The compromise solution of the multi-criteria decision-making (MCDM) problem by the existing VIKOR method for Pythagorean fuzzy sets (PyFSs) is not closest to the positive ideal solution. This is because the defining function for VIKOR does not obey the axioms for a dissimilarity measure. Thus in this context, the existing notion of dissimilarity measures and the VIKOR method are controversial. This study aims to provide a new dissimilarity measure and refine the VIKOR method for PyFSs accordingly. We define a new dissimilarity measure for PyFSs and refine the existing VIKOR method. We discuss the additional properties of dissimilarity measures and improve the ideas of remoteness and ranking indexes. We provide numerical examples to support the analysis and findings of our study. Finally, we solve the MCDM problems to illustrate the proposed method.

There has been a quick development in construction activities during the last couple of decades attributable to a general improvement in all features of humankind. Because of innovative progressions and regularly expanding human progress, there is a diligent requirement of power. Close by the ordinary energy sources, renewable energy sources have likewise lead significantly to the rising power requirement. All over the world in the past, a number of small hydropower plants (SHPPs) have been developed, as a renewable energy source. Generally, these SHPPs are being manufactured and worked by the private designers consenting to the administration rules. So as to help a designer in choosing the most productive and doable SHPP for development and consequent activity, the concept of the intuitionistic cubic fuzzy set (ICFS) theory is established and a few important operations for ICFSs are characterized, and also a strategy dependent on intuitionistic cubic fuzzy Hamacher hybrid averaging (ICFHHA) operator, intuitionistic cubic fuzzy Hamacher order weighted averaging (ICFHOWA) operator, and intuitionistic cubic fuzzy Hamacher weighted averaging (ICFHWA) operators is utilized in the present paper. The financial criteria and technobusiness, as assumed for examining the practicality of the candidate SHPPs, are presented qualitatively utilizing intuitionistic cubic fuzzy numbers (ICFNs). Further study their fundamental properties and the relationship among these aggregation operators. Developed group decision-making (DM) algorithm under intuitionistic cubic fuzzy (ICF) environment. An interpretative case for the analysis of SHPP for construction is given to demonstrate the feasibility and practicality of the mentioned new techniques. Further validate its effectiveness and benefits via a comparative analysis with pre-existing aggregation operators, and the outcomes demonstrate that the proposed SHPP determination model has some special favorable circumstances, which is progressively practical and adaptable for SHPP choice under a complex and uncertain environment.

The protection of copyrights of digital media uploaded to the Internet is a growing problem. In this paper, first, we present a unified framework for embedding and detecting watermark in digital data. Second, a new robust watermarking scheme is proposed considering this concern. The proposed work incorporates three chaotic maps which specify the location for embedding the watermark. Third, a new chaotic map, the Extended Logistic map, is proposed in this work. The proposed map has a bigger range than logistic and cubic maps. It has shown good results in a bifurcation, sensitivity to initial conditions, and randomness tests. Furthermore, with the detailed analysis of initial parameters, it is justified that Extended Logistic map can be used in secure communication, particularly watermarking. Fourth, to check the robustness of proposed watermarking scheme, we have done a series of analyses and standard attacks. The results confirm that the proposed watermarking scheme is robust against visual and statistical analysis and can resist the standard attacks.