1. Flexible and Interactive Tradeoff Elicitation Procedure
FITradeoff Method
Flexible and Interactive Tradeoff Elicitation Procedure

2. Multicriteria Decision problems
Practical applications in organizations lead to several critical issues
Structuring the problem;
Building a model;
Choosing a multicriteria method
Let us consider Additive model
Another critical issue is:
Elicitation of preferences

3. Elicitation of preferences in MAVT context
Additive Model for aggregation of Criteria
Elicitation of ki.
ki - Weights or scales constant
Compensation amongst criteria

4. Basic Procedures for Weights Elicitation
Weights Elicitation Procedures for Additive Model aggregation
Tradeoff
Swing
Ratio
Inconsistencies reported in behavioral studies (Borcherding et al, 1991):
30% of the time using the ratio
50% of the time using the swing
67% of the time using the tradeoff method

5. MCDM/A Methods for Additive model in MAVT context
A few methods using the additive model for aggregation
SMART; SMARTER
AHP
MACBETH
TOPSIS
FITradeoff
Several others 5

6. MCDM/A Methods for Additive model in MAVT context
Methods using the additive model for aggregation
SMART; SMARTER
Swing procedure
AHP
Ratio procedure
MACBETH
TOPSIS
No clear procedure
FITradeoff
Tradeoff procedure
Several others 6

7. Tradeoff elicitation procedure
First step: intra-criteria evaluation
Second step: ranking of weights
Third sep: evaluating ki:
obtaining information of indifferences between consequences
And equivalent equations
The tradeoff procedure is classified as (Weber and Borcherding, 1993):
Algebraic
(n-1) equations are built during the process
Decomposed
indirect procedure
infer weights from preference judgments on consequences

8. Tradeoff elicitation procedure
Compare two criteria. The procedure seeks the outcome in the second criterion, so that there is an indifference between A and C (Keeney and Raiffa, 1976)
If there is indifferenrce: value of consequence A = value of consequence C
v(A) = k1v1(b1) = k1; v(C) = k2v2(x2)
k1 = k2v2(x2) 8

9. Two main benefits of FITradeoff
Reduces information required from the DM
Information required is cognitively easier (de Almeida et al., 2016)
The two main benefits of FITradeoff are first, it reduces the information required from the decision maker and secondly it enables an elicitation that requires preference information which is cognitively easier to provide 9

10. FITradeoff - Information cognitively easier:
Decision process is based on strict preference statements rather than indifference (de Almeida et al., 2016)
DM does not have to make adjustments for the indifference between two consequences (trade-off)
The information required is cognitively easier since the decision process is based on strict preference statements rather than indifference, which avoids the decision maker needing to establish indifference values between two consequences, which is a critical issue for the traditional tradeoff procedure. 10

11. Additive Models - MAVT
The traditional tradeoff procedure has a strong axiomatic foundation (Weber & Borcherding, 1993)
However, inconsistencies have been reported in behavioral studies:
67% of the time using the tradeoff method (Borcherding et al, 1991)
Reducing DM’s cognitive effort is a way to minimize such inconsistencies
FITradeoff improves the decision process by reducing inconsistencies (de Almeida et al., 2016)
For the additive models within the scope of MAVT, the literature points out that the traditional tradeoff procedure has strong axiomatic foundations
Due to the high level of inconsistencies detected in the traditional tradeoff procedure, FITradeoff is an alternative that minimizes inconsistencies without compromising its axiomatic premises by reducing the cognitive effort that the decision-maker has to make. 11

12. FITradeoff - Flexible and Interactive Tradeoff
Uses partial information in the tradeoff procedure
The indirect process is kept, using strict preferences instead of indifferences between consequences

13. Partial information – some methods
Additive value functions in the MAVT context
PAIRS (Salo and Hämäläinen, 1992)
VIP Analysis (Dias and Climaco, 2000)
Mármol et al (2002) consider the interactive process
the DM offers the information in a sequential way
PRIME (Salo; Hämäläinen, 2001) - swing method.
RICH (Salo and Punkka, 2005).
After examining results, the DM may either
choose to accept one of the alternatives in the kernel, or
continue with the specification of further preference information.
Mustajoki & Hamalainen (2005) integrate preference elicitation in the partial information framework, for the SMART/SWING method.
White III & Holloway (2008) also consider an interactive process to collect information
they use Markov process and dynamic programming analysis in order to reduce the number of questions.

14. FITradeoff procedure
First two steps (similar in the standard tradeoff procedure)
Step 1 - Intra-criteria evaluation
Step 2.1 consists of eliciting the order of values for ki.

15. FITradeoff procedure available space of weights:
Simulations studies have shown that depending on the pattern of distribution of weights
nearly to 50% of situations may be solved at this step
with the information of ranked weights, only.

16. The decision maker is asked to provide information on his/her preferences16

17. When the decision maker is able to commit with a preference statement the system collects the strict preference relation provided by the decision maker 17

18. FITradeoff
A preference relation (P) is easier to establish than an indifference relation (I).
Therefore, it is better to think about x2’ P b3 and b3 P x2’’, than to think about Indifference between x2 and b3. 18

19. FITradeoff : Graphical visualization
This information is shown with a Graphical visualization 19

20. From the decision maker’s preferential statements (between X and Y), it is possible to build inequalities between scale constants and establish constraints that define the space of weights 20

21. From the space of weights updated with the decision maker’s preferential information, LPP models are used to (identify and) evaluate potentially optimal alternatives 21

22. FITradeoff Flexible and Interactive Tradeoff
If required, the System shows the performance of the remaining alternatives (Potentially optimal), at each interaction:
The DM has different options for the visualization of potentially optimal alternatives under evaluation 22

23. FITradeoff Flexible and Interactive Tradeoff
Also, graphical information shows the performance of the Potentially optimal alternatives:
The DM has different options for the visualization of potentially optimal alternatives under evaluation 23

24. FITradeoff Flexible and Interactive Tradeoff
Graphical information - Potentially optimal alternatives:
Different formats
The DM has different options for the visualization of potentially optimal alternatives under evaluation 24

25. When a unique solution is found, i. e
When a unique solution is found, i.e., the system classifies this alternative as an optimal solution, and provides reports on the current weights space;
Such a result is similar to that of a complete information process; 25

26. If a unique solution is not found, the system starts another iteration to gather more preferential information from the decision maker 26

27. If the decision maker is not able to give any additional information, the elicitation procedure is finished and the system reports the potentially optimal alternatives found so far with the current space of weights
Such information is similar to that of an imprecise information process 27

28. Conclusions
Use of the concept of flexible elicitation for implementing a decision process on a tradeoff procedure for additive model.
More reliable elicitation procedure,
Since less effort is required from the DM
This results in reducing of elicitation errors.
Applications conducted

29. Feedback welcome! FITradeoff: Software available on request
Reference: de Almeida, A.T.; de Almeida, J.A.; Costa, A.P.C.S.; de Almeida -Filho, A.T. (2016) A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research. v. 250, p doi: /j.ejor
FITradeoff: Software available on request
Feedback welcome!