F-rough law and the discovery of rough law

By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.

Investigating the Effect of Relative Width on Momentum Transfer between Main Channel and Floodplain in Rough Rectangular Compound Channel Sunder Varius Relative Depth Condition

Compound section is referred to a section the surface of which is made of several sub-sections with different flow characteristics. The difference in the hydraulic and geometry characteristics causes a complexity in flow hydraulic and creates an interaction between the main channel and floodplains, resulting in an apparent shear stress and a transverse momentum transfer. The amount of such a stress plays an important role in many river engineering measures [1]. Due to the flow complexity, the common approximate analytical methods are not enough to identify the flow profile. The FLOW3D Software with its great features in three-dimensional analysis of flow field is used as a tool to investigate the shear stress in a direct symmetrical compound rectangular channel. After the simulation of models, it is found that an increase in the relative width and relative depth parameters decreases the percentage of apparent shear stress and an increase in the relative roughness causes it to be increased [2].

Cost Sensitive Multi-Granulation Preference Relation Rough Set for Ordinal Decision System

The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.

Analytical solution of the low Reynolds third-grade non-Newtonian fluids flow inside rough circular pipes

The present paper focuses on finding an analytical solution for fully developed third-grade non-Newtonian fluids flows inside rough circular pipes at low Reynolds numbers(Stokes flows).The wall roughness is modeled by two different periodic morphologies based on sinusoidal and triangular geometries.In this study,the relative roughness(ratio of the roughness amplitude to the pipe hydraulic diameter)is selected to be a small value,which is appropriate for the perturbation analysis.The governing parameters including the axial and radial velocity profiles,stream function,wall shear stress,pressure gradient,and friction factor are expressed in analytical formulas and they are compared to the smooth pipe.The effect of the relative roughness,the wall wave number,and the non-Newtonian parameter on the governing parameters are investigated.The results show that modeling the roughness by triangular geometry has a better prediction of pressure drop regarding the basic solution of the smooth pipe.

Fuzzy Rough Relation and Its Properties

In this paper, the concept of fuzzy rough relation(FRR) and the max-min composition of FRR are given. Then the properties of the composition of FRRs are studied.

SOME NEW DATA AND FORMULAS FOR RESISTANCE FLOW IN FLUVIAL OPEN CHANNELS

Flow resistance in fluvial open channels, especially in steep gravel-bed channels, still presents challenges to researchers and engineers. This article presents some new data from both the flume experiments and field measurements. Data analysis using the divided hydraulic radius approach shows that the relative roughness plays a significant role in the bed form resistance. A new set of formulas that incorporate the relative roughness are proposed. As compared with several existing formulas, the proposed formulas can be used to better estimate the bed form resistance.