An analytic approach to obtain the least square deviation OWA operator weights

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.

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The General Model for Least Convex Disparity RIM Quantifier Problems

Mathematics ◽

10.3390/math7070576 ◽

2019 ◽

Vol 7 (7) ◽

pp. 576

Author(s):

Dug Hun Hong

Keyword(s):

Least Squares ◽

General Model ◽

Least Square ◽

Weighted Averaging ◽

Owa Operator ◽

Ordered Weighted Averaging ◽

Full Solution

Hong (Mathematics 2019, 7, 326) recently introduced the general least squares deviation (LSD) model for ordered weighted averaging (OWA) operator weights. In this paper, we propose the corresponding generalized least square disparity model for regular increasing monotone (RIM) quantifier determination under a given orness level. We prove this problem mathematically. Using this result, we provide the full solution of the least square disparity RIM quantifier model as an illustrative example.

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An analytic approach for obtaining maximal entropy OWA operator weights

Fuzzy Sets and Systems ◽

10.1016/s0165-0114(01)00007-0 ◽

2001 ◽

Vol 124 (1) ◽

pp. 53-57 ◽

Cited By ~ 245

Author(s):

Robert Fullér ◽

Péter Majlender

Keyword(s):

Analytic Approach ◽

Maximal Entropy ◽

Owa Operator

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Least-square refinement of structure parameters from CBED integrated intensities: application to determination of temperature factors in Y BA2CU3O7

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100131917 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1456-1457

Author(s):

Kjersti Gjønnes ◽

Jon Gjønnes

Keyword(s):

Least Square ◽

Measured Intensity ◽

Structure Information ◽

Accurate Temperature ◽

Least Square Fit ◽

Case Application ◽

Integrated Intensities ◽

Temperature Factors ◽

Narrow Bands

Electron diffraction intensities can be obtained at large scattering angles (sinθ/λ ≥ 2.0), and thus structure information can be collected in regions of reciprocal space that are not accessable with other diffraction methods. LACBED intensities in this range can be utilized for determination of accurate temperature factors or for refinement of coordinates. Such high index reflections can usually be treated kinematically or as a pertubed two-beam case. Application to Y Ba2Cu3O7 shows that a least square refinememt based on integrated intensities can determine temperature factors or coordinates.LACBED patterns taken in the (00l) systematic row show an easily recognisable pattern of narrow bands from reflections in the range 15 < l < 40 (figure 1). Integrated intensities obtained from measured intensity profiles after subtraction of inelastic background (figure 2) were used in the least square fit for determination of temperature factors and refinement of z-coordinates for the Ba- and Cu-atoms.

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