Parameter Selection and Uncertainty Measurement for Variable Precision Probabilistic Rough Set

In this paper, we consider the problem of parameter selection and uncertainty measurement for a variable precision probabilistic rough set. Firstly, within the framework of the variable precision probabilistic rough set model, the relative discernibility of a variable precision rough set in probabilistic approximation space is discussed, and the conditions that make precision parameters α discernible in a variable precision probabilistic rough set are put forward. Concurrently, we consider the lack of predictability of precision parameters in a variable precision probabilistic rough set, and we propose a systematic threshold selection method based on relative discernibility of sets, using the concept of relative discernibility in probabilistic approximation space. Furthermore, a numerical example is applied to test the validity of the proposed method in this paper. Secondly, we discuss the problem of uncertainty measurement for the variable precision probabilistic rough set. The concept of classical fuzzy entropy is introduced into probabilistic approximation space, and the uncertain information that comes from approximation space and the approximated objects is fully considered. Then, an axiomatic approach is established for uncertainty measurement in a variable precision probabilistic rough set, and several related interesting properties are also discussed. Thirdly, we study the attribute reduction for the variable precision probabilistic rough set. The definition of reduction and its characteristic theorems are given for the variable precision probabilistic rough set. The main contribution of this paper is twofold. One is to propose a method of parameter selection for a variable precision probabilistic rough set. Another is to present a new approach to measurement uncertainty and the method of attribute reduction for a variable precision probabilistic rough set

Critical factors of the application of nanotechnology in construction industry by using ANP technique under fuzzy intuitionistic environment

Nanotechnology plays a significant role in construction industry. The construction industry has been employed nanomaterials to improve the performance of construction components and the safety of the structure and to reduce the energy consuming and the cost of maintenance. In other words, nanotechnology has a substantial impact on the construc­tion industry. Therefore, it is necessary to identify and evaluate the critical factors of the application of nanotechnology in construction in order to concentrate on the most critical factors. However, several techniques have been developed to prioritize the evaluation criteria. Analytical network process (ANP) technique, a branch of multi criteria decision mak­ing (MCDM) methods, is a powerful tool to rank a limited number of criteria. This technique takes into account both tangible and intangible criteria in the process of formulation of a decision making problem. This method is capable of handling all types of independence and dependence relationships. On the other hand, intuitionistic fuzzy set (IFS) is a well-known technique in considering the inherent uncertainty involved in the process of modelling a decision making problem. In this paper, a new model based on the IFS and ANP technique is proposed to evaluate the critical factors of the application of nanotechnology in the construction industry. The results demonstrate that the proposed model has a high potential for taking into account the uncertainty in the form of a three dimension function, including membership, non-membership, and non-determinacy

Advanced Theoretical and Computational Methods for Complex Materials and Structures

The broad use of composite materials and shell structural members with complex geometries in technologies related to various branches of engineering has gained increased attention from scientists and engineers for the development of even more refined approaches and investigation of their mechanical behavior. It is well known that composite materials are able to provide higher values of strength stiffness, and thermal properties, together with conferring reduced weight, which can affect the mechanical behavior of beams, plates, and shells, in terms of static response, vibrations, and buckling loads. At the same time, enhanced structures made of composite materials can feature internal length scales and non-local behaviors, with great sensitivity to different staking sequences, ply orientations, agglomeration of nanoparticles, volume fractions of constituents, and porosity levels, among others. In addition to fiber-reinforced composites and laminates, increased attention has been paid in literature to the study of innovative components such as functionally graded materials (FGMs), carbon nanotubes (CNTs), graphene nanoplatelets, and smart constituents. Some examples of smart applications involve large stroke smart actuators, piezoelectric sensors, shape memory alloys, magnetostrictive and electrostrictive materials, as well as auxetic components and angle-tow laminates. These constituents can be included in the lamination schemes of smart structures to control and monitor the vibrational behavior or the static deflection of several composites. The development of advanced theoretical and computational models for composite materials and structures is a subject of active research and this is explored here for different complex systems, including their static, dynamic, and buckling responses; fracture mechanics at different scales; the adhesion, cohesion, and delamination of materials and interfaces