Satisfiability in intuitionistic fuzzy logic with realistic tautology

Authors

  • Ali Muhammad Rushdi Professor Department of Electrical Engineering and Computer Engineering Faculty of Engineering King Abdulaziz University Phone: 6402000 Ext. 68013 Email: arushdi @ kau.edu.sa http://orcid.org/0000-0001-5021-2368
  • Muhammad Ali Rushdi Department of Biomedical and Systems Engineering, Faculty of Engineering, Cairo University, Giza 12613, Arab Republic of Egypt {mrushdi@eng.cu.edu.eg}
  • Mohamed Zarouan Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia
  • Waleed Ahmad Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia { uetian_elec@yahoo.com}

Keywords:

Intuitionistic fuzzy logic, Realistic fuzzy tautology, Boolean satisfiability, CNF expression, Disjoint DNF expression.

Abstract

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.

Author Biography

Waleed Ahmad, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia { uetian_elec@yahoo.com}

PhD Student

Department of Electrical and Computer Engineering, Faculty of Engineering,
King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia
{ uetian_elec@yahoo.com}

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Published

02-05-2018

Issue

Vol. 45 No. 2 (2018): Kuwait Journal of Science

Section

Computer Science