A Hybrid Model through the Fusion of Type-2 Fuzzy Logic Systems and Sensitivity-Based Linear Learning Method for Modeling PVT Properties of Crude Oil Systems

Algorithm 2

Iterative algorithm to compute 𝑦_𝑟.

(1) Arrange the precalculated 𝑦^𝑖_𝑟 from Figure 2 in an ascending order, that is, 𝑓¹_𝑟≤𝑓²_𝑟≤⋯≤𝑓^𝑀_𝑟

(2) Set 𝑓^𝑖_𝑟=(𝑓^𝑖_𝑟+𝑓^𝑖_𝑟)/2 for 𝑖=1,2,…𝑀, and calculate 𝑦_𝑟 using (6)

(3) Find 𝑅∈[1,𝑀−1] such that 𝑦^𝑅_𝑟≤𝑦^′_𝑟≤𝑓_𝑟^𝑅+1

(4) Set 𝑓^𝑖_𝑟=𝑓^𝑖_𝑟 for 𝑖≤𝑅 and 𝑓^𝑖_𝑟=𝑓^𝑖_𝑟+𝑓^𝑖_𝑟 for 𝑖>𝑅; and compute 𝑦_𝑟^′′ using (6)

(5) Stop if 𝑦_𝑟^′′=𝑦^′_𝑟, otherwise set 𝑦^′_𝑟=𝑦_𝑟^′′ and return to step 3