Interval Type-2 Fuzzy Logic Stuff

This repo has python implementation for some Interval Type 2 Fuzzy Set (IT2 FS) concepts. Each module contains a main function that shows the usage of that module.

Enhanced Interval Approach (EIA)

The eia package contains the implementation of the enhanced interval approach for encoding words into interval type-2 fuzzy sets. It both contains the "Data Part" and the "Fuzzy Set Part":

• eia/data_part.py: This is the Data Part module which does the interval preprocessing. It can read word intervals from an Excel file (sample-data.xlsx also provided) and will write results to words.json file. You can also extend it and use whatever input/output type you want.
• eia/fuzzy_set_part.py: This is the Fuzzy Set Part which will generate FOUs from the word intervals of the previous phase. FOUs are stored to words_status.json file. They contain "Shape (interior, left/right-shoulder)", "Embedded Interval Type-1s" and "Type-2 Membership values" for each word. The membership values are saved in a 9-point shape like this:

Utilities

The utils package contains some other tools and measures for IT2 FSs:

• utils/centroid_it2fs.py:
  • centroid_it2: Computes the centroid of an IT2 FS. Returns centroid boundaries and the center of centroid.
  • ekm: Implementation of the Enhanced KM algorithm.
• linguistic_weighted_average.py:
  • fwa: Computing the Fuzzy Weighted Average for trapezoidal T1 FSs.
  • lwa: Computing the Linguistic Weighted Average for IT2 FSs.
• ranking_methods.py:
  • centroid_rank: Implementation of the center-of-centroid based ranking method.
• similarity_measures.py:
  • jaccard: computing the Jaccard similarity measure between two IT2 FSs.