Multi-attribute decision making application using hybridly modelled Gaussian Interval Type-2 Fuzzy sets with uncertain mean

Perceptual computing (Per-C) is a branch of CWW (Computing with words) that assist people in making subjective decisions. Their applications take linguistic inputs (i.e., words) from the user and return a linguistic output (i.e., word). The perception of these linguistic inputs suffers from uncertainties, for which IT2FSs (Interval Type-2 Fuzzy Sets) are considered better than T1FSs (Type-1 Fuzzy Sets) to capture it. In these applications, the IT2FSs are constructed either by application developers or by consulting experts. Due to the manual introduction of biases, these methods cannot capture uncertainties appropriately, so constructing IT2FS using data intervals is a better approach. The Trapezoidal IT2FS is the only available through this approach, but it has a linear membership function. In real life, the distribution observed is primarily non-linear. The paper presents an experimental method to construct the GIT2FSUM (Gaussian IT2FSs with Uncertain Mean) following statistical (i.e. pruning) and heuristical (i.e. selection of underlying T1FS) steps on data intervals. In order to show its capability in capturing uncertainties, a MADM (Multi-attribute decision making) application following the Per-C framework is developed. The application recommends the suitability of the Online Study Platforms (OSP) to a student. LWA (Linguistic weighted average) operation is performed to obtain OWR (Output Word Representation) for selecting the recommendation word corresponding to an OSP. In this experiment, we compare our GIT2FSUM with the existing Trapezoidal IT2FS (i.e., also formed using data-interval). The average Jaccard similarity between OWR (using GIT2FSUM) and recommendation word is (0.67 ± 0.12), while for OWR (using Trapezoidal IT2FS) is (0.55 ± 0.11). It indicates that the GIT2FSUM is much better than Trapezoidal IT2FS in capturing uncertainties present in the perception of words. In addition, the number of parameters to model GIT2FSUM is comparatively less than Trapezoidal IT2FS.