Markov chain based on neutrosophic numbers in decision making

Authors

  • Kuppuswami Govindan SRI VENKATESWARAA COLLEGE OF TECHNOLOGYCHENNAITAMILNADU
  • Sujatha Ramalingam SSN COLLEGE OF ENGINEERINGCHENNAIINDIA
  • Nagarajan Deivanayagampillai Hindustan Institute of Science and TechnologyChennaiIndia.
  • Said Broumi Laboratory of Information Processing, Faculty of Science Ben MSik University Hassan II,Casablanca, Morocco
  • Kavikumar Jacob Faculty of Applied Science and Technology, Universiti Tun Hussein Onm Malaysia, Malaysia

DOI:

https://doi.org/10.48129/kjs.v48i4.9849

Keywords:

Markov chain, neutrosophic Markov chain, neutrosophic numbers, traffic, ergotic neutrosophic Markov chain

Abstract

Markov chain is a stochastic model for estimating the equilibrium of any system.  It is a unique mathematical model in which the future behavior of the system depends only on the present.  Often biased possibilities can be used over biased probabilities for handling uncertain information to define Markov chain using fuzzy environment.  Indeterminacy is different from randomness due to its construction type where the items involved in the space are true and false in the same time.   In this context as an extension of conventional and fuzzy probabilities neutrosophic probability (NP) was introduced.  These neutrosophic probabilities can be captured as neutrosophic numbers.  In this paper, Markov chain based on neutrosophic numbers is introduced and a new approach the ergoticity for the traffic states in the neutrosophic markov chain based on neutrosophic numbers is verified. The proposed approach is applied to decision making in prediction of traffic volume.

Author Biographies

Kuppuswami Govindan, SRI VENKATESWARAA COLLEGE OF TECHNOLOGYCHENNAITAMILNADU

ASSISTANT PROFESSOR

DEPARTMENT OF MATHEMATICS

 

Sujatha Ramalingam, SSN COLLEGE OF ENGINEERINGCHENNAIINDIA

ASSOCIATE PROFESSOR

DEPARTMENT OF MATHEMATICS

 

Nagarajan Deivanayagampillai, Hindustan Institute of Science and TechnologyChennaiIndia.

ASSOCIATE PROFESSOR

DEPARTMENT OF MATHEMATICS

Said Broumi, Laboratory of Information Processing, Faculty of Science Ben MSik University Hassan II,Casablanca, Morocco

PROFESSOR

DEPARTMENT OF MATHEMATICS

Kavikumar Jacob, Faculty of Applied Science and Technology, Universiti Tun Hussein Onm Malaysia, Malaysia

PROFESSOR

DEPARTMENT OF MATHEMATICS

References

Alhabib,R., Ranna,M. M., Farah,H., & Salama,

A. A. (2018). Some Neutrosophic Probability

Distributions. Neutrosophic Sets and Systems,

, 30-38.

Awiszus, M., & Rosenhahn, B., (2018). Markov

Chain Neural Networks. IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)

Broumi, S., Talea, M., Bakali, A., Smarandache,

F., Nagarajan, D., Lathamaheswari, M., &

Parimala, M. (2019). Shortest path problem

in fuzzy, intuitionistic fuzzy and neutrosophic

environment: an overview. Complex & Intelligent Systems, 5, 371-378.

Broumi, S., Nagarajan, D., Bakali, A., Talea,

M., Smarandache, F., & Lathamaheswari, M.

(2019). The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment. Complex & Intelligent

Systems, 5, 391-402.

Broumi, S., NDey, A., Talea, M., Bakali, A.,

Smarandache, F., Nagarajan, D., Lathamaheswari, M,. & Kumar, R. (2019). Shortestpath problem using Bellman algorithm under

neutrosophic environment. Complex & Intelligent Systems, 5, 409-416.

Garcia, J. C. F., Arcos, L. C. G., & Rivera, S. K. L.,

(2016). Quasi Type-2 fuzzy Markov chains:

An approach. IEEE International Conference

on Fuzzy Systems (FUZZ-IEEE).

Irfan, Deli., (2017). Interval-valued neutrosophic

soft sets and its decision making. International Journal of Machine Learning and Cybernetics, 8, 665–676.

Irfan, Deli., (2018). Expansions and reductions

on neutrosophic classical soft set. Journal of

Natural and Applied Sciences, 22, 478-486.

Irfan, Deli., & Yusuf Subas., (2017). Some

weighted geometric operators with SVTrNnumbers and their application to multicriteria decision making problems. Journal of

Intelligent and Fuzzy Systems, 32, 291-301.

Irfan, Deli., (2018). Operators on Single Valued Trapezoidal Neutrosophic Numbers and

SVTN-Group Decision Making. Neutrosophic Sets and Systems, 22, 131-150.

Irfan, Deli., Selim, Eraslan., & Naim, Cagman.,

(2018). ivnpiv-Neutrosophic soft sets and

their decision making based on similarity

measure. Neural Computing and Application,

, 187-203.

Kanyinda, J. P. M., Matendo, R. M. M., Lukata,

B. U. E., & Ibula, D. N., (2015). Fuzzy

Eigenvalues and Fuzzy Eigenvectors of Fuzzy

Markov Chain Transition Matrix under Maxmin Composition. Journal of Fuzzy Set Valued Analysis, 1, 25-35.

Kaufmann, A., & Gupta, M. M., (1985). Introduction to Fuzzy Arithmetic. Van Nostrand Reinhold Company,USA.

Kong, L., Wu, Y., & Ye, J., (2015). Misfire fault

diagnosis method of gasoline engines using

the cosine similarity measure of neutrosophic

numbers. Neutrosophic Sets and Systems, 8,

-46.

