Some explanation of decision measure Γ1 is in point here. Γ1 **is an equities weighted**
ratio of dominations and subjections of a city. The role of Ω, total number of attributes having equal membership grades may be considered less useful for **certain situations. In** such case we may compute Γ2 **given as:**

## Γ2 = ▽ (Ψi ) − ∆ (Ψi ).

Clearly Γ2 **is simple measure of differentiation or distance between the dominations and** subjections of a city. Yet another decision measure is Γ3 **which scales total decision** attributes by the equity factor and is given as:

$$\Gamma_{3}=\frac{\nabla\left(\psi_{i}\right)+\Delta\left(\psi_{i}\right)}{\Omega\left(\psi_{i}\right)}$$
.
In general, ρ ψi
, ψj
+ χ ψi
, ψj 6= kΞk . **This makes all three measures independent of**
each other and thus providing three different views of the same decision environment. 3.3. Computer Implementation of FSP. **For computer implementation a class** named FSS is introduced which specifies the notion of fuzzy soft sets. The basic data structure of FSP is a two dimensional array. This array is constructed in Step 3 from the available sets in Step 1, **2 and is a member of the class FSS. First part of Step 4 (lines 4**−7)
determines the attribute set for each pair of cities where first city **dominates others and**
second part compares for dominated-by pairs. Thus ρ ψi
, ψj
**is the domination attribute**
set of ψi and χ ψi
, ψj is the dominated-by attribute set of cities ψi and ψj
. **Step 8 (lines**
8 − 11) collects total number of dominations, subjections and equities **for each city** ψi
.

Line 12 computes the decision measure Γ1.

For further explaining the algorithm we give an illustrative example in the following:
Example 3.6. **Since 9/11 in USA, there have been some 247 suicide attacks in Pakistan** killing about 3000 innocent lives.. On 12th March 2010, Lahore, one of **the five major**
cities of Pakistan, encountered a spate of nine bombings in a single day killing about 100 people. Out of the nine incidents 4 **were suicide attacks. In this example we apply our** model of factors and the algorithm FSP to a multi-observer based committee of experts' opinion about the next possible suicide attack in Pakistan. We specifically consider 4 provincial capitals and the national capital. Figure ?? **shows map of Pakistan with all**
the major cities.

ψ1 = **Karachi**

$$\psi_{2}=$$

ψ2 = **Lahore**

$$\psi_{3}=$$

ψ3 = **Quetta**

$$\psi_{4}=$$

![0_image_0.png](0_image_0.png)

