Sage Journals: Discover world-class research

Abstract

The normal parameter reduction is used as a useful approach to identify the irrelevant parameters in soft set-based decision making systems. It finds a subset with least number of parameters that preserve the original classification of the decision alternatives. A number of algorithms have been developed for the normal parameter reduction of soft set but the case of repeated columns (i.e., e_i = e_j) was only considered by Danjuma et al. In this study, first we address the limitations of the Danjuma et al.’s approach to normal parameter reduction of soft set. Then, we propose a new algorithm for normal parameter reduction of soft set which is free of all such limitations. Moreover, we compare the proposed algorithm with some of the existing algorithms of normal parameter reduction of soft set to show its efficiency. Finally, the application of the proposed algorithm is elaborated by a medical diagnostic problem.

Keywords

Soft set normal parameter reduction decision making medical diagnosis

Get full access to this article

View all access options for this article.

References

J.C.R.

Alcantud ,

Santos-García and

Hernändez-Galilea , Glaucoma diagnosis: A soft set based decision making procedure, In Conference of the Spanish Association for Artificial Intelligence, Springer, (2015), pp. 49–60.

M.I.

Ali , Another view on reduction of parameters in soft sets, Applied Soft Computing 12(6) (2012), 1814–1821.

A.O.

Atagün ,

Kamaci and

Oktay , Reduced soft matrices and generalized products with applications in decision making, Neural Computing and Applications 29(9) (2018), 445–456.

K.T.

Atanassov , Intuitionistic fuzzy sets, In Intuitionistic fuzzy sets, Springer, (1999), pp. 1–137.

Chen ,

Tsang ,

D.S.

Yeung and

Wang , The parameterization reduction of soft sets and its applications, Computers & Mathematics with Applications 49(5-6) (2005), 757–763.

Danjuma ,

Herawan ,

M.A.

Ismail ,

Chiroma ,

A.I.

Abubakar and

A.M.

Zeki , A review on soft set-based parameter reduction and decision making, IEEE Access 5 (2017), 4671–4689.

Danjuma ,

M.A.

Ismail and

Herawan , An alternative approach to normal parameter reduction algorithm for soft set theory, IEEE Access 5 (2017), 4732–4746.

Feng ,

Cho ,

Pedrycz ,

Fujita and

Herawan , Soft set based association rule mining, Knowledge-Based Systems 111 (2016), 268–282.

Feng ,

Li ,

Davvaz and

M.I.

Ali , Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Computing 14(9) (2010), 899–911.

10.

M.B.

Gorzałczany , A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21(1) (1987), 1–17.

11.

Han , Comments on “normal parameter reduction in soft set based on particle swarm optimization algorithm”, Applied Mathematical Modelling 40(23-24) (2016), 10828–10834.

12.

Herawan , Soft set-based decision making for patients suspected influenza-like illness, In International Journal of Modern Physics: Conference Series, volume 1, (2010), pp. 1–5.

13.

Herawan and

M.M.

Deris , A soft set approach for association rules mining, Knowledge-Based Systems 24(1) (2011), 186–195.

14.

Jiang ,

Zhan and

Chen , Covering based variable precision (i, t)-fuzzy rough sets with applications to multiattribute decision-making, IEEE Transactions on Fuzzy Systems (2018).

15.

Kamaci ,

A.O.

Atagün and

Sönmezoğlu , Row-products of soft matrices with applications in multiple-disjoint decision making, Applied Soft Computing 62 (2018), 892–914.

16.

Kamaci ,

Saltik ,

Fulya Akiz and

A. Osman

Atagün , Cardinality inverse soft matrix theory and its applications in multicriteria group decision making, Journal of Intelligent & Fuzzy Systems 34(3) (2018), 2031–2049.

17.

A.Z.

Khameneh and

Kilicman , Parameter reduction of fuzzy soft sets: An adjustable approach based on the three-way decision, International Journal of Fuzzy Systems 20(3) (2018), 928–942.

