A novel extension of TOPSIS to MCGDM with bipolar neutrosophic soft topology

Abstract

In this paper, we bring out the idea of bipolar neutrosophic soft topology based on bipolar neutrosophic soft set (BNS-set). We study the properties of classical topology under bipolar neutrosophic soft (BNS) vagueness. The BNS-topology is the generalization of the fuzzy topology. We discuss certain properties of BNS-topology including, BNS-closure, BNS-interior, BNS-exterior and BNS-frontier by utilizing BNS-points. We also study the concept of BNS-subspace, BNS-neighborhoods and BNS-base for BNS-topology with the help of detailed examples and theorems. Furthermore, we propose: Technique for Order Preferences by Similarity to an Ideal Solution (TOPSIS) method under BNS-topological environment to deal with similarities in medical diagnosis. We see the importance of BNS-topology in multi criteria group decision making (MCGDM) as well. We present a numerical example with real background to demonstrate the validity of our model. Finally, we make a method-based and set-based comparison analysis of proposed method with some existing methods. Compared with existing MCGDM models, this study provides a flexible framework to form an approximate decision model to real-world MCGDM problems.

Keywords

BNS-topology,BNS-topological properties,BNS-TOPSIS,MCGDM,medical diagnosis

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References

Aktas and

Cagman , Soft sets and soft groups, Inf Sci 177 (2007), 2726–2735.

M.I.

Ali ,

Feng ,

X.Y.

Liu ,

W.K.

Min and

Shabir , On some new operations in soft set theory, Comput Math Appl 57 (2009), 1547–1553.

Ali and

Smarandache , The theory of neutrosophic cubic sets and their applications in pattern recognition, Journal of Intelligent and Fuzzy Systems 30 (4) (2016), 1957–1963.

Ali ,

L.H.

Son ,

Deli and

N.D.

Tien , Bipolar neutrosophic soft sets and application in decision making, Int J Intell Fuzzy Syst 33 (2017), 4077–4087.

Benayoun ,

Roy and

Sussman , Manual de reference du programme electr, In: Note de synthese et Formation, Direction Scientific SEMA Paris, France, (25) (1966).

Bosc and

Pivert , On a fuzzy bipolar relational algebra, Inf Sci 219 (2013),1–16.

J.P.

Brans and

Vincke , A preference ranking organization method: The PROMETHEE method for MCDM, Management Science 31 (6) (1985), 647–656.

Çağman ,

Karataş and

Enginoglu , Soft topology, Comput Math Appl 62 (2011), 351–358.

C. L.

Chang , Fuzzy topological spaces, J Math Anal Appl 24 (1968), 182–190

10.

Deli ,

Ali and

Smarandache , Bipolar neutrosophic sets and their application based on multi-criteria decision making problems, Proceedings of the 2015 International Conference on Advanced Mechatronic Systems, Beijing, China, 2015.

11.

P.P.

Dey ,

Pramanik and

B.C.

Giri , TOPSIS for solving multi-attribute decision-making problems under bi-polar neutrosophic environment. New Trends in Neutrosophic Theory and Applications; Pons Editions Brussels, Belgium, (2016), 65–77.

12.

Dong ,

Zhang , and

Herrera-Viedma , Consensus reaching model in the complex and dynamic MAGDM problem. Knowledge-based Systems 106 (2016), 206–219.

13.

Dong ,

Liu ,

Liang ,

Chiclana and

Herrera-Viedma , Strategic weight manipulation in multiple attribute decision making. Omega 75 (2018), 154–164.

14.

Eraslan and

Karaasalan , A group decision making method based onTOPSIS under fuzzy soft environment, J of New Theory 3 (2015), 30–40.

15.

C.L.

Hwang and

Yoon , Methods for multiple attribute decision-making, In: Fandel

, Trockel

(eds), Multiple attribute decision making. Springer, Berlin, (1981), 58–191.

16.

Jiang ,

Zhan and

Chen , Covering based variable precision (I,T)-fuzzy rough sets with applications to multi-attribute decision-making, IEEE Transactions on Fuzzy Systems, DOI 10.1109/TFUZZ.2018.2883023.

17.

Kelava and

Seikkala , On fuzzy metric spaces, Fuzzy Sets Syst 3(12) (1984), 215–229.

18.

K.M.

Lee , Bipolar-valued fuzzy sets and their basic operations, Procceeding International Conference, Bangkok, Thailand, (2000), P.

19.

k.M.

Lee and

K.J.

Cios , Comparison of interval-valued fuzzy sets, intuitionistic fuzzy set and bipolar valued fuzzy set, Journal of Fuzzy Logic and Intelligent 14(2) (2004), 125–129.

20.

D.F.

Li ,

G.H.

Chen and

Z.G.

Huang , Linear programming method for multiattribute group decision making using IF sets. Information Sciences 180(9) (2010), 1591–1609.

21.

D.F.

Li and

S.P.

Wan , Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection. Expert Systems with Applications 41(6) (2014), 3047–3059.

22.

D.F.

Li and

S.P.

Wan , A fuzzy inhomogenous multi-attribute group decision making approach to solve outsourcing provider selection problems, Knowledge-Based Systems 67 (2014), 71–89.

23.

Liu ,

Dong ,

Liang ,

Chiclana and

Herrera-Viedma , Multiple attribute strategic weight manipulation. please see Multiple attribute strategic weight manipulation with minimum cost in a group decision making context with interval attribute weights information. IEEE Transactions on Systems, Man and Cybernetics: Systems, DOI: 10.1109/TSMC.2018.2874942 (in press)

24.

P.K.

