Pythagorean fuzzy full implication multiple I method and corresponding applications

2021 ◽  
pp. 1-15
Author(s):  
TaiBen Nan ◽  
Haidong Zhang ◽  
Yanping He
Keyword(s):  
Decision Making ◽  
Modus Ponens ◽  
Pythagorean Fuzzy Set ◽  
Implication Operator ◽  
Continuity Properties ◽  
Fuzzy Implication ◽  
Decision Making Problem ◽  
Fuzzy Implication Operator ◽  
Degree Of Similarity ◽  
Fuzzy Modus Ponens

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

scholarly journals Influence of the fuzzy implication operator on the method-of-cases inference rule

1990 ◽  
Vol 4 (4) ◽  
pp. 307-318 ◽  
Author(s):  
Ruan Da ◽  
E.E. Kerre ◽  
G. De Cooman ◽  
B. Cappelle ◽  
F. Vanmassenhove
Keyword(s):  
Inference Rule ◽  
Implication Operator ◽  
Fuzzy Implication ◽  
Fuzzy Implication Operator ◽  
Method Of Cases

scholarly journals Lukasiewicz Fuzzy Implication Operator on Pythagorean Fuzzy Tautological Matrices

2021 ◽  
Vol 9 (6) ◽  
pp. 01-05
Author(s):  
Venkatesan Dhanan
Keyword(s):  
Implication Operator ◽  
Fuzzy Implication ◽  
Fuzzy Implication Operator

In this paper, introduced Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices and some properties of Lukasiwicz implication operator over Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices are discussed. Also discussed the relation between implication with Lukasiewicz disjunction and conjunction operations of PFCMs and PFCTMs.

scholarly journals Willmott Fuzzy Implication in Fuzzy Databases

2021 ◽  
Vol 19 ◽  
pp. 647-661
Author(s):  
Sanela Nesimovic ◽  
Dzenan Gusic
Keyword(s):  
Opposite Direction ◽  
Unit Interval ◽  
Fuzzy Relation ◽  
Functional Dependency ◽  
Functional Dependencies ◽  
Implication Operator ◽  
Fuzzy Implication ◽  
The World ◽  
Relation Scheme ◽  
Fuzzy Implication Operator

The object of the research are fuzzy functional dependencies on given relation scheme, and the question of their obtaining using the classical and innovated techniques. The attributes of the universal set are associated to the elements of the unit interval, and are turned into fuzzy formulas in this way. We prove that the dependency (which is treated as a fuzzy formula with respect to appropriately chosen valuation) is valid whenever it agrees with the attached two-elements fuzzy relation instance. The opposite direction of the claim is proven to be incorrect in this setting. Generalizing things to sets of attributes, we prove that particular fuzzy functional dependency follows form a set of fuzzy dependencies (in both, the world of two-element and the world of arbitrary fuzzy relation instances) if and only if the dependency is valid with respect to valuation anytime the set of fuzzy formulas agrees with the valuation. The results derived in paper show that the classical techniques in the procedure for generating new fuzzy dependencies may be replaced by the resolution ones, and hence automated. The research is conducted with respect to Willmott fuzzy implication operator

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