has to be eliminated thus modelling the incomplete information aspect of the problem.

Secondly, as the linguistic terms used by experts are fuzzy sets we **are naturally driven**
to model this decision making problem using fuzzy soft sets. Therefor we first examine some basic notions from Soft Set Theory and their relevance to our **model.**

## 3. **Development Of Algorithm**

As mentioned earlier this prediction problem has two peculiar characteristics:

1. Use of linguistic terms by counter-terror experts in their subjective assessments, 2. Incomplete information and hence the presence of approximate **descriptions of different factors of interest.**
It is well established now that linguistic vagueness is best tackled by Fuzzy Set Theory
[14]. On the other hand, Molodtsov [9] introduced the Theory off Soft Sets to handle the approximate descriptions. Maji, Biswas and Roy [8] combined both these theories as Fuzzy Soft Sets. Naturally this synergy of views is better suited to deal with the problems of linguistic vagueness coupled with approximate descriptions. Thus we **intend to develop** an algorithm using fuzzy soft sets. For this we first introduce the basic notions of theory:
Definition 3.1. A pair (F, A) is called a soft set [9] over X, where F **is a mapping given**
by F : A → P(X). In other words, a soft set over X **is a parametrized family of subsets of the universe** X.

For ε ∈ A, F(ε) may be considered as the set of ε**-approximate elements of the soft set** (F, A)**. Clearly a soft set is not a set in ordinary sense.** Definition 3.2. [4] Let X be a universe and E a set of attributes. Then the pair (**X, E**), called a soft space, is the collection of all soft sets on X **with attributes from** E.

Maji *et al.* **defined a fuzzy soft set in the following manner:**
Definition 3.3. [8] A pair (Λ, Σ) is called a fuzzy soft set over X, where **Λ : Σ** → Pe (X)
is a mapping, Pe(X) **being the set of all fuzzy sets of** X.

For our model the set of cities is the universal set and the factors **of decision making**
may be viewed as the set E. **As the factors for decision making are linguistic variables** thus E has to be a set of linguistic variables rendering (X, E**) to be a fuzzy soft space.**
Fuzzy soft space is defined as:
Definition 3.4. [3] Let X be an universe and E **a set of attributes. Then the collection** of all fuzzy soft sets over X with attributes from E **is called a fuzzy soft class and is**
denoted as (^**X, E**).

Example 3.5. Let X = {a, b, c, d, e} be the set of cities and E, **the set of decision factors**
given as:

| ε1 =   | High count of casualties            | ε6 =   | Cultural proximity to terrorists' ethnicity   |
|--------|-------------------------------------|--------|-----------------------------------------------|
| ε2 =   | Damage to infrastructure            | ε7 =   | Pre attack hiding                             |
| ε3 =   | Economic damage                     | ε8 =   | Post attack hiding                            |
| ε4 =   | Media Coverage                      | ε9 =   | Physical security                             |
| ε5 =   | Distance from terrorist strongholds | ε10 =  | Psychological impact                          |
