Login Register Cart 0
Generic placeholder image

Journal of Fuzzy Logic and Modeling in Engineering

Editor-in-Chief

ISSN (Print): 2666-2949
ISSN (Online): 2666-2957

Back
Journal Home About Journal Editorial Board Current Issue Volumes/Issues
Subscribe
Research Article

Application of Fuzzy Neutrosophic Cone in Decision Making

Author(s): Sujit Kumar De*, Kousik Bhattacharya and Biswajit Roy

Volume 1, Issue 2, 2022

Published on: 07 October, 2022

Article ID: e200822207820 Pages: 10

DOI: 10.2174/2666294901666220820180818

Price: $65

conference banner
Abstract

Aims: This article deals with a new decision-making process under a neutrosophic fuzzy environment. First of all, we develop various types of neutrosophic set by means of neutrosophic cones. In fact, this set has been developed from the general equation of second degree in the field of classical geometry. Considering the neutrosophic components “true membership”, the “falsity membership” and the “indeterminacy” as the three variables of three-dimensional rectangular axes we develop various types of cones like structures of the traditional neutrosophic set and hence a new defuzzification method.

Background: Fuzzy set has some limitations in its domain [0,1] to describe real-life decisionmaking problems. The problem of difficulties lies in the variation of lower and upper bound and also the single valued logic (membership function only) systems. In reality, three valued logics (membership function, non-membership function and indeterminacy) have been established in the name of Neutrosophic logic/sets, and two valued logics (membership and non-membership functions) have developed in the name of Intuitionistic fuzzy logic/sets. In three valued logic system, the concepts of negation are now a growing subject of any group decision making problems. However, to draw a clear estimation of a neutrosophic decision has not yet been studied by modern researchers.

Objective: Various kinds of new establishments of the Neutrosophic set have been studied from the algebraic point of view, along with some polynomial structures. We have seen that; no finite geometric structures have been developed yet to qualify the real-world problems.

Methods: We consider the three components of a neutrosophic set as the variables of threedimensional geometry. Since, the decisions are compact and constructive, we may consider the convex neutrosophic cone for analyzing single/ multiple group decision making problems.

Results: Various definitions are made over the cone- fundamentals using non-standard neutrosophic set in the domain [−1,1] × [−1,1] × [−1,1]. Then, we studied the constructions of several expressions/ functions of neutrosophic cones, such as reciprocal cone, and enveloping cone via a novel thinking process. Then using some examples, we have developed a new ranking method along with their geometric structures exclusively.

Conclusion: In this changing world, the nature of decision-making behaviors is also changing rapidly. So, the need of establishing new concepts is an emerging area of research. However, more attention is required in discussing such vital issues in near future. The proposed approach may be applied to the decision-making problems of global issues also.

Keywords: Neutrosophic set, Neutrosophic cone, Neutrosophic volume, Decision- making

