Satisfiability in intuitionistic fuzzy logic with realistic tautology - Rushdi, Ali Muhammad; Rushdi, Muhammad Ali; Zarouan, Mohamed; Ahmad, Waleed (Kuwait Journal of Science, 2018)
Any variable in Intuitionistic Fuzzy Logic (IFL) is either a Realistic Fuzzy Tautology (RFT) with a Truth exceeding one half, or a non-Realistic Fuzzy Tautology (nRFT) with a Truth less than or equal to one half. This results in a dichotomy somewhat similar to that of the Excluded Middle in Ordinary Logic (OL) albeit allowing both Falsity and Hesitancy in addition to Truth in an IFL variable. Consequently, many problems (and solutions) in Boolean logic can be fuzzified without any significant change in their essence. We show herein that one such problem is that of Boolean satisfiability. We handle this problem by converting a CNF expression into a disjoint DNF one, and solving the resulting two-valued Boolean equation. This solution strategy is essentially retained in IFL, thanks to the RFT concept. All steps needed in the fuzzification process are proved, and a demonstrative example illustrates the method in both crisp and intuitionistic fuzzy cases.