Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 12

α 3 >α 1 >α 2 >α 4 >α 5 .

(ii) By the formulas ( 1.3 ) and ( 1.5 ), we get

α 3 = α 1 >α 2 >α 4 >α 5 .

(iii) By the formula ( 1.8 ), we get

(iv) By the formula ( 1.9 ), we get α 1 = α 2 >α 3 >α 4 >α 5 .

(v) By the formula ( 1.10 ), we get α 2 >α 1 >α 3 >α 4 = α 5 .

(vi) By the formula ( 1.11 ), we get α 3 >α 1 >α 2 >α 4 >α 5 .

(vii) By the formula ( 1.16 ), we get α 1 >α 2 >α 3 >α 4 >α 5 .

From the results above, we can see that the derived rankings in both (ii) and (vi)
are the same, but all the other methods get different rankings. However, if we choose
other values of , then the results in (ii) and (vi) may be different. Now let's

give a detailed analysis on the results in (i)-(vii). The rankings in (iii), (iv) and (v)
are mainly based on the distance measures of IFVs, the used methods sometimes
cannot distinguish IFVs. The used methods in (i) and (ii) focus on the differences
between the membership degrees and the non-membership degrees, and consider
these differences as a main factor in ranking IFVs. The used method in (vi) tries
to decrease the uncertainty of an IFV by dividing its hesitancy degree into three
parts, and uses the method of limit to turn an IFV into a fuzzy value. The different
divisions may lead to different ranking results, in actual applications, the decision
maker sometimes cannot give a precise division of the hesitancy degree because of
the complexity and uncertainty of objective thing and the fuzziness of human thought.
Zhang and Xu (2012)'s method in (vii) focuses on the similarity measure between an
IFV and the positive ideal point, by using this method, we can solve lots of problems
such as described in Example 1.2. In short, different methods may produce different
results, and thus, we should choose appropriate ones in accordance with the actual
demands.

σ and θ

1.1.3 The Application of Ranking IFVs Using the Similarity
Measure and the Accuracy Degree in Multi-Attribute
Decision Making

In the above subsection, we have introduced Zhang and Xu (2012)'s method for
ranking IFVs. In what follows, we shall demonstrate how to use the method to solve
a multi-attribute decision making problem through an illustrative example (Zhang
and Xu 2012).
In modern warfare, the status of communication command is very important, and
it plays a key role in campaign's success and failure. So in order to improve the
capacity of communication jamming, a military unit decides to equip with a commu-
nication jamming system. According to the consultations with different suppliers,
there are four possible systems (alternatives) y j ( j = 1 , 2 , 3 , 4 ) to choose from.

Then the leaders of the military unit invite three experts e k ( to evaluate

these systems so as to choose the most reasonable one. Based on the expertise and
experiences of these experts, the leaders give the weight vector of these experts as

k = 1 , 2 , 3 )