Graphical Abstract

[1]
F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability., American Research Press: Rehoboth, 2003.
[2]
F. Smarandache, "n-Valued refined neutrosophic logic and its applications in physics", Prog. Phys., vol. 4, pp. 143-146, 2013.
[3]
F. Smarandache, Neutrosophic Theory and Applications., Le Quy Don Technical University, Faculty of Information Technology: Hanoi, Vietnam, 2016.
[4]
H. Khaled, F. Smarandache, and A. Essa, "A neutrosophic binomial factorial theorem with their refrains", Neutrosophic Sets Syst., vol. 14, pp. 7-11, 2016.
[5]
H. Khaled, A. Younus, and A. Mohammad, "The rectangle neutrosophic fuzzy matrices", J. Educ. Fac., vol. 15, pp. 3015-3024, 2019.
[6]
F. Smarandache, and M. Abobala, "n-refined neutrosophic vector spaces", Int. J. Neutrosophic Sci., vol. 7, pp. 47-54, 2020.
[http://dx.doi.org/10.54216/IJNS.070104]
[7]
M. Abobala, "AH-subspaces in neutrosophic vector spaces", Int. J. Neutrosophic Sci., vol. 6, pp. 80-86, 2020.
[http://dx.doi.org/10.54216/IJNS.060204]
[8]
M. Abobala, "On some neutrosophic algebraic equations", J. New Theory, vol. 33, pp. 26-32, 2020.
[9]
M. Abobala, "On refined neutrosophic matrices and their applications in refined neutrosophic algebraic equations", J. Math.. vol. 2022, p. 2071887, 2021.
[10]
M. Abobala, "Neutrosophic real inner product spaces", Neutrosophic Sets Syst., vol. 43, pp. 225-246, 2021.
[11]
M. Abobala, "On some algebraic properties of n-refined neutrosophic elements and n-refined neutrosophic linear equations", Math. Probl. Eng., vol. 2021, no. 5573072, 2021.
[12]
M. Abobala, "On some special substructures of refined neutrosophic rings", Int. J. Neutrosophic Sci., vol. 5, pp. 59-66, 2020.
[http://dx.doi.org/10.54216/IJNS.050105]
[13]
M. Abobala, "On the representation of neutrosophic matrices by neutrosophic linear transformations", J. Math., vol. 2021, no. 5591576, 2021.
[14]
M. Abobala, and A. Hatip, "An algebraic approach to neutrosophic euclidean geometry", Neutrosophic Sets Syst., vol. 43, pp. 114-123, 2021.
[15]
M. Abobala, A. Hatip, N. Olgun, S. Broumi, A. Salama, and E.H. Khaled, "The algebraic creativity in the neutrosophic square matrices", Neutrosophic Sets Syst., vol. 40, pp. 1-11, 2021.
[16]
R. Ali, Neutrosophic matrices and their properties., Hal- Archives, 2021.
[17]
R. Ali, "A short note on the solution of n-refined neutrosophic linear diophantine equations", Int. J. Neutrosophic Sci., vol. 15, pp. 43-51, 2021.
[18]
M. Aswad, "A study of neutrosophic differential equation by using a neutrosophic thick function", Neutrosophic Knowledge, vol. 1, pp. 14-23, 2020.
[19]
M. Aswad, "A study of the integration of neutrosophic thick function", Int. J. Neutrosophic Sci., vol. 6, pp. 97-105, 2020.
[20]
F.M. Aswad, "A study of neutrosophic Bi matrix", Neutrosophic Knowledge, vol. 2, pp. 1-10, 2021.
[21]
N. Olgun, and A. Hatip, The effect of the neutrosophic logic on the decision making. In: Quadruple Neutrosophic Theory and Applications., EU, Pons Editions Brussels: Belgium, 2020, pp. 238-253.
[22]
N. Olgun, A. Hatip, M. Bal, and M. Abobala, "A novel approach to necessary and sufficient conditions for the diagonalization of refined neutrosophic matrices", Int. J. Neutrosophic Sci., vol. 16, pp. 72-79, 2021.
[http://dx.doi.org/10.54216/IJNS.160202]
[23]
M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, and S.A. Akinleye, "On refined neutrosophic vector spaces II", Int. J. Neutrosophic Sci., vol. 9, pp. 22-36, 2020.
[24]
H. Sankari, and M. Abobala, "Neutrosophic linear diophantine equations with two variables", Neutrosophic Sets Syst., vol. 38, pp. 22-30, 2020.
[25]
H. Sankari, and M. Abobala, "Solving three conjectures about neutrosophic quadruple vector spaces", Neutrosophic Sets Syst., vol. 38, pp. 70-77, 2020.
[26]
M.B. Zeina, "Erlang service queueing model with neutrosophic parameters", Int. J. Neutrosophic Sci., vol. 6, pp. 106-112, 2020.
[http://dx.doi.org/10.54216/IJNS.060202]
[27]
M.B. Zeina, "Neutrosophic event-based queueing model", Int. J. Neutrosophic Sci., vol. 6, pp. 48-55, 2020.
[http://dx.doi.org/10.54216/IJNS.060103]
[28]
M. Ibrahim, and M. Abobala, "An introduction to refined neutrosophic number theory", Neutrosophic Sets Syst., vol. 45, pp. 40-53, 2021.
[29]
P. Biswas, S. Pramanik, and B.C. Giri, "Cosine similarity measure based multi-attribute decision making with trapezoidal fuzzy neutrosophic numbers", Neutrosophic Sets and System, vol. 8, pp. 46-56, 2014.

Rights & Permissions Print Cite
Article Metrics
1
© 2024 Bentham Science Publishers | Privacy Policy