Sage Journals: Discover world-class research

Abstract

The Cubic soft sets are primarily concerned with generalizing the soft sets by using fuzzy sets and interval valued fuzzy sets. We introduce the concept of cubic soft expert sets (CSESs) which can be considered as a generalization of both soft expert and cubic soft expert sets. The notions of internal cubic soft expert sets (ICSESs), external cubic soft expert sets (ECSESs), P-order, P-union, P-intersection, P-AND, P-OR and R-order, R-union, R-intersection, R-AND, R-OR have been defined for cubic soft expert sets (CSESs). We also investigate structural properties of these operations on cubic soft expert sets (CSESs). It has also been proved that cubic soft expert sets (CSESs) satisfy commutative, associative, De Morgan’s, distributive, idempotent and absorption laws. In last section, we provide the application of a cubic soft expert sets (CSESs) in multi-criteria decision making problem. We present the algorithm of a cubic soft expert decision making and give the numerical application.

Keywords

Cubic soft expert sets internal cubic soft expert sets external cubic soft expert sets interval valued fuzzy sets

Get full access to this article

View all access options for this article.

References

Ali

M.I.

, Feng

, Liu

, Min

W.K.

, and Shabir

, On some new operations in soft set theory, Comput Math Appl57 (2009), 1547–1553.

Alkhazaleh

, and Salleh

A.R.

, Soft expert sets, Adv Decis Sci (2011), 1–12(Article ID 757868).

Cagman

, and Enginoglu

, Soft set theory uni-int decision making, European J Oper Res207 (2010), 845–855.

Cagman

, Enginoglu

, and Citak

, Fuzzy soft set theory and its application, Iran J Fuzzy Syst8(3) (2011), 137–147.

Chen

, Tsang

E.C.C.

, Yeung

D.S.

, and Wang

, The parameterization reduction of soft sets and its applications, Comput Math Appl49 (2005), 757–763.

Feng

, Jun

Y.B.

, Liu

, and Li

, An adjustable approach to fuzzy soft set based decision making, J Comput Appl Math234(1) (2010), 10–20.

Gorzaldivczany

M.B.

, A method of inference in approximate reasoning based on interval valued fuzzy sets, Fuzzy Sets Syst21 (1987), 1–17.

Jun

Y.B.

, Kim

C.S.

, and Yang

K.O.

, Cubic sets, Ann Fuzzy Math Inform4 (2012), 83–98.

Khan

, Jun

Y.B.

, Gulistan

, and Yaqoob

, The generalized version of Jun.s cubic sets in semigroups, J Intell Fuzzy Syst28(2) (2015), 947–960.

10.

Kohout

L.J.

, and Bandler

, Fuzzy interval inference utilizing the checklist paradigm and BK relational products, in: Kearfort

R.B.

, et al., (Eds.)Appl Interval Comput, Kluwer, Dordrecht, 1996, pp. 291–335.

11.

Kong

, Gao

, and Wang

, A fuzzy soft set theoretic approach to decision making problems, J Comput Appl Math223(2) (2009), 540–542.

12.

D.F.

, An approach to fuzzy multiattribute decision making under uncertainty, Inform Sci169 (2005), 97–112.

13.

Maji

P.K.

, Biswas

, and Roy

A.R.

, Fuzzy soft sets, J Fuzzy Math9(3) (2001), 589–602.

14.

Maji

P.K.

, and Roy

A.R.

, Soft set theory, Comput Math Appl45 (2003), 555–562.

15.

Maji

P.K.

, Roy

A.R.

, and Biswas

, An application of soft sets in a decision making problem, Comput Math Appl44(8–9) (2002), 1077–1083.

16.

Molodtsov

D.A.

, Soft set theory-first results, Comput Math Appl37 (1999), 19–31.

17.

Molodtsov

D.A.

, The description of a dependence with the help of soft sets, J Comput Sys Sc Int40(6) (2001), 977–984.

18.

Molodtsov

D.A.

, Yu Leonov

, and Kovkov

D.V.

, Soft sets technique and its application, Nechetkie Sistemi I Myakie Vychisleniya1 (2006), 8–3.

19.

Muhiuddin

, and Al-roqi

A.M.

, Cubic soft sets with applications in BCK/BCI-algebras, Ann Fuzzy Math Inform8(2) (2014), 291–304.

20.

Pei

, and Miao

, From soft sets to information systems, in Proceedings of the IEEE International Conference on Granular Computing2 (2005), 617–621.

21.

Roy

A.R.

, and Maji

P.K.

, A fuzzy soft set theoretic approach to decision making problems, J Comput Appl Math203(2) (2007), 412–418.

22.

Sezgin

, and Atagun

A.O.

, On operations of soft sets, Comput Math Appl61(5) (2011), 1457–1467.

23.

Turksen

I.B.

, Interval-valued fuzzy sets based on normal forms, Fuzzy Sets Syst20 (1986), 191–210.

24.

Turksen

I.B.

, Interval-valued fuzzy sets and compensatory AND, Fuzzy Sets Syst51 (1992), 295–307.

25.

Turksen

I.B.

, Interval-valued strict preference with Zadeh triples, Fuzzy Sets Syst78 (1996), 183–195.

26.

Z.S.

, Methods for aggregating interval valued intuitionistic fuzzy information and their application to decision making, Control Decis22(2) (2007), 215–219.

27.

Zadeh

L.A.

, Fuzzy sets, Inform Control8 (1965), 338–353.

28.

Zadeh

L.A.

, The concept of a linguistic variable and its application to approximate reasoning-I, Inform Sci8 (1975), 199–249.

Cubic soft expert sets and their application in decision making

Abstract

Keywords

Get full access to this article

References