Maji ,

Biswas and

A. R.

Roy , An application of soft sets in decision making problem, Computer and Mathematics with Applications 44 (2002), 1077–1083.

25.

P.K.

Maji ,

Biswas and

A.R.

Roy , Soft set theory, Comput Math Appl 45 (2003), 555–562.

26.

Molodtsov , Soft set theory-first results, Computers and Mathematics with Applications 37 (1999), 19–31.

27.

Nan ,

Wang and

An , Intuitionistic fuzzy distance based TOPSIS method and application to MADM, International Journal of Fuzzy System Applications 5 (1) (2016), 43–56.

28.

Opricovic , Multicriteria optimization of civil engineering systems. Faculty of Pennsylvania, Belgrade, 1998.

29.

Pao-Ming and

Ying-Ming , Fuzzy topology I neighborhood structure of a fuzzy point and Moore-Smith convergence, J Math Anal Appl 76 (1980), 571–599.

30.

Pao-Ming and

Ying-Ming , Fuzzy topology II product and quotient spaces, J Math Anal Appl 77 (1980), 20–37.

31.

Riaz and

M.R.

Hashmi , Fuzzy Parameterized Fuzzy Soft Topology with Applications, Annals of Fuzzy Mathematics and Inf 13 (5) (2017), 593–613.

32.

Riaz ,

Samrandache ,

Firdous and

Fakhar , On Soft Rough Topology with Multi-Attribute Group Decision Making, Mathematics 7 (67) (2019), doi:10.3390/math7010067.

33.

Riaz ,

Davvaz ,

Firdous and

Fakhar , Novel Concepts of Soft Rough Set Topology with Applications, Journal of Intelligent & Fuzzy Systems 36 (4) (2019), 3579–3590. DOI: 10.3233/JIFS-181648.

34.

Riaz ,

Çağman ,

Zareef and

Aslam , N-Soft Topology and its Applications to Multi-Criteria Group Decision Making, Journal of Intelligent & Fuzzy Systems 36 (6) (2019), 6521–6536. DOI:10.3233/JIFS-182919.

35.

Riaz and

S.T.

Tehrim , Certain properties of bipolar fuzzy soft topology via Q-neighborhood, Punjab University Journal of Mathematics 51 (3) (2019), 113–131.

36.

Riaz and

S. T.

Tehrim , Cubic bipolar fuzzy ordered weighted geometric aggregation operators and their application using internal and external cubic bipolar fuzzy data, Computational & Applied Mathematics 38 (87) (2019), 1–25.

37.

Riaz and

S. T.

Tehrim , Multi-attribute group decision making based cubic bipolar fuzzy information using averaging aggregation operators, Journal of Intelligent & Fuzzy Systems (In Press) (2019), DOI:10.3233/JIFS-182751.

38.

Sahin and

Yigider , A Multi-criteria neutrosophic group decision making metod based TOPSIS for supplier selection, Zenodo, (2015) Doi:10.5281/zenodo.32238.

39.

L.A.

Saaty , The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, ISBN 0-07-054371-2, McGraw-Hill, (1980).

40.

Samrandache , A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic, rehoboth: American Research press, (1999).

41.

Shabir and

Naz , On soft topological spaces, Comput Math Appl 61 (2011), 1786–1799.

42.

B.P.

Varol and

Aygun , Fuzzy soft topology, Hacettepe J Mathematics and Statistics 41 (3) (2012), 407–419.

43.

Z. S.

Xu and

X. L.

Zhang , Hesitant fuzzy multi-attribute decision-making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52 (2013), 53–64.

44.

X. L.

Zhang ,

Z. S.

Xu , Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets, International Journal of Intelligent Systems, 29 (12) (2014), 1061–1078.

45.

Z. S.

Xu , Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy. Syst., 15 (6) (2007), 1179–1187.

46.

G.F.

GF, D.F.

Li and

Fei , A novel method for heterogeneous multi-attribute group decision making with preference deviation, Computers and Industrial Engineering 124 (2018), 58–64.

47.

G.F.

Yu ,

Fei and

D.F.

Li , A compromise-typed variable weight decision method for hybrid multi-attribute decision making, IEEE Transactions on Fuzzy Systems 27 (5) (2019), 861–872.

48.

L.A.

Zadeh , Fuzzy sets, Information and Control, 8(3) (1965), 338–353.

49.

Zhan ,

H.M.

Malik and

Akram , Novel decision-making algorithms based on intuitionistic fuzzy rough environment, International Journal of Machine Learning and Cybernetics 10 (2019), 1459–1485.

50.

Zhan and

Wang , Certain types of soft coverings based rough sets with applications, International Journal of Machine Learning and Cybernetics 10 (2019), 1065–1076.

51.

Zhan ,

Sun and

J.C.R.

Alcantud , Covering based multigranulation (I,T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences 476 (2019), 290–318.

52.

Zhang and

Zhan , Fuzzy soft β-covering based fuzzy rough sets and corresponding decision-making applications, International Journal of Machine Learning and Cybernetics 10 (2019), 1487–1502.

53.

Zhang ,

Zhan and

Xu , Covering-based generalized IF rough sets with applications to multi-attribute decision-making, Information Sciences 478 (2019), 275–302.

54.

Zhang L,

Zhan ,

Xu and

J.C.R.

Alcantud , Covering-based general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multi-attribute group decision-making, Information Sciences 494 (2019), 114–140.

55.

W.R.

Zhang , Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, Proceedings of IEEE conference fuzzy information processing society biannual conference, 1994, 305–309.

56.

Zorlutuna and

Atmaca , Fuzzy parameterized fuzzy soft topology. New Trends in Math Sci 4(1) (2016), 142–152.