This paper introduced a reversible data hiding method based on pixel value ordering with the prediction-error expansion technique and the average value of end pixels'. A host image is first segmented into non-overlapping sub-blocks of three pixels and ordered them as ascending order. For each subblock maximum pixel value and the minimum pixel value is predicted by the middle pixel value and also the middle pixel value is predicted by the average of the maximum and minimum pixel values. Then by using prediction-error expansions, we can embed secret bits into maximum pixel and minimum pixel and also by using the average value of these two pixels we can embed secret bit into the middle pixel of every sub-block. All secret bits can be recovered and restored the cover image completely from watermarked image. Experimental result of this scheme demonstrates that the embedding capacity and average PSNR value is larger than another pixel value ordering and prediction error expansion based approach for relatively smooth images. Also, the visual quality of the obtained marked image is better than other Pixel Value Ordering and Prediction Error Expansion based method.

In this paper, we have proposed a stochastic Knapsack Problem (KP) based mathematical model for small-scale vegetable sellers in India and solved it by an advanced Genetic Algorithm. The knapsack problem considered here is a bounded one, where vegetables are the objects. In this model, we have assumed that different available vegetables (objects) have different weights (that are available), purchase costs, and profits. The maximum weight of vegetables that can be transported by a seller is limited by the carrying capacity of the vegetable carrier and the business capital of the seller is also limited. The aim of the proposed mathematical model is to maximize the total profit of the loaded/traded items, with a set of predefined constraints on the part of the vegetable seller or retailer. This problem has been solved in a Type-2 fuzzy environment and the Critical Value (CV) reduction method is utilized to defuzzify the objective value. We have projected an improved genetic algorithm based approach, where we have incorporated two features, namely refinement and immigration. We have initially considered benchmark instances and subsequently some redefined cases for experimentation. Moreover, we have solved some randomly generated proposed KP instances in Type-2 fuzzy environment.