420 204
Full Length Article
Volume 4 , Issue 2, PP: 104-116 , 2020

Title

The Special Neutrosophic Functions

Authors Names :   Ahmed Hatip   1 *  

1  Affiliation :  Department of Mathematics, Gaziantep University, Turkey

    Email :  kollnaar5@gmail.com



Doi   :  10.5281/zenodo.3782888


Abstract :

In this study, we introduce the notion of special neutrosophic functions as new kinds of neutrosophic function defined in a neutrosophic logic. As particular cases, we present the notions of neutrosophic Floor (greatest integer), neutrosophic Absolute Function and neutrosophic Signum Function. Moreover, we draw its neutrosophic graph representation and discuss similarities and differences for these special neutrosophic functions between the classic case and neutrosophic case. We investigate some properties and prove them. However, we often need the definition of absolute value function, especially in the metric space. Therefore, we introduce its initial definition in this study.

Keywords :

Neutrosophic relation , Neutrosophic function , Neutrosophic derivative , Neutrosophic integral Neutrosophic representation.

References :

[1]       L. Zadeh, , Fuzzy sets, Inform and Control, 8, pp. 338-353, 1965.

[2]       K.Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, pp.87-96, 1986

[3]       F.Liu, XH.Yuan, Fuzzy number intuitionistic fuzzy set,  Fuzzy Syst. Math, 21(1),pp.88–91, 2007.

[4]       H.Wang, F.Smarandache, YQ. Zhang, R. Sunderraman, Single valued neutrosophic sets. Multi-space Multi-struct 4, pp.410–413, 2010. 

[5]       F. Smarandache, Neutrosophy. Neutrosophic Logic, Set , Probability and Statistics. American Research Press, Rehoboth, 1998.

[6]       F. Smarandache, Neutrosophic Precalculus and Neutrosophic Calculus, Brussels: EuropaNova, 2015. 

[7]       F. Smarandache, Introduction To Neutrosophic Measure, Neutrosophic Integral, And Neutrosophic Probability, Craiova-Ohio: Sitech - Education , 2013.

[8]       A. Chakraborty, A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem, International Journal of Neutrosophic Science, Volume 1 , Issue 1, pp. 40-51 , 2020.

[9]       A. Chakraborty, S. Broumi, P.K Singh, Some properties of Pentagonal Neutrosophic Numbers and its Applications  in  Transportation  Problem  Environment,  Neutrosophic  Sets  and  Systems, vol.28, pp.200-215, 2019.

[10]     S. Broumi, M. Talea, A. Bakali, F. Smarandache, Single Valued Neutrosophic Graphs,Journal of New Theory, N 10,  pp. 86-101, 2016.

[11]     S. Broumi, M. Talea, A. Bakali,  F. Smarandache, “On Bipolar Single Valued Neutrosophic Graphs,” Journal of New Theory, N11, pp.84-102,2016

[12]     S. Broumi, M. Talea, A. Bakali, F. Smarandache, Interval Valued Neutrosophic Graphs, SISOM & ACOUSTICS 2016, Bucharest 12-13 May, pp.79-91, 2016.

[13]     S. Broumi, A. Bakali, M, Talea, and F, Smarandache, Isolated Single Valued Neutrosophic Graphs. Neutrosophic Sets and Systems, Vol. 11, pp.74-78, 2016.

[14]     S. Broumi, M. Talea, F. Smarandache and A. Bakali, Single Valued Neutrosophic Graphs:  Degree, Order and Size. IEEE International Conference on Fuzzy Systems (FUZZ), pp.2444-2451,2016.

[15]     Madeleine Al- Tahan, Some Results on Single Valued Neutrosophic (Weak) Polygroups, International Journal of Neutrosophic Science,   Volume 2 , Issue 1, PP: 38-46 , 2020.

[16]     E.O. Adeleke , A.A.A. Agboola , F. Smarandache, Refined Neutrosophic Rings II, International Journal of Neutrosophic Science,   Volume 2 , Issue 2, PP: 89-94 , 2020

[17]     Khatib, Ahmed, “neutrosophic modules,” mauritius: lap lambert, 2018.

[18]     K. A. Olgun N, "Neutrosophic Modules," Journal of Biostatistics and Biometric Applications, pp. 7-8, 2018. 

[19]     A. B.AL-Nafee, R.K. Al-Hamido, F. Smarandache, “Separation Axioms In Neutrosophic Crisp Topological Spaces”, Neutrosophic Sets and Systems, vol. 25, 25-32, 2019.

[20]     R.K. Al-Hamido, “Neutrosophic Crisp Bi-Topological Spaces”, Neutrosophic Sets and Systems, vol. 21, 66-73, 2018.