Krasner hyperrings are a generalization of rings. Indeed, in a Krasner hyperring the addition is a hyperoperation, while the multiplication is an ordinary operation. On the other hand, a generalization of rough set theory is the near set theory. Now, in this paper we are interested in combining these concepts. We study and investigate the notion of near Krasner  hyperrings on a nearness APPROXIMATION SPACE. Also, we define near subhyperring, near hyperideal, near homomorphism  and prove some results and present several examples in this respect.

To tackle the problem with inexact, uncertainty and vague knowledge, constructive method is utilized to formulate lower and upper APPROXIMATION sets. Rough set model over dual-universes in fuzzy APPROXIMATION SPACE is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy APPROXIMATION SPACE by means of cut set. Then, we discuss properties of rough set over dual-universes in fuzzy APPROXIMATION SPACE from two viewpoints: APPROXIMATION operators and cut set of fuzzy set. Reduction of attributes and rules extraction of rough set over dual-universes in fuzzy APPROXIMATION SPACE are presented. Finally, an example of disease diagnoses expert system illustrates the possibility and eciency of rough set over dual-universes in fuzzy APPROXIMATION SPACE.

In this paper, the structural optimization of a SPACE capsule has been discussed by approximating a thin-walled cylindrical shell with a certain length under the axial compression force and constant lateral pressure. Design variables include the outer diameter and cylinder thickness. The purpose of optimization is to minimize the mass and maximize the frequency of the first vibration shape mode of the cylinder. The design constraints include the buckling load multiplier (buckling safety factor) above 1. 5 and Von Mises stress below 100 MPa. In this article, first, according to the permissible limits of the design variables, a design of experiment (DOE) and then a sensitivity analysis was carried out to check the sensitivity of the objective functions and constraints to the design variables. After numerically solving the output values with the help of Ansys software and preparing the response surface, the optimal design point has been identified with the help of the two objectives optimization Genetic algorithm. Then, with the numerical simulation of the optimal point, the accuracy of the values obtained from the response surface method was checked and their accuracy was confirmed. The results show that at the selected design point, Von Mises stress becomes less than its allowed value, i. e. 100 MPa, and also the buckling load factor is more than twice its minimum allowed value. However, this point has the smallest distance from the origin and the optimum point has been chosen as the knee point.

We study the thoery of best APPROXIMATION in tensor product SPACE and the direct sum of some lattice normed SPACEs Xi: We introduce quasi tensor product SPACE and discuss about the relation between tensor product SPACE and this new SPACE which we denote it by X⊠ Y. We investigate best APPROXIMATION in direct sum of lattice normed SPACEs by elements which are not necessar-ily downward or upward and we call them Im􀀀 quasi downward or Im􀀀 quasi upward. We show that these sets can be interpreted as downward or upward sets. The relation of these sets with down-ward and upward subsets of the direct sum of lattice normed SPACEs Xi is discussed. This will be done by homomorphism functions. Fi-nally, we introduce the best APPROXIMATION of these sets.