A Stone Resource Assignment Model under the Fuzzy Environment

Algorithm 1

Fuzzy simulation for possibilistic constraints.

Input: Decision variables 𝑌_𝑖 and 𝑋_𝑖𝑗

Output: The minimum 𝐹₁

Step 1. Set 𝐹₁=𝑀, where 𝑀 is sufficiently large number;

Step 2. Randomly generate 𝜆_𝑖, 𝜂_𝑖𝑗 and 𝜅_𝑖𝑗 from the 𝛿^𝑈₁-level set of the fuzzy numbers 𝐸𝑑_𝑖,

𝑒𝑑_𝑖𝑗 and 𝑒𝑤_𝑖𝑗 respectively;

Step 3. Compute 𝑓=∑^𝑚_𝑖=1𝜆_𝑖𝑌_𝑖+∑^𝑚_𝑖=1∑^𝑛_𝑗=1(𝜂_𝑖𝑗+𝜅_𝑖𝑗)𝑋_𝑖𝑗 and replace 𝐹₁ with 𝑓 provided

that 𝐹₁>𝑓;

Step 4. Repeat the second and third steps 𝑁 times;

Step 5. Return 𝐹₁.