1 -In this paper, the fuzzy multi-objective reliability-redundancy allocation problem (FMORRAP) is proposed, which maximizes the system reliability while simultaneously minimizing the system cost under the type-2 fuzzy uncertainty. In the proposed formulation, the higher order uncertainties (such as parametric, manufacturing, environmental and designers' uncertainty) associated with the system are modeled with interval type-2 fuzzy sets (IT2 FS). The footprint of uncertainty of the interval type-2 membership functions (IT2 MFs) accommodates these uncertainties by capturing the multiple opinions from several system experts. We consider IT2 MFs to represent the sub-system reliability and cost, which are to be further aggregated by using extension principle to evaluate the total system reliability and cost according to their configurations, i.e., series-parallel and parallel-series. We proposed a particle swarm optimization (PSO) based novel solution approach to solve the FMORRAP. To demonstrate the applicability of two formulations, namely series-parallel FMORRAP and parallel-series FMORRAP, we performed experimental simulations on various numerical datasets. The decision makers/system experts assign different importance to the objectives (system reliability and cost), and these preferences are represented by sets of weights. The optimal results are obtained from our solution approach, and the Pareto-optimal front is established by using these different weight sets. The genetic algorithm (GA) was implemented to compare the results obtained from our proposed solution approach. A statistical analysis was conducted between PSO and GA, and it was found that the PSO based Pareto solution outperforms the GA.
A B S T R A C TSimilarity measure, also called information measure, is a concept used to distinguish different objects. It has been studied from different contexts by employing mathematical, psychological, and fuzzy approaches. Image steganography is the art of hiding secret data into an image in such a way that it cannot be detected by an intruder. In image steganography, hiding secret data in the plain or non-edge regions of the image is significant due to the high similarity and redundancy of the pixels in their neighborhood. However, the similarity measure of the neighboring pixels, i.e., their proximity in color space, is perceptual rather than mathematical. Thus, this paper proposes an interval type-2 fuzzy logic system (IT2 FLS) to determine the similarity between the neighboring pixels by involving an instinctive human perception through a rule-based approach. The pixels of the image having high similarity values, calculated using the proposed IT2 FLS similarity measure, are selected for embedding via the least significant bit (LSB) method. We term the proposed procedure of steganography as 'IT2 FLS-LSB method'. Moreover, we have developed two more methods, namely, type-1 fuzzy logic system based least significant bits (T1FLS-LSB) and Euclidean distance based similarity measures for least significant bit (SM-LSB) steganographic methods. Experimental simulations were conducted for a collection of images and quality index metrics, such as PSNR (peak signal-to-noise ratio), UQI (universal quality index), and SSIM (structural similarity measure) are used. All the three steganographic methods are applied on dataset and the quality metrics are calculated. The obtained stego images and results are shown and thoroughly compared to determine the efficacy of the IT2 FLS-LSB method. We have also demonstrated the high payload capacity of our proposed method. Finally, we have done a comparative analysis of the proposed approach with the existing well-known steganographic methods to show the effectiveness of our proposed steganographic method.
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