Inertial s-iteration forward-backward algorithm for a family of nonexpansive operators with applications to image restoration problems

Image restoration is an important branch of image processing which has been studied extensively while there are several methods to solve this problem by many authors with the challenges of computational speed and accuracy of algorithms. In this paper, we present two methods, called ?Inertial S-iteration forward-backward algorithm (ISFBA)? and ?A fast iterative shrinkage-thresholding algorithm-Siteration (FISTA-S)?, for finding an approximate solution of least absolute shrinkage and selection operator problem by using a special technique in fixed point theory and prove weak convergence of the proposed methods under some suitable conditions. Moreover, we apply our main results to solve image restoration problems. It is shown by some numerical examples that our algorithms have a good behavior compared with forward-backward algorithm (FBA), a new accelerated proximal gradient algorithm (nAGA) and a fast iterative shrinkage-thresholding algorithm (FISTA).

The General Least Square Deviation OWA Operator Problem

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 Extended Minimax Disparity RIM Quantifier Problem

An interesting regular increasing monotone (RIM) quantifier problem is investigated. Amin and Emrouznejad [Computers & Industrial Engineering 50(2006) 312–316] have introduced the extended minimax disparity OWA operator problem to determine the OWA operator weights. In this paper, we propose a corresponding continuous extension of an extended minimax disparity OWA model, which is the extended minimax disparity RIM quantifier problem, under the given orness level and prove it analytically.

Spotty scope and our relation to fictions

Whatever the attractions of Tolkein’s world, irrealists about fictions do not believe literally that Bilbo Baggins is a hobbit. Instead, irrealists believe that, according to The Lord of the Rings {Bilbo is a hobbit}. But when irrealists want to say something like ‘I am taller than Bilbo’, there is nowhere good for them to insert the operator ‘according to The Lord of the Rings’. This is an instance of the operator problem. In this paper, I outline and criticise Sainsbury’s (2006) spotty scope approach to the operator problem. Sainsbury treats the problem as syntactic, but the problem is ultimately metaphysical.Published in Noûs 46.2: 243–58.