In this paper, we introduce some certain fuzzy soft algebraic notions of generalized concepts in LA-Γ-semigroups and study some properties of their families.

An image adaptive noise reduction enhancement algorithm based on NSCT is proposed to perform image restoration preprocessing on the defocused image obtained under the microscope. Defocused images acquired under micro-nano scale optical microscopy, usually with inconspicuous details, edges and contours, affect the accuracy of subsequent observation tasks. Due to its multi-scale and multi-directionality, the NSCT transform has superior transform functions and can obtain more textures and edges of images. Combined with the characteristics of micro-nanoscale optical defocus images, the NSCT inverse transform is performed on all sub-bands to reconstruct the image. Finally, the experimental results of the standard 500 nm scale grid, conductive probe and triangular probe show that the proposed algorithm has a better image enhancement effect and significantly improves the quality of out-of-focus images.

Among major global threats to papaya cultivation, papaya ringspot virus (PRSV) is the most challenging one. In the absence of any PRSV resistant commercial papaya cultivar, PRSV management is restricted to minimizing yield losses. ICAR-Indian Agricultural Research Institute, Regional Station, Pune has developed PRSV tolerant dioecious papaya lines, Pune Selection (PS)-1, PS-2, PS-3 and PS-5. Being dioecious these lines have limited acceptability among farmers. Gynodioecious population from these lines were developed and characterized. They are numbered PS-1-1, PS-2-1, PS-3-1 and PS-5-1. These lines were characterized against prevailing commercial gynodioecious cultivar, Red Lady, for five generations. The average plant height of PS-2-1 and PS-5-1 (183 cm) was more than Red Lady (158 cm), however, stem girth of all lines was lesser than Red Lady. The fruiting height of all lines was less than Red Lady (87 cm). Length of the fruiting column of all lines was more than Red Lady (37 cm), except in PS-1-1. Fruit yield of all lines was more than Red Lady (16 kg/plant). Intensity of PRSV infection in Red Lady (48%) was considerably more than all lines. These lines can be used for developing PRSV tolerant gynodioecious papaya variety.