Correlation of Neutrosophic Sets in Probability Spaces

Open access


In this paper, we introduce and study the concepts of correlation and correlation coefficient of neutrosophic data in probability spaces. In the case of finite spaces, these results give the results due to Salama et al. [16, 17, 18] and study some of their properties.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] A. A. Salama and S. A. Alblowi (2012) “Generalized neutrosophic set and generalized neutrosophic topological spaces” Computer Science and Engineering 2 (7).

  • [2] A. A. Salama and S. A. Alblowi (2012) “Neutrosophic set and neutrosophic topological spaces “IOSR Journal of Mathematics (IOSR-JM) 3(4) 31-35.

  • [3] A. A. Salama Mohamed Eisa and M. M. Abdelmoghny (2014) Neutrosophic Relations Database International Journal of Information Sciences and intelligent Systems Vol. (4) No.2. pp33-46.

  • [4] A. A. Salama and F. Smarandache (2013) Filters via Neutrosophic Crisp Sets Neutrosophic Sets and Systems Vol.1 No. 1 (2013) pp. 34-38.

  • [5] A. A. Salama and H. Elagamy (2013) Neutrosophic Filters International Journal of Computer Science Engineering and Information Technology Reseearch (IJCSEITR) Vol.3 Issue(1) Mar 2013 pp 307-312.

  • [6] A. A. Salama F. Smarandache and Valeri Kroumov (2014) Neutrosophic crisp Sets & Neutrosophic Crisp Topological Spaces Neutrosophic Sets and Systems Vol. (2) pp 25-30.

  • [7] A. A. Salama Said Broumi and Florentin Smarandache (2014) Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals I.J. Information Engineering and Electronic Business Published Online October 2014 in MECS.

  • [8] A. Robinson (1960) “Non-Standard analysis” Princeton University Press Princeton New Jersey.

  • [9] C. Yu (1993) “Correlation of fuzzy numbers”. Fuzzy Sets and Systems 55:303-307.

  • [10] D. H. Hong S.Y. Hwang (1995) “Correlation of Intuitionistic fuzzy sets in probability spaces” Fuzzy Sets and Systems 75:77-81.

  • [11] F. Smarandach (2002) “A new branch of philosophy in multiple valued logic” An International Journal 8(3): 297- 384.

  • [12] F. Smarandach (2003) “Neutrosophic set a generalization of the intuitionistic fuzzy sets” Proceedings of the third conference of the European Society for fuzzy logic and Technolgye EUSFLAT Septamper Zittau Geamany; Univ. of Applied Sciences at Zittau Goerlit 2 141-146.


  • [14] F. Smarandache (1999) A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy Neutrosophic Set Neutrosophic Probability. American Research Press Rehoboth NM

  • [15] F. Smarandache (2005) Neutrosophic set a generalization of the intuitionistics fuzzy sets Inter. J. Pure Appl. Math. 24 287 - 297.

  • [16] I. M. Hanafy A. A. Salama and K. M. Mahfouz (2012) “Correlation of neutrosophic data” International Refereed Journal of Engineering and Science 1(2): 39-43.

  • [17] I. M. Hanafy A.A. Salama and K. M. Mahfouz (2013)” Neutrosophic Classical Events and Its Probability” International Journal of Mathematics and Computer Applications Research(IJMCAR) Vol. (3) Issue 1 pp171-178.

  • [18] I. M. Hanafy A. A. Salama and K. Mahfouz (2013) “Correlation Coefficient of Neutrosophic Sets by Centroid Method” Internationals Journal of International Journal of Probability and Statistics 2(1) pp 912.

  • [19] K. T. Atanassov (1983) “Intuitionistic fuzzy sets”. Central Tech. Library Bulgarian Academy Science Sofia Bulgaria Rep. No. 1697/84. [20] K. T. Atanassov (1983) “Intuitionistic fuzzy sets”. Proc. of Polish Symp. On Interval and Fuzzy mathematics Poznan 23-26.

  • [21] K. T. Atanassov (1986) “Intuitionistic fuzzy sets”. Fuzzy Sets and Systems 20:87-96.

  • [22] M. Masjed-Jamei S. S. Dragomir H.M. Srivastava (2008) “Some generalizations of the Cauchy-Schwarz and the Cauchy-Bunyakovsky inequalities involving four free parameters and their applications” RGMIA Res. Rep. Coll. 11 (3) Article 3 pp.1-12 (electronic).

  • [23] S. S. Dragomir (2004) “Discrete inequalities of the Cauchy-Bunyakovsky-Schwarz type” Nova Science Publishers Inc. Hauppauge NY.

  • [24] T. Gerstenkorn J. Manko (1991) “Correlation of intuitionistic fuzz sets “ Fuzzy Sets and Systems 44: 39-43. [25] W. L. Hung and J. W. Wu (2002) “Correlation of intuitionistic fuzzy sets by centroid method”. Information Sciences 144: 219-225.

  • [26] L. A. Zadeh (1965) “Fuzzy sets”. Information and Control 8: 338-353.

Journal information
Impact Factor

Mathematical Citation Quotient (MCQ) 2018: 0.06

Target audience:

researchers in the fields of informatics, information technologies, statistics and mathematics

Cited By
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 304 150 5
PDF Downloads 146 76 5