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Multi-Attribute Decision Making Approach Based on Neutral Membership Degree of Picture Fuzzy Set

Amalendu Si1 , Surajit Dan2 , Sujit Das3

Section:Research Paper, Product Type: Journal Paper
Volume-11 , Issue-01 , Page no. 89-94, Nov-2023

Online published on Nov 30, 2023

Copyright © Amalendu Si, Surajit Dan, Sujit Das . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: Amalendu Si, Surajit Dan, Sujit Das, “Multi-Attribute Decision Making Approach Based on Neutral Membership Degree of Picture Fuzzy Set,” International Journal of Computer Sciences and Engineering, Vol.11, Issue.01, pp.89-94, 2023.

MLA Style Citation: Amalendu Si, Surajit Dan, Sujit Das "Multi-Attribute Decision Making Approach Based on Neutral Membership Degree of Picture Fuzzy Set." International Journal of Computer Sciences and Engineering 11.01 (2023): 89-94.

APA Style Citation: Amalendu Si, Surajit Dan, Sujit Das, (2023). Multi-Attribute Decision Making Approach Based on Neutral Membership Degree of Picture Fuzzy Set. International Journal of Computer Sciences and Engineering, 11(01), 89-94.

BibTex Style Citation:
@article{Si_2023,
author = {Amalendu Si, Surajit Dan, Sujit Das},
title = {Multi-Attribute Decision Making Approach Based on Neutral Membership Degree of Picture Fuzzy Set},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {11 2023},
volume = {11},
Issue = {01},
month = {11},
year = {2023},
issn = {2347-2693},
pages = {89-94},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=1417},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=1417
TI - Multi-Attribute Decision Making Approach Based on Neutral Membership Degree of Picture Fuzzy Set
T2 - International Journal of Computer Sciences and Engineering
AU - Amalendu Si, Surajit Dan, Sujit Das
PY - 2023
DA - 2023/11/30
PB - IJCSE, Indore, INDIA
SP - 89-94
IS - 01
VL - 11
SN - 2347-2693
ER -

           

Abstract

In this study we proposed a new weighted aggregation operator for ranking the picture fuzzy numbers (PFNs) which is based on neutral membership value of PFN. As the picture fuzzy set (PFS) is an extension version of intuitionistic fuzzy set theory with introducing the neutral membership value during data analysis. The neutral membership value in PFS reflecting the ambiguous nature of the subject to judgment. The ambiguity is depending on the neutral membership value of PFN. The proposed weighted aggregation operator manages the ambiguity according to neutral membership value. Then, the aggregation operator applies in a multi attribute decision making method where attribute value of the alternative are picture fuzzy numbers. In the decision making process, the weight of attributes are calculated according to neutral values and aggregate the multiple attributes into a single PFN. Then estimate the individual score value of the alternatives. Lastly, ranking the alternative according to score value. Finally, a practical example for students’ performance in the multiple paper examination is highlighted for verifying the developed approach and demonstrates its practicality and effectiveness.

Key-Words / Index Term

Aggregation operators, Decision-making, Picture fuzzy set, Weighted Aggregation operators.

