In contemporary mathematics, the use of generalized techniques via fuzzy soft set theory can solve complicated problems in the domain of Applied Sciences. Possibility fuzzy soft set theory is one of the aforementioned techniques. The aim of this paper is to introduce the notion of possibility fuzzy soft left (resp. right) ideals of ordered semigroup based on possibility fuzzy soft sets. Various characterization results of ordered semigroups, using possibility fuzzy soft sets under the basic operations (including Union, Intersection, AND and OR operation) have been obtained. These results are further validated with the help of examples. A practical example of possibility fuzzy soft set in decision making induces to explain the depth of understanding the point of view for readers. Furthermore, the notions of l-idealistic (resp. r-idealistic) possibility fuzzy soft ordered semigroups has been introduced that will enhance the ability to grasp these notions. Authors have proved several algebraic properties along with suitable examples.
A.Al-Quran and N.Hassan, The complex neutrosophic soft expert set and its application in decision making, Journal of Intelligent & Fuzzy Systems34 (2018), 569–582.
2.
A.Al-Quran and N.Hassan, Neutrosophic vague soft expert set theory, Journal of Intelligent and Fuzzy Systems30(6), (2016), 3691–3702.
3.
A.Chaudhuri, K.De and D.Chatterjee, Solution of the decision making problems using fuzzy soft relations, International Journal of Information Technology15 (2009), 78–106.
4.
D.Molodtsov, Soft set theory first results, Computers, and Mathematics with Applications37 (1999), 19–31.
5.
D.Molodtsov, The theory of soft sets, URSS Publishers, Moscow, 2004, (in Russian).
6.
F.Smarandache, Neutrosophic set-A generalization of the intuitionistic fuzzy sets, International Journal of Pure and Applied Mathematics24(3) (2005), 287–297.
7.
G.Selvachandran and P.K.Singh, Interval-valued complex fuzzy soft set, and its application, International Journal for Uncertainty Quantification8(2) (2018), 101–117.
8.
H.Wang, F.Smarandache, Y.Q.Zhang and R.Sunderraman, Single valued neutrosophic sets, Multispace and Multistruc-ture4 (2010), 410–413.
9.
K.Alhazaymeh and N.Hassan, Vague soft expert set and its application in decision making, Malaysian Journal of Mathematical Sciences11(1) (2017), 23–39.
10.
K.Alhazaymeh and N.Hassan, Interval-valued vague soft sets and its application, Advances in Fuzzy Systems (2012), Article ID 208489.
L.A.Zadeh, Fuzzy sets, Information Science and Control8 (1965), 338–353.
14.
M.Bashir, A.R.Salleh and S.Alkhazaleh, Possibility intu-itionistic fuzzy soft set,Advances in Decision Sciences (2012), 404325.
15.
M.Bashir and A.R.Salleh, Possibility fuzzy soft expert Set, Journal of Applied Sciences on Engineering and Technology2012 (2012).
16.
N.Kehayopulu, Ideals and Green's relations in ordered semigroups, International Journal of Mathematics61286 (2006), 1–8.
17.
N.Kehayopulu, On weakly prime ideals of ordered semigroups, Japanese Journal of Mathematics35 (1990), 1051–1056.
18.
P.K.Maji, A.R.Roy and R.Biswas, An application of soft Sets in a decision making problems, Computers and Mathematics with Applications44 (2002), 1077–1083.
19.
P.K.Maji, A.R.Roy and R.Biswas, Fuzzy soft sets, Journal of Fuzzy Mathematics9 (2001), 589–602.
20.
P.K.Maji, R.Biswas and A.R.Roy, Soft set theory, Computers and Mathematics with Applications45 (2003), 555–562.
21.
R.X.Liang, J.Q.Wang and H.Y.Zhang, A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information, Neural Computing and Applications (2017), 2925–2928.
22.
S.Alkhazaleh and A.R.Salleh, Soft expert sets, Advances in Decision Sciences2011 (2011).
S.Alkhazaleh, A.R.Salleh and N.Hassan, Possibility fuzzy soft set, Advances in Decision Sciences2011 (2011).
26.
S.Broumi and F.Smarandache, Intuitionistic fuzzy soft expert sets and its application in decision making, Journal of New Theory1 (2015), 89–105.
27.
S.Broumi and F.Smarandache, Single valued neutrosophic soft expert sets and their application in decision making, Journal of New Theory3 (2015), 67–88.
28.
X.B.Yang, T.Y.Lin, J.Y.Yang, Y.Li and D.Yu, Combination of the interval-valued fuzzy set and soft set, Computers and Mathematics with Applications58(3) (2009), 521–527.
29.
C.F.Yang, Fuzzy soft semigroups and fuzzy soft ideals, Computers and Mathematics with Applications61 (2011), 255–261.
30.
Y.B.Jun, K.J.Lee and A.Khan, Soft ordered semigroups, Journal of Mathematical Logic Quarterly56 (2009), 42–50.
31.
Y.Yin and J.Zhan, The characterization of ordered semigroups in terms of fuzzy soft ideals, The Bulletin of the Malaysian Mathematical Society Series24(4) (2012).
32.
Y.Y.Li, H.Y.Zhang and J.Q.Wang, Linguistic neutrosophic sets and their application in multicriteria decision-making problems, International Journal for Uncertainty Quantification7(2) (2017), 135–154.
