IT2FS

IT2FS denotes Interval Type‑2 Fuzzy Systems, a specific class within the broader field of type‑2 fuzzy logic. In a conventional (type‑1) fuzzy system each membership grade is a precise value between zero and one. Type‑2 fuzzy sets extend this by assigning a secondary membership function to each primary grade, allowing the degree of membership itself to be fuzzy. In an interval type‑2 system the secondary membership functions are bounded by an interval, simplifying computation while retaining the ability to model higher‑order uncertainty.

An IT2FS typically consists of an antecedent (if–then rules), a consequent (output rule bodies), and a defuzzification module. The rule antecedents are expressed as interval‑type‑2 fuzzy sets, and the consequent can be a linguistic variable or a parametric function. During inference, the system computes an interval‑type‑2 firing strength, aggregates the interval outputs, and finally applies a defuzzification technique such as the centroid of the footprint of uncertainty. Common approaches include interval‑type‑2 Mamdani models, Sugeno‑style models with interval‑type‑2 consequents, and hybrid neuro‑fuzzy architectures.

The primary advantage of IT2FS over type‑1 systems is their enhanced robustness to measurement noise and modeling errors. By explicitly representing the uncertainty in membership grades, interval type‑2 systems achieve smoother, more reliable control actions, which is valuable in domains with substantial data variability. Typical application areas include fault‑tolerant control of industrial processes, adaptive cruise control in automotive systems, medical diagnosis, image segmentation, and pattern recognition tasks.

Research on IT2FS has evolved since the early 1990s, with significant contributions from researchers such as J. Zadeh, L. Song, and R. Oates. Modern investigations focus on efficient inference algorithms, reduced computational burden, and real‑time implementation on embedded platforms. The field continues to grow as demand for intelligent systems that can cope with high‑level uncertainty increases across engineering, science, and business domains.