Pythagorean Fuzzy N-Soft Groups

MUHAMMAD Haris Mateen


We elaborate in this paper a new structure Pythagorean fuzzy
$N$-soft groups which is the generalization of intuitionistic fuzzy
soft group initiated by Karaaslan in 2013. In Pythagorean fuzzy
N-soft sets concepts of fuzzy sets, soft sets, N-soft sets, fuzzy
soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft
sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets are
generalized. We also talk about some elementary basic concepts and
operations on Pythagorean fuzzy N-soft sets with the assistance of
illusions. We additionally define three different sorts of
complements for Pythagorean fuzzy N-soft sets and examined a few
outcomes not hold in Pythagorean fuzzy N-soft sets complements as
they hold in crisp set hypothesis with the assistance of counter
examples. We further talked about {$(\alpha, \beta, \gamma)$-cut of
Pythagorean fuzzy N-soft set and their properties}. We likewise talk
about some essential properties of Pythagorean fuzzy N-soft groups
like groupoid, normal group, left and right cosets, $(\alpha, \beta,
\gamma)$-cut subgroups and some fundamental outcomes identified with
these terms. Pythagorean fuzzy N-soft sets is increasingly efficient
and adaptable model to manage uncertainties. The proposed models of
Pythagorean fuzzy N-soft groups can defeat a few disadvantages of
the existing statures.


Pythagorean fuzzy N-soft sets; Pythagorean fuzzy N-soft sets complements; {$(\alpha, \beta, \gamma)$-cut of Pythagorean fuzzy N-soft set; Pythagorean fuzzy N-soft groups; groupoid; normal group;left and right cosets; $(\alpha, \beta, \gamma)$-cut subgr



H. Aktas and N. c{C}au{g}man, textit{Soft sets and soft group},

Information Sciences {bf1}(77)(2007), 2726-2735.


M. I. Ali, F. Feng, X. Y. Liu, W. K. Min and M. Shabir, textit{On some new operations in soft set theory}, Computers and Mathematics with Applications {bf57}(2009), 1547-1553.


K. T. Atanassov, textit{Intuitionistic fuzzy sets}, in: V. Sgurev, Ed., VII ITKRs Session, Sofia, June 1983

(Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984).


K. T. Atanassov and S. Stoeva, textit{Intuitionistic fuzzy sets}, in: Polish Symp. on Interval $&$ Fuzzy

Mathematics, Poznan (Aug. 1983), 23-26.


K. T. Atanassov, textit{Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, {bf20}(1986), 87-96.


J.M. Anthony, H. Sherwood, textit{Fuzzy groups redefined} Journal of mathematical analysis and applications, 69(1) (1979), 124-130.


M. Aslam and S. M. Qurashi, textit{ Some contributions to soft groups}, Ann. Fuzzy Math.

biInform. 4(1) (2012) 177-195.


P.S. Das, textit{Fuzzy groups and level subgroups}. Journal of Mathematical Analysis and Applications, 84(1)( 1981),264-269.


F. Fatimah, D. Rosadi, R. B. F. Hakim and J. C. R. Alcantud, textit{N-soft sets and their decision-making algoritms}, Soft Computing {bf22}(2018), 3829-3842.


M. Fathi, A.R. Sallah , textit{The intuitionist Fuzzy group}, Asian Journal of Algebra, 2(1)(2009)1-10.


F. Karaaslan, K. Kaygisiz, Çagman, N., 2013. On intuitionistic fuzzy

soft groups. Journal of New Results in Science, 2(3), pp.72-86.


A. Guleria and R. K. Bajaj, textit{On Pythagorean fuzzy soft matrices, operations and their applications

in decision making and medical diagnosis}, Soft Computing, (2018),


M. Gulistan, S. Nawaz, S. Z. Abbas, textit{Direct product of general intuitionistic fuzzy sets of subtraction algebras}. Cogent Mathematics, 3(1) 2(016),1176619.


K. Naeem, M. Riaz, X.D. Peng and D. Afzal, textit{Pythagorean Fuzzy Soft MCGDM Methods Based on TOPSIS, VIKOR and Aggregation Operators}, Journal of Intelligent & Fuzzy Systems, {bf37}(5)(2019), 6937-6957. DOI:10.3233/JIFS- 190905.


K. Naeem, M. Riaz, X. D. Peng and D. Afzal, textit{Pythagorean fuzzy soft MCGDM methods based on TOPSIS, VIKOR and aggregation operators}, Journal of Intelligent and Fuzzy Systems {bf37}(5)(2019), 6937-6957, DOI: 10.3233/JIFS-190905.


