Soft Expert Sets

,


Introduction
Most of the problems in engineering, medical science, economics, environments, and so forth, have various uncertainties. Molodtsov  Many researchers have studied this theory, and they created some models to solve problems in decision making and medical diagnosis, but most of these models deal only with one expert, and if we want to take the opinion of more than one expert, we need to do some operations such as union, intersection, and so forth. This causes a problem with the user, especially with those who use questionnaires in their work and studies. In our model the user can know the opinion of all experts in one model without any operations. Even after any operation on our model the user can know the opinion of all experts. So in this paper we introduce the concept of a soft expert set, which will be more effective and useful. We 2 Advances in Decision Sciences also define its basic operations, namely, complement, union intersection AND and OR and study their properties. Finally, we give an application of this concept in a decision-making problem.

Preliminaries
In this section, we recall some basic notions in soft set theory. Molodtsov 1 defined soft set in the following way. Let U be a universe and E be a set of parameters. Let P U denote the power set of U and A ⊆ E.
In other words, a soft set over U is a parameterized family of subsets of the universe U. For ε ∈ A, F ε may be considered as the set of ε-approximate elements of the soft set F, A .
The following definitions are due to Maji Definition 2.10. The union of two soft sets F, A and G, B over a common universe U is the

2.3
The following definition is due to Ali et al. 8 since they discovered that Maji et al.'s definition of intersection in 3 is not correct.
Definition 2.11. The extended intersection of two soft sets F, A and G, B over a common

Soft Expert Set
In this section, we introduce the concept of a soft expert set, and give definitions of its basic operations, namely, complement, union, intersection, AND, and OR. We give examples for these concepts. Basic properties of the operations are also given. Let U be a universe, E a set of parameters, and X a set of experts agents .LetO be a set of opinions, Z E × X × O and A ⊆ Z.
where P U denotes the power set of U.
Note 3.2. For simplicity we assume in this paper, two-valued opinions only in set O,thatis, O {0 disagree, 1 agree}, but multivalued opinions may be assumed as well.
Example 3.3. Suppose that a company produced new types of its products and wishes to take the opinion of some experts about concerning these products. Let U {u 1 ,u 2 ,u 3 ,u 4 } be a set of products, E {e 1 ,e 2 ,e 3 } a set of decision parameters where e i i 1, 2, 3 denotes the 4 Advances in Decision Sciences decision "easy to use," "quality," and "cheap," respectively, and let X {p, q, r} be a set of experts.
Suppose that the company has distributed a questionnaire to three experts to make decisions on the company's products, and we get the following:

3.2
Then we can view the soft expert set F, Z as consisting of the following collection of approximations:

3.3
Notice that in this example the first expert, p, "agrees" that the "easy to use" products are u 1 ,u 2 ,a n du 4 . The second expert, q, "agrees" that the "easy to use" products are u 1 and u 4 , and the third expert, r, "agrees" that the "easy to use" products are u 3 and u 4 . Notice also that all of them "agree" that product u 4 is "easy to use." Example 3.13. Consider Example 3.3. Then the disagree-soft expert set F, A 0 over U is

3.10
Proposition 3.14. If F, A is a soft expert set over U,then Proof. The proof is straightforward.

Advances in Decision Sciences
Assume that a company wants to fill a position. There are eight candidates who form the universe U {u 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 ,u 7 ,u 8 }. The hiring committee considers a set of parameters, E {e 1 ,e 2 ,e 3 ,e 4 ,e 5 } where the parameters e i i 1, 2, 3, 4, 5 stand for "experience," "computer knowledge," "young age," "good speaking," and "friendly," respectively. Let X {p, q, r} be a set of experts committee members .Suppose In Tables 1 and 2 we present the agree-soft expert set and disagree-soft expert set, respectively, such that if u i ∈ F 1 ε then u ij 1 otherwise u ij 0, and if u i ∈ F 0 ε then u ij 1 otherwise u ij 0 where u ij are the entries in Tables 1 and 2.
The following algorithm may be followed by the company to fill the position.