References

[1]. L. A. Zadeh, “Fuzzy sets. Information Control,” Vol.8, pp.338–356, 1965.
[2]. H. Liao, Z. Xu, “A VIKOR-based method for hesitant fuzzy multi-criteria decision making,” Fuzzy Optim. Decis. Mak., Vol.12, No.4, pp.373–392, 2013.
[3]. H Garg, “Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making”, Arab J SciEng, Vol.42, pp.5275–5290, 2017.
[4]. G WEI, “TODIM Method for Picture Fuzzy MultipleAttribute Decision Making”, INFORMATICA, Vol.29, No.3, pp.555–566, 2018.
[5]. C Wang, X Zhou, H Tu, S Tao, “Some Geometric Aggregation Operators Based on Picture Fuzzy Sets and Their Application in Multiple Attribute Decision Making”, Italian journal of pure and applied mathematics No.37, pp.477-492, 2017.
[6]. S. Das, M. B. Kar, S Kar, “Group Multi-criteria Decision Making Using Intuitionistic Multi-fuzzy Stes”, Journal of Uncertainty Analusis and Applications, Vol.1, No.10, 2013.
[7]. H. Garg, “Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making”, Arab J Sci Eng, Vol.42, pp.5275–5290, 2017.
[8]. Z. S. Xu, R. R.Yager, “Some geometric aggregation operators based on intuitionistic fuzzy sets”, Int. J. Gen. Syst, Vol.35, pp.417–433, 2006.
[9]. Z.S. Xu, “Intuitionistic fuzzy aggregation operators”, IEEE Transaction on Fuzzy System, Vol.15, pp.1179–1187, 2007.
[10]. F. E. Mohamed, “A VIKOR Method for Solving Personnel Training Selection Problem”, International Journal of Computer Science, Vol.1, No.2, 2012.
[11]. H. Shiha, H Shyurb, E. S. Leec, “An extension of TOPSIS for group decision making”, Mathematical and Computer Modelling, Vol.45, pp.801–813, 2007.
[12]. L.A. Zadeh, “Fuzzy-set-theoretic interpretation of linguistic hedges”, Journal of Cybernetics Vol.2, pp.4–34, 1972.
[13]. S. M. Chen, J.M. Tan, “Handling multi criteria fuzzy decision-making problems based on vague set theory.” Fuzzy Set Syst. Vol.67, pp.163–172, 1994.
[14]. V. Belton, T. Gear, “On a Short-coming of Saaty`s Method of Analytic Hierarchies”, Omega, pp.228-230, 1983.
[15]. C.L. Hwang, K. Yoon, Multiple Attribute Decision Making, Springer-Verlag, Berlin, 1981.
[16]. J. Grant, “Churn modeling by rough set approach”, manuscript, 2001.
[17]. P. Majumdar, S.K. Samanta, “Generalised fuzzy soft sets”, Comput. Math. Appl. Vol.59, pp.1425–1432, 2010.
[18]. P.K. Maji, More on intuitionistic fuzzy soft sets, Lect. Notes Comput. Sci. 5908, pp.231–240, 2009.
[19]. Z.M. Zhang, S.H. Zhang, “Type-2 fuzzy soft sets and their applications in decision making”, J. Appl. Math. p.1–35, 2012.
[20]. W. Xu, J. Ma, S.Y. Wang, G. Hao, “Vague soft sets and their properties”, Comput. Math. Appl. 59, pp.787–794, 2010.
[21]. K.T.Atanassov, “Intuitionistic fuzzy sets, Fuzzy Sets and Systems”, Vol.20, pp.87-96, 1986.
[22]. D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. of General Systems, Vol.17, pp.191-209, 1990.
[23]. M.B. Gorzalczany, “Interval-valued fuzzy controller based on verbal model of object”’, Fuzzy Sets and Systems Vol.28, No.1, pp.45–53, 1988.
[24]. V. Torra, “Hesitant fuzzy sets”. Int. J. Intell. Syst., Vol.25, pp.529–539, 2010.
[25]. J.C. Leyva-Lópezand, E. F. González, “A new method for group decision support based on ELECTRE III methodology,” European Journal of Operational Research, Vol. 148, pp.14-27, 2003.
[26]. B.C.Cuong, V. Kreinovich, “Picture fuzzy sets,” J. Comput. Sci. Cybern. Vol.30, No.4, pp.409–416, 2014.
[27]. A Si, S Das, S Kar, An approach to rank picture fuzzy numbers for decision making problems. Decision Making: Applications in Management and Engineering, Vol.2, No.2. pp.54-64, 2019.
[28]. S. Dan, M. B. Kar, S. Majumder, B. Roy, S. Kar, D. Pamucar, “Intuitionistic type-2 fuzzy set and its properties”, Symmetry, Vol.11, No.6, pp.808, 2019.
[29]. A. Si, S. Das, S. Kar, “Extension of TOPSIS and VIKOR method for decision-making problems with picture fuzzy number” In Proceedings of the Global AI Congress, Springer Singapore, pp.563-577, 2019.