18.

A.Z.

Khameneh ,

Kilicman and

A.R.

Salleh , An adjustable approach to multi-criteria group decision-making based on a preference relationship under fuzzy soft information, International Journal of Fuzzy Systems 19(6) (2017), 1840–1865.

19.

M.S.

Khan ,

M.A.

Al-Garadi ,

A.W.A.

Wahab and

Her-awan , An alternative data filling approach for prediction of missing data in soft sets (adfis), Springer Plus 5(1) (2016), 1348.

20.

Kolmogorov , Foundations of the Theory of Probability: Second English Edition.

21.

Kong ,

Ai ,

Wang ,

Li ,

Ma and

Lu , New normal parameter reduction method in fuzzy soft set theory, IEEE Access 7 (2019), 2986–2998.

22.

Kong ,

Gao ,

Wang and

Li , The normal parameter reduction of soft sets and its algorithm, Computers & Mathematics with Applications 56(12) (2008), 3029–3037.

23.

Kong ,

Jia ,

Zhang and

Wang , Normal parameter reduction in soft set based on particle swarm optimization algorithm, Applied Mathematical Modelling 39(16) (2015), 4808–4820.

24.

Ma ,

Sulaiman ,

Qin ,

Herawan and

J.M.

Zain , A new efficient normal parameter reduction algorithm of soft sets, Computers & Mathematics with Applications 62(2) (2011), 588–598.

25.

Ma ,

Zhan ,

M.I.

Ali and

Mehmood , A survey of decision making methods based on two classes of hybrid soft set models, Artificial Intelligence Review 49(4) (2018), 511–529.

26.

Maji ,

A.R.

Roy and

Biswas , An application of soft sets in a decision making problem, Computers & Mathematics with Applications 44(8-9) (2002), 1077–1083.

27.

Molodtsov , Soft set theory—first results, Computers & Mathematics with Applications 37(4-5) (1999), 19–31.

28.

Pawlak , Rough sets, International Journal of Computer & Information Sciences 11(5) (1982), 341–356.

29.

Renukadevi and

Sangeetha , Characterizations of normal parameter reductions of soft sets, Annals of Fuzzy Mathematics and Informatics (2015).

30.

Yuksel ,

Dizman ,

Yildizdan and

Sert , Application of soft sets to diagnose the prostate cancer risk, Journal of Inequalities and Applications 2013(1) (2013), 229.

31.

L.A.

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

32.

Zhan and

J.C.R.

Alcantud , A novel type of soft rough covering and its application to multicriteria group decision making, Artificial Intelligence Review (2018), 1–30.

33.

Zhan and

J.C.R.

Alcantud , A survey of parameter reduction of soft sets and corresponding algorithms, Artificial Intelligence Review (2018), 1–34.

34.

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.

35.

Zhan and

Wang , Certain types of soft coverings based rough sets with applications, International Journal of Machine Learning and Cybernetics (2018), 1–12.

36.

Zhan and

Zhu , Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets, Journal of Intelligent & Fuzzy Systems 29(3) (2015), 1169–1176.

37.

Zhang and

Zhan , Fuzzy soft β-covering based fuzzy rough sets and corresponding decision-making applications, International Journal of Machine Learning and Cybernetics, (2018), pp. 1–16.

38.

Zhang ,

Zhan and

J.C.R.

Alcantud , Novel classes of fuzzy soft β-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making, Soft Computing (2018), 1–25.

39.

Zhang ,

Guo and

Martínez , Managing multi-granular linguistic distribution assessments in large-scale multiattribute group decision making, IEEE Transactions on Systems, Man, and Cybernetics: Systems 47(11) (2017), 3063–3076.

40.

Zou and

Xiao , Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems 21(8) (2008), 941–945.

An improved algorithm for normal parameter reduction of soft set

Abstract

Keywords

Get full access to this article

References