Efficient Membership Function Computation Using a Modified Bisection Algorithm

Fuzzy set theory, proposed by Lotfi Zadeh, is applied with great success in embedded, control-oriented systems based on microcontrollers or programmable logic devices. Algorithms used in these systems operate on fuzzy sets represented by membership functions. In practically implemented control systems, these functions typically possess simple linear shapes, such as trapezoidal or triangular. To compute the function value, the classical method relies on multiplication and division. These operations are complex to implement in software or hardware, consume significant resources, and are time-consuming. This paper proposes a fixed-point computation method to obtain the value of a membership function without relying on these operations. For this purpose, the bisection algorithm was adopted, replacing its complex arithmetic with addition and binary shift operations. This approach allows for a reduction in computation time and the hardware or software overhead required by resource-constrained embedded systems, especially architectures without dedicated hardware accelerators for multiplication and division. Sample software and hardware implementations demonstrate its suitability for real-world systems.