A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology
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 M...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/327390 |
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| author | Ali Muhammad Rushdi Mohamed Zarouan Taleb Mansour Alshehri Muhammad Ali Rushdi |
| author_facet | Ali Muhammad Rushdi Mohamed Zarouan Taleb Mansour Alshehri Muhammad Ali Rushdi |
| author_sort | Ali Muhammad Rushdi |
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| description | 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. |
| format | Article |
| id | doaj-art-3ea276273ac4418498589ac65d3fa39d |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-3ea276273ac4418498589ac65d3fa39d2025-02-03T06:13:19ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/327390327390A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic TautologyAli Muhammad Rushdi0Mohamed Zarouan1Taleb Mansour Alshehri2Muhammad Ali Rushdi3Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi ArabiaDepartment of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi ArabiaDepartment of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi ArabiaDepartment of Biomedical and Systems Engineering, Cairo University, Giza 12613, EgyptThe 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.http://dx.doi.org/10.1155/2015/327390 |
| spellingShingle | Ali Muhammad Rushdi Mohamed Zarouan Taleb Mansour Alshehri Muhammad Ali Rushdi A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology The Scientific World Journal |
| title | A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology |
| title_full | A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology |
| title_fullStr | A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology |
| title_full_unstemmed | A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology |
| title_short | A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology |
| title_sort | modern syllogistic method in intuitionistic fuzzy logic with realistic tautology |
| url | http://dx.doi.org/10.1155/2015/327390 |
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