A Comparative Study of Some Soft Rough Sets

Abstract

Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some existing hybrid models has been carried out. Some foundational properties of modified soft rough sets (MSR sets) are analyzed. It is pointed out that MSR approximation operators are some kinds of Pawlak approximation operators, whereas approximation operators of Z-soft rough fuzzy sets are equivalent to approximation operators of rough fuzzy sets. The relationships among F-soft rough fuzzy sets, M-soft rough fuzzy sets and Z-soft rough fuzzy sets are surveyed. A new model called soft rough soft sets has been provided as the generalization of F-soft rough sets, and its application in group decision-making has been studied. Various soft rough sets models show great potential as a tool to solve decision-making problems, and a depth study of the connections among these models contributes to the flexible application of soft rough sets based decision-making approaches.

A Hybrid Mechanism for Helicopters

“…Such a device generally uses two or more diverse forms of power sources in various situations, shown as Figure 1. The basic principle is that the different motors work better at different speeds; the electric motor is more efficient at producing torque, or turning power, and the combustion engine is better for maintaining a high speed (better than a typical electric motor) [11]. Changing power sources with appropriate timing and in the right circumstances facilitates energy efficacy and fuel efficiency.…”

“…Changing power sources with appropriate timing and in the right circumstances facilitates energy efficacy and fuel efficiency. Abundant hybrid models (i.e., the Boeing Fuel Cell Demonstrator Airplane, Hybrid FanWings) have been presented in order to take advantage of each and handle uncertainties [11]. This hybrid methodology is proposed, taking benefits of both the conventional power source (i.e., a turbine engine's consistent output) and an electricity power system (i.e., fastest response for utility) [12] so as to enhance safety if engine failure happens.…”

“…In more specific terms, number in Figure 3 denote the following: 100-hybrid mechanism; 11-driver shaft for propellers; Operationally, once we start the turbine engine (12), this engine rotates the first output shaft (121) and the first bevel driving gear (122) so as to drive first bevel gear (123). Consequently, through the first transmission gear (111), the one-way bearing module (113) is driven to turn the driver shaft for the propellers (11). Finally, the propellers (22) revolve at a specified speed so as to provide sufficient thrust for lifting the remote control helicopter.…”

“…In more specific terms, we set the turbine engine's (12) output shaft rpm to 9000; the gear ratio between the first bevel driving gear (122) and the first bevel gear (123) was 1:4. Accordingly, the rpm of driver shaft for propellers (11) was 2250. However, the realistic rpm reaches only 70%-80% (1575-1800) of the calculated result due to aerodynamic drag [13,14].…”

“…On the other hand, if accidentally, the turbine engine suffers from lack of fuel/engine failure, the electronic motor (13) works right away to drive second output shaft (131), second driving shaft (132), and second v-shaped teeth gear (133) so as to rotate first v-shaped teeth gear (116). Consequently, the second transmission gear (112) and one-way bearing module (114) are driven to turn driver shaft for the propellers (11). Finally, propellers (22) revolve at specified speed so as to provide sufficient thrust Symmetry 2020, 12, 33 5 of 8 for lifting the remote control helicopter.…”