AN APPLICATION OF SIMILARITY OF FUZZY SOFT SETS IN RECRUITMENT PROBLEM

Abstract: Uncertainty plays an important role in everyday life. The theory of fuzzy soft sets is an important tool to deal with uncertainty. This paper aims to study the notion of similarity of fuzzy soft sets and its application in a decision making problem. We have taken a hypothetical case study while applying the notion of similarity in a recruitment problem.


INTRODUCTION
In 1965, L.A. Zadeh [3] initiated Fuzzy Sets. Fuzzy set theory is a very useful tool to deal with uncertainty. In 1999, D.A. Molodstov [2] initiated Soft Set Theory and showed that fuzzy sets are special cases of Soft Sets. Use of parameters to describe a vague concept was indeed a window towards a new beginning. In 2001, P.K. Maji [5] combined fuzzy sets with soft sets and developed fuzzy soft sets. Ahmed and Kharal [1]  Similarity measure between fuzzy soft sets has been very widely applied in different fields. It has been applied in pattern recognition, region extraction, coding theory, image processing and in many other areas. The notion of similarity between fuzzy soft sets has been studied by Majumder and Samanta in [4] and Neog and Dutta in [6]. In this paper, we are using our notion of similarity of fuzzy soft sets in solving a decision problem.

PRELIMINARIES
In this section, we recall some concepts and definitions which will be needed in the sequel.

Soft Set [2]
A pair (F, E) is called a soft set (over U) if and only if F is a mapping of E into the set of all subsets of the set U. In other words, the soft set is a parameterized family of subsets of the set U.

Every set
, from this family may be considered as the set of  -elements of the soft set (F, E), or as the set of  -approximate elements of the soft set.

Fuzzy Soft Set [5]
A pair (F, A) is called a fuzzy soft set over U where represents the fuzzy subsets of U.

SIMILARITY BETWEEN TWO FUZZY SOFT SETS
In order to define similarity of fuzzy soft sets in our way, first we define scalar cardinality of a fuzzy soft set in the following way. Let ( ) ( ) ( )

Scalar cardinality of a fuzzy soft set
are the fuzzy soft matrices corresponding to the fuzzy soft sets (P, E) and (Q, E) respectively.
denote the similarity between the fuzzy soft sets (F, E) and (G, E).

Proposition
Let (F, E), (G, E) and (H, E) be three fuzzy soft sets over (U, E). Then the following results are valid.
be the fuzzy soft matrices corresponding to the fuzzy soft sets (P, E) and (Q, E) respectively. Then respectively. Then

Significantly Similar Fuzzy Soft Sets
Let ( ) be two fuzzy soft sets over the same soft universe (u, e). these two fuzzy soft sets will be called significantly similar if

Illustration
Suppose an organization wants to recruit a person for the post of Personal Relation Officer. Step 1. A model fuzzy soft set is set by an expert committee of the organization.
Step 2. We form the fuzzy soft set of parameters for each candidate.
Step 3. We find the similarity of the model fuzzy soft set and the fuzzy soft set for each candidate. In this way, we can find the significantly similar fuzzy soft sets.
Step 4. Higher the similarity value, greater is the chance for recruitment.    We have,  We have, In view of our discussion, we can conclude that the first candidate has greater chance of recruitment.

CONCLUSION
We have applied the notion of similarity of fuzzy soft sets in a decision problem. It is hoped that our findings would help enhancing this study in fuzzy soft sets.

ACKNOWLEDGEMENT
Our special thanks to the reviewers and editor of the journal for their valuable comments and suggestions.