Novel Concept of Cubic Picture Fuzzy Sets

Year 2018, Issue: 24, 59 - 72, 14.08.2018

Shahzaib Ashraf Saleem Abdullah Abbas Qadir

Abstract

As a new extension of a cubic set, the notion of a cubic picture fuzzy set is introduced.
The propose work is separated into two portions. Firstly, establish the concept of cubic picture
fuzzy set and explore associated properties. Secondly, establish internal (external) cubic picture
fuzzy sets and define P-order and R-order union and intersection. Deliver some examples to support
of established P-order and R-order union and intersection of internal (external) cubic picture fuzzy
sets.

Keywords

Cubic Picture fuzzy set, P-order union and intersection, R-order union and intersection

References

• [1] S. Ashraf, T. Mahmood, S. Abdullah and Q. Khan, Different Approaches to Multi-Criteria Group Decision Making Problems for Picture Fuzzy Environment, Bulletin of the Brazilian Mathematical Society, New Series, 2018. https://doi.org/10.1007/s00574-018-0103 -y.
• [2] S. Ashraf, T. Mahmood and Q. Khan, Picture Fuzzy Linguistic Sets and Their Applications for Multi-Attribute Group Decision Making Problems, The Nucleus 55(2), 66-73, 2018.
• [3] K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61(2), 137-142, 1994.
• [4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96, 1986.
• [5] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31, 343-349, 1989.
• [6] K. Atanassov, Remark on intuitionistic fuzzy numbers, Notes on intuitionistic fuzzy sets, 13, 29-32, 2007.
• [7] B. C. Cuong, V. H. Phan, some fuzzy logic operations for picture fuzzy sets, In preceding of seventh international conference on knowledge and system engineering (IEEE), 2015.
• [8] B. C. Cuong, T. N. Roan, A classification of representable t-norm operators for picture fuzzy sets, In preceding of eight international conference on knowledge and system engineering (IEEE), 2016.
• [9] B. C. Cuong, Picture Fuzzy Sets- a new concept for computational intelligence problems, In Proceedings of the Third World Congress on Information and Communication Technologies, 1-6, 2013.
• [10] B. C. Cuong, Picture fuzzy sets, journal of computer science and cybernetics, 30(4) 409-420, 2001.
• [11] Y. B. Jun, C. S. Kim and K. O. Yang, Cubic sets, Ann. Fuzzy Math. Inform. 4(1), 83–98, 2012.
• [12] Y. B. Jun, C. S. Kim and M. S. Kang, Cubic subalgebras and ideals of BCK/BCIalgebras, Far East. J. Math. Sci. 44, 239–250, 2010.
• [13] Y. B. Jun, C. S. Kim and J. G. Kang, Cubic q-ideals of BCI-algebras, Ann. Fuzzy Math. Inf. 1, 25–34, 2011.
• [14] T. Mahmood, F. Mehmood, Q. Khan, Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making, International Journal of Algebra and Statistics, 5(1), 19–51, 2016.
• [15] T. Mahmood, S. Abdullah, S. Rashid, M. Bilal, Multicriteria Decision Making Based On Cubic Sets, Journal of New Theory, 16, 01-09, 2017.
• [16] H. W. Liu, G. J. Wang, Multi-criteria methods based on intuitionistic fuzzy sets, European Journal Operational Research, 179(1), 220–233, 2007.
• [17] R. R. Yager, Pythagorean fuzzy subsets, In Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, June 24-28, 57-61, 2013.
• [18] L. A. Zadeh Fuzzy sets, Information and Control, 8(3), 338- 356, 1965.
• [19] H. Zhao, Z. S. Xu, M. F. Ni, S. S. Liu, Generalized aggregation operator for intuitionistic fuzzy sets, International Journal of Intelligent Systems, 25(1), 1-30, 2010.
• [20] L. G. Zhou, Z. F. Tao, H. Y. Chen, J. Liu, Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making. Appl Math Model, 38, 2190-2205, 2014.