Silver nanoparticles (AgNPs) of different shapes and sizes were prepared by solution-based chemical reduction routes. Silver nitrate was used as a precursor, tri-sodium citrate (TSC) and sodium borohydride as reducing agents, while polyvinylpyrrolidone (PVP) was used as a stabilizing agent. The morphology, size, and structural properties of obtained nanoparticles were characterized by scanning electron microscopy (SEM), UV-visible spectroscopy (UV-VIS), and X-ray diffraction (XRD) techniques. Spherical AgNPs, as depicted by SEM, were found to have diameters in the range of 15 to 90 nm while lengths of the edges of the triangular particles were about 150 nm. The characteristic surface plasmon resonance (SPR) peaks of different spherical silver colloids occurring in the wavelength range of 397 to 504 nm, whereas triangular particles showed two peaks, first at 392 nm and second at 789 nm as measured by UV-VIS. The XRD spectra of the prepared samples indicated the face-centered cubic crystalline structure of metallic AgNPs. The in vitro antibacterial properties of all synthesized AgNPs against two types of Gram-negative bacteria, Pseudomonas aeruginosa and Escherichia coli were examined by Kirby–Bauer disk diffusion susceptibility method. It was noticed that the smallest-sized spherical AgNPs demonstrated a better antibacterial activity against both bacterial strains as compared to the triangular and larger spherical shaped AgNPs.

Group decision‐making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well‐known method for multiple‐criteria decision‐making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision‐making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF‐TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF‐TOPSIS are solved.

We introduce the notion of strong intuitionistic fuzzy graphs and investigate some of their properties. We discuss some propositions of self complementary and self weak complementary strong intuitionistic fuzzy graphs. We introduce the concept of intuitionistic fuzzy line graphs.