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The Scientific World Journal
Volume 2015, Article ID 327390, 12 pages
http://dx.doi.org/10.1155/2015/327390
Research Article

A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology

1Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
2Department of Biomedical and Systems Engineering, Cairo University, Giza 12613, Egypt

Received 9 May 2015; Accepted 27 July 2015

Academic Editor: Guilong Liu

Copyright © 2015 Ali Muhammad Rushdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Modern Syllogistic Method (MSM) of propositional logic ferrets out from a set of premises all that can be concluded from it in the most compact form. The MSM combines the premises into a single function equated to 1 and then produces the complete product of this function. Two fuzzy versions of MSM are developed in Ordinary Fuzzy Logic (OFL) and in Intuitionistic Fuzzy Logic (IFL) with these logics augmented by the concept of Realistic Fuzzy Tautology (RFT) which is a variable whose truth exceeds 0.5. The paper formally proves each of the steps needed in the conversion of the ordinary MSM into a fuzzy one. The proofs rely mainly on the successful replacement of logic 1 (or ordinary tautology) by an RFT. An improved version of Blake-Tison algorithm for generating the complete product of a logical function is also presented and shown to be applicable to both crisp and fuzzy versions of the MSM. The fuzzy MSM methodology is illustrated by three specific examples, which delineate differences with the crisp MSM, address the question of validity values of consequences, tackle the problem of inconsistency when it arises, and demonstrate the utility of the concept of Realistic Fuzzy Tautology.