In this paper, we propose the concept of complex vague soft sets which are vague soft sets defined in a complex setting. Based on this new concept we define some concepts related to this notion as well as some basic operations namely the complement, union, intersection, AND and OR. The basic properties and relevant laws pertaining to this concept such as the De Morgan’s laws are also verified. We introduce the axiomatic definition of the distance function between two complex vague soft sets and subsequently define several distance measures between complex vague soft sets. Finally some of the algebraic properties of these distance measures are verified.
ZhangG., DillonT.S., CaiK.Y., MaJ. and LuJ., Operation properties and delta-equalities of complex fuzzy sets, International Journal of Approximate Reasoning50 (2009), 1227–1249.
13.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
14.
GauW.L. and BuehrerD.J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics23(2) (1993), 610–614.
15.
MolodtsovD., Soft set theory - First results, Computers and Mathematics with Applications37(4-5) (1999), 19–31.
16.
MajiP.K., BiswasR. and RoyA.R., Fuzzy soft sets, Journal of Fuzzy Mathematics3(9) (2001), 589–602.
17.
XuW., MaJ., WangS. and HaoG., Vague soft sets and their properties, Computers and Mathematics with Applications59 (2010), 787–794.
18.
LuA. and NgW., Vague sets or intuitionistic fuzzy sets for handling vague data: Which one is better?Lecture Notes in Computer Science3716 (2005), 401–416.
19.
LiuX.C., Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems52 (1992), 305–318.
