The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

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A large–scale mating disruption trial for the control of Pectinophora gossypiella (Saund.) was carried out in the Fayoum Province of Egypt during the 1981 cotton season. Two areas, each of 50 ha, were sprayed with a microencapsulated formulation of the sex pheromone (a 1:1 mixture of (Z, Z)- and (Z, E)-1, 11-hexadecadienyl acetate) as the sole means of controlling this pest. Five applications of 10 g a.i./ha were made during the season using fixed-wing aircraft. The pheromone treatments were compared with conventional insecticide spray treatments in two other 50-ha areas of cotton. From comparisons of treatments in terms of various plant damage criteria including the percentage of rosetted flowers, percentage boll infestation, gross yield of seed cotton and lint quality, it was concluded that the pheromone treatment was equal in effect to the insecticide sprays.

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