F. Karaaslan, K. Kaygisiz and N. c{C}au{g}man, textit{On Intuitionistic Fuzzy Soft Groups}

Journal of New Results in Science {bf37}(2)(2018), 1319-1329.


P. K. Maji, R. Biswas and A. R. Roy, textit{ Fuzzy Soft sets}, Journal of Fuzzy Mathematics, {bf9}(3)(2001), 589-602.


P. K. Maji, R. Biswas and A. R. Roy, textit{Intuitionistic fuzzy soft sets}, Journal of Fuzzy Mathematics, {bf9}(3)(2001), 677-691.


F. Karaaslan, K . Kaygisiz, N. c{C}au{g}man, , textit{On

intuitionistic fuzzy soft groups}. Journal of New Results in

Science, 2(3) (2013),72-86.


D. Molodtsov, textit{Soft set theory-first results}, Computers and Mathematics with Applications, {bf37}(1999), 19-31.


N. P. Mukherjee P. Bhattacharya, textit{ Fuzzy normal subgroups and fuzzy cosets}, Inform.bibitem{sumera}

Sci.34(1984), 225-239.


S. Naz, S. Ashraf and M. Akram, textit{A Novel Approach to

Decision-Making with Pythagorean Fuzzy Information}, Mathematics,

{bf95}(6)(2018), 1-28.


M. Riaz, K. Naeem, I. Zareef and D. Afzal,

Neutrosophic N-soft sets with TOPSIS method for multiple attribute

decision making, Neutrosophic Sets and Systems, 32(2020), 146-170.


X.D. Peng, Y. Yang, textit{Some results for Pythagorean fuzzy sets}, International Journal of Intelligent Systems, {bf30}(2015), 1133-1160.


X.D. Peng, H.Y. Yuan and Y. Yang, textit{Pythagorean fuzzy information measures and their applications}, International Journal of Intelligent Systems, 2017, 32(10), 991-1029.


X.D. Peng,Y. Y. Yang, J. Song and Y. Jiang, textit{Pythagorean Fuzzy Soft Set and Its Application}, Computer Engineering, {bf41}(7)(2015), 224-229.


X.D. Peng and J. Dai, textit{Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function},

Neural Computing and Applications, {bf29}(10)(2018), 939-954.


H. R. Patel, R. Bhardwaj, S. Choudhary, S. Garge, textit{ On normal fuzzy soft group}, Mathematical Theory and Modeling, 5(7) (2015), 26-32.


M. Riaz, N. c{C}au{g}man, I. Zareef and M. Aslam, textit{N-Soft Topology and its Applications to Multi-Criteria Group Decision Making},

Journal of Intelligent & Fuzzy Systems 36(6)(2019), 6521-6536. DOI:10.3233/JIFS-182919. DOI:10.3233/JIFS-182919.


A. Rosenfeld, textit{Fuzzy groups}, Journal of Mathematical Analysis and Applications {bf35}(1971), 512-517.


N. Sarala, B. Suganya, textit{ Some Properties of Fuzzy Soft Groups}, International

Organization of scientific research, 10( 2014), 36-40.


P.K. Sharma, Intuitionistic fuzzy groups. IFRSA International

journal of data warehousing and mining, 1(1)(2017),86-94.


L. Wangjin , textit{ Fuzzy invariant subgroups and fuzzy ideals}, Fuzzy Sets and Systems,

(1982), 133-139.


R. R. Yager, textit{Pythagorean fuzzy subsets}, IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint, Edmonton, Canada, IEEE (2013), 57-61.


R. R. Yager and A. M. Abbasov, textit{Pythagorean membership grades, complex numbers, and decision making}, International Journal of Intelligent Systems, {bf28}(5)(2013), 436-452.


R. R. Yager, textit{Pythagorean membership grades in multi-criteria decision making}, IEEE Transactions on Fuzzy Systems, {bf22}(4)(2014), 958-965.


N. Yaqoob, M. Akram, M. Aslam, textit{Intuitionistic fuzzy soft

groups induced by $(t, s)$-norm}. Indian Journal of Science and

Technology. 2013;6(4):4282-9.


L. A. Zadeh, textit{Fuzzy sets}, Information and Control, {bf8}(1965), 338-353.


The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences {bf8}(1975), 199-249.


X. Zhang, Z. Xu, textit{Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets}, International Journal of Intelligent Systems, {bf29}(2014), 1061-1078.


J. Zhou, Y. Li, Y. Yin, textit{Intuitionistic fuzzy soft semigroups}. Mathematica Aeterna, 1(03) (2011),173-183.

Total views : 35 times


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

shopify stats IJEECS visitor statistics