-linear constraints. Constrained optimization arises in several branches of science, ranging from applied mathematics [14][15][16] to information sciences [14,17,18]. In [19,20], optimization-based mean-computation problems over the space of the symmetric positive-definite matrices, the special Euclidean group and the space of unipotent matrices were studied.…”