Koukol, M., Zajilkova, L., Marek, L., & Tulek, P.,

(2015). Fuzzy logic in traffic engineering: A

review on signal control. Mathematical Problems in Engineering, 2015, 1-14.

Lei, M., Li, S., & Tan, Q., (2016). Intermittent

demand forecasting with fuzzy markov chain

and multi aggregation prediction algorithm.

Journal of Intelligent and Fuzzy Systems, 31,

-2918.

Liu, B., & Liang, Y., (2017). An introduction of Markov chain Monte Carlo method

to geochemical inverse problems: Reading

melting parameters from REE abundances

in abyssal peridotites. Geochimica et Cosmochimica Acta, 203, 216–234.

Mallak, S.F., Beh,M.M & Zaiqan,A., (2011).

”A Particular Class of Ergodic Finite Fuzzy

Markov Chains”. Advances In Fuzzy Mathematics, 6(2), 253-268.

Manley,E., (2015). ”Estimating Urban Traffic Patterns through Probabilistic Interconnectivity

of Road Network Junctions”. Plos one, 10(5),

-17.

Mohammed,A.B.,Manogaran,G.,Gamal.A.,&

Smarandache,F., (2018). ”A hybrid approach

of neutrosophic sets and DEMATEL method

for developing supplier selection criteria”.

Design Automation for Embedded System,

, 257–278.

Mohammed,A.B.,Zhou,Y.,Mohammed,M.,&

Chang,V.(2018). ”A group decision making

framework based on neutrosophic VIKOR

approach for e-government website evaluation”. Journal of Intelligent and Fuzzy

Systems, 34(6),4213–4224.

Mohammed,A.B.,Mohammed,M.,&

Chang,V.(2018). ”NMCDA: A Framework for Evaluating Cloud Computing

Services”. Future Generation Computer

Systems, 86,12-29.

Mohammed,A.B.,Atef,A.,& Smarandache,F.(2018). ”A hybrid neutrosophic

multiple criteria group decision making

approach for project selection”. Cognitive

Systems Research,1-12.

Nagarajan,D., Lathamaheswari,M.,Broumi,S.,&

Kavikumar,J.(2019). ”Dombi Interval Valued

Neutrosophic Graph and its Role in Traffic

Control Management”. Neutrosophic Sets

and Systems, 24,114-133

Nagarajan,D.,Lathamaheswari,M.,Broumi,S.,&

Kavikumar,J.(2019). ”A new perspective on

traffic control management using triangular interval type-2 fuzzy sets and interval

neutrosophic sets”. Operations Research

Perspectives, 6,1-13.

Ning,Wu.,(2013). ”A Stochastic Model for Reliability Analysis in Freeway Networks”.

Procedia- Social and Behavioral Sciences,

,2823-2834.

Olaleye,O.T.,Sowunmi,F.A.,Abiola,O.S.,Salako,M.O.,&

Eleyoowo,I.O.(2009). ”A Markov Chain Approach to the Dynamics of Vehicular Traffic

Characteristics in Abeokuta metropolis”.

Research Journals of Applied Sciences,

Engineering and Technology, 1,160-166.

Petrov,T.,(2009). ”Markov Chain Aggregation and

Its Application to Rule-Based Modelling”. In

book: Modeling Biomolecular Site Dynamics,DOI: 10.1007/978 − 1 − 4939 − 9102 −

Periyakumar,J.A.,Sreevinotha,V.,.(2016). ”On The

Ergodic Behaviour of Fuzzy Markov Chains”.

IOSR Journal of Mathematics (IOSR-JM),

(5),28-34.

Pranab,B.,Surapati,P.,Abiola,O.S.,& Bibhas,C.G.(2018). ”Distance Measure Based

MADM Strategy with Interval Trapezoidal

Neutrosophic Numbers”. Neutrosophic Sets

and Systems, 19,40-46.

Rui,J.,Cheng,J.J.,Zhang,H.M.,Huang,Y.X.,Tian,J.F.,Hu,M.B.,Wang,H

& Jia,B.(2017). ”Experimental and empirical

investigations of traffic flow instability”.

Transportation Research Procedia, 23,157-

Smarandache,F.,(2014). ”Introduction to Neutrosophic Statistics”. Sitech: Craiova, Romania,

Education Publishing, USA.

Smarandache,F.,Abbas,N.,Chibani,Y.,Hadjadji,B.,

& Omar,Z.A.(2016). ”PCR5 and Neutrosophic Probability in Target Identification”.

Progress in Nonlinear Dynamics and Chaos,

(2),45-50.

Sujatha,R.,(2012). ”An Introduction to Intuitionistic Markov Chain”. International Mathematical Forum, 7(50),2449-2456

Vajargah,B.F.,& Gharehdaghi,M.(2014). ”Ergodicity of Fuzzy Markov Chains Based on Simulation Using Sequences”. Journal of mathematics and computer Science, 11,159-165.

Ye,J.,(2016). ”Multiple-attribute group decisionmaking method based on linguistic neutrosophic numbers”. Journal of Intelligent systems, 25,377-386.

Ye,J.,(2016). ”Fault diagnoses of steam turbine using the exponential similarity measure of neutrosopic numbers”. Journal of Intelligent &

Fuzzy Systems, 30(4),1927-1934.

Ye,J.,(2017). ”Bidirectional projection method for

multiple attributed group decision making

with neutrosophic numbers”. Neural Computing and Applications, 28(5),1021-1029.

Zadeh,L.A.,(1965). ”Fuzzy sets”. Information and

Control, 8,338-353.

Zhu,D.M.,Ching,W.K.,& Guu,S.M.,(2017). ”Sufficient conditions for the ergodicity of

fuzzy Markov chains”. Fuzzy Sets and Systems,DOI: 10.1016/j.fss.2016.01.005.

Published

16-08-2021