A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology
Joint Authors
Zarouan, Mohamed
Alshehri, Taleb Mansour
Rushdi, Muhammad Ali
Rushdi, Ali Muhammad Ali
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-08-24
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
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.
American Psychological Association (APA)
Rushdi, Ali Muhammad Ali& Zarouan, Mohamed& Alshehri, Taleb Mansour& Rushdi, Muhammad Ali. 2015. A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology. The Scientific World Journal،Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1078676
Modern Language Association (MLA)
Rushdi, Ali Muhammad Ali…[et al.]. A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology. The Scientific World Journal No. 2015 (2015), pp.1-12.
https://search.emarefa.net/detail/BIM-1078676
American Medical Association (AMA)
Rushdi, Ali Muhammad Ali& Zarouan, Mohamed& Alshehri, Taleb Mansour& Rushdi, Muhammad Ali. A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology. The Scientific World Journal. 2015. Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1078676
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1078676