Implication Operator On Pythagorean Fuzzy Set

Pythagorean fuzzy sets,involvoing membership, non membership and hesitancy considerations present mathematically a very general structure. Because of these considerations, if is possible to define several operations/ compositions of these sets. In the existing literature ten different operations on such sets are defined. These ten operations on Pythagorean fuzzy sets bear intersting properties. In this paper, we have identified and proved several of these properties, particularly those involving the operation A→B defined as pythagorean fuzzy implication with other operations.

REFERENCES

[1] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy set and Systems, Vol.20(1)(1986),87-96.
[2] K. T. Atanassov, New operators defined over the intuitionistic fuzzy sets, Fuzzy Set and Systems, 61(1994), 137-142. North Holland.
[3] K.T. Atanassov, Intuitionistic fuzzy sets, Springer Physica-Verlag, Heidelberg, 1999.
[4] K.T. Atanassov, Remarks on equalities between intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, Vol.16 (3) (2010), 40-41.
[5] X. Peng and Y. Yang, �Some results for Pythagorean fuzzy sets,� International Journal of Intelligent Systems, vol. 30, no. 11, pp. 1133�1160,(2015).
[6] Peng, X.D. and Yuan, H.Y. "Fundamental properties of Pythagorean fuzzy aggregation operators", Fund. Inform., Vol.147(4), pp. 415-446(2016).
[7] X.Peng, Algorithm for Pythagorean Fuzzy Multi-criteria Decision Making Based on WDBA with New Score Function, Fundamanta Informaticae, Vol.165(2019) 99-137. DOI: 10.3233/FI-2019-1778.
[8] X.Peng, New Operators for Intervl-valued Pythagorean Fuzzy Set, Scientia Iranica E (2019) 26(2), 1049-1076.
[9] R.K. Verma and B.D. Sharma, Intuitionistic fuzzy sets; Some new results, Notes on Intuitionistic Fuzzy Sets, Vol.17(3)(2011),1-10.
[10] R. R. Yager, Pythagorean fuzzy subsets, In:Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013) 57-61.
[11] R. R. Yager, Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems, Vol.22 (2014) 958-965.