Density aggregation operators based on the intuitionistic trapezoidal fuzzy numbers for multiple attribute decision making

With respect to the multiple attribute decision making problems in which the attribute values take the form of the intuitionistic trapezoidal fuzzy numbers, some methods based on density aggregation operators are proposed. Firstly, the definition, expected value and the ranking method of intuitionistic trapezoidal fuzzy numbers are introduced, and the method of calculating density weighted vector is proposed. Then some density aggregation operators based on interval numbers and intuitionistic trapezoidal fuzzy numbers are developed, and a multiple attribute decision making method is presented. Finally an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness

Microstructure and Mechanical Properties in a Gd-Modified Extruded Mg-4Al-3.5Ca Alloy

In the present study, the microstructure and mechanical properties of a new Mg-4Al-3.5Ca-2Gd (AXE432) alloy are investigated. The microstructure of the as-cast AXE432 alloy consists of α-Mg, C14 (Mg2Ca), and C36((Mg, Al)2Ca) phases. After the heat treatment at 480 °C for 8 h, the C14 with fine lamellar structure changes from narrow stripes to micro-scale particles, and part of the C36 and the C14 dissolve into the α-Mg matrix, with many short needle-shaped C15 (Al2Ca) phase precipitating in the primary a-Mg grains. The AXE432 alloy extruded at a temperature as high as 420 °C exhibits a refined dynamically recrystallized (DRXed) microstructure with grain sizes less than 1.5 ± 0.5 μm and a strong {0001}1¯0> basal texture with a maximum intensity of 5.62. A complex combination of the effects from grain size, texture, second-phase particles, and strain hardening results in balanced mechanical properties, with the tensile yield strength (TYS), ultimate tensile strength (UTS), elongation (El), compressive yield strength (CYS), and ultimate compressive strength (UCS) of 331.4 ± 2.1 MPa, 336.9 ± 3.8 MPa, 16.1 ± 2.3%, 270.4 ± 1.6 MPa and 574.5 ± 12.4 MPa, respectively