1. FITradeoff Method (Flexible and Interactive Tradeoff)

2. Multicriteria Decision Problems
Practical applications in organizations lead to several critical issues, such as:
Structuring the problem;
Building a model;
Choosing a multicriteria method
Considering the 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
Limited Rationality (Simon)

4. Featured Topics
In additive models for aggregation (weighted sum), the following points should be highlighted:
Elicitation procedures
Multicriteria Methods

5. 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% using the ratio
50% using the swing
67% using the tradeoff

6. Tradeoff Elicitation Procedure
First step: intracriteria evaluation
Second step : ranking the weights
Third step: determining ki:
Obtaining indifference information between consequences
and equivalent equations
The tradeoff procedure is classified as (Weber and Borcherding, 1993):
Algebraic
(n-1) equations are constructed during the process
Decomposed
Indirect procedure
Inference of weights through consequences judgments

7. Tradeoff Elicitation Procedure
Comparing two consequences of type A and C, the procedure seeks the value of the second criterion such that there is indifference between the two consequences.(Keeney and Raiffa, 1976)
If there is indifference
– v(A) = v(C)
– v(A) = k1v1(b1) = k1; v(C) = k2v2(x2)
– k1 = k2v2(x2) 7

8. Elicitation Methods 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 8

9. Elicitation Methods in MAVT Context
SWING
(von Winterfeldt and Edwards, 1986)
TRADEOFF
(Keeney and Raiffa, 1976)
Easier procedure for the decision maker (Edwards and Barron, 1994)
50% of inconsistency reported in behavioral studies (Borcherding et al, 1991)
Elicitation error x Modeling error (Edwards and Barron, 1994): Supports only linear value function
Strong axiomatic structure (Weber and Borcherding, 1993)
Difficult for the decision maker (Edwards and Barron, 1994)
67% of inconsistency reported in behavioral studies (Borcherding et al, 1991)
Elicitation error x Modeling error (Edwards and Barron, 1994): high inconsistency rate
FITradeoff is based on TRADEOFF procedure

10. Partial Information Methods
Additives in the context of MAVT using partial information:
Salo and Hämäläinen (1992): PAIRS
Edwards and Barron (1994): SMARTER
Dias and Climaco (2000): VIP ANALYSIS
Salo and Hämäläinen (2001): PRIME
Mármol et al (2002)
Salo and Punkka (2005): RICH
Mustajoki, Hamalainen and Salo (2005): INTERVAL SMART/SWING
White III & Holloway (2008)
Most of these methods do not have a structured elicitation or are based on the swing procedure, which is a simplified method, applicable only to the linear value function.

11. Partial Information Methods
The tradeoff procedure is rarely used, because of its difficulty for the decision maker, and high rate of inconsistency.
But it has a strong axiomatic structure, and it also can be appied to nonlinear value functions.
The FITradeoff elicitation procedure was developed to improve the applicability of the traditional tradeoff, making the method easier for the decision maker and maintaining its axiomatic structure.

12. FITradeoff – Flexible and Interactive Tradeoff
Two main benefits:
Reduces the information required by the decision maker
Required information is cognitively easier to provide (de Almeida et al., 2016)
Decision making process is based on strict preference statements rather than indifference. (de Almeida et al., 2016)
It uses partial information in the tradeoff procedure 12

13. FITradeoff – Flexible and Interactive Tradeoff
FLEXIBLE: The elicitation process can be adapted to different conditions and circumstances.
INTERACTIVE: The entire process is conducted based on alternate steps involving interaction with the decision maker and evaluation of alternatives.
Informação completa
Informação parcial
Reduced cognitive effort
Less inconsistency is expected
High cognitive effort
67% of inconsistencies
TRADEOFF
FITRADEOFF

14. FITradeoff – Flexible and Interactive Tradeoff
Initially developed to solve problems of choice based on the verification of the potential optimality of the alternatives through linear programming (LP) problems (de Almeida et al., 2016).
FITradeoff applicability was expanded also for ranking problematic. The concept of pairwise dominance relations between the alternatives is employed so that, for each interaction with the decision maker, a partial or complete order of the alternatives is found (Frej et al., 2019).

15. FITradeoff Procedure
First two steps (similar to the traditional tradeoff procedure):
Step 1: intracriteria assessment
Step 2: Order criteria scale constants ki:
Weights Space:
In some situations the problems can be solved in this step, with information only of the order of the weights.

16. FITradeoff Collecting the preferences of the decision maker:
Consequence A
Consequence B
From the declarations of strict preference of the decision maker (between X and Y), it is possible to construct relations of inequalities between the constants of scale, thus establishing the constraints that define the space of weights.
Weights Space
If x = x2’
APB
k2v2(x’2) > k3
Declaration of strict preference between consequences - easier than finding relationships of indifference
If x = x2’’
BPA
k2v2(x’’2) < k3 16

17. FITradeoff
Collecting the preferences of the decision maker:

18. FITradeoff – choice problematic

19. FITradeoff – choice problematic
Graphical display of potentially optimal alternatives

20. FITradeoff - Ranking Problematic
The FITradeoff for ranking problematic differs from that of choice by incorporating the concept of pairwise dominance relations between the alternatives so that, at each interaction with the decision maker, a partial or complete order of the alternatives is found.
The available DSS offers a tool to visualize the ranking of alternatives to the decision maker through a Hasse diagram, facilitating the visualization of the dominance relations between the alternatives.

21. FITradeoff - Ranking Problematic
To verify the dominance relations between the alternatives, for each interaction, a linear programming model is run for each pair of alternatives.
Thus, we search for dominance relations and build the ranking based on these relations.

22. FITradeoff - Ranking Problematic

23. FITradeoff - Ranking Problematic
Hasse diagram for ranking visualization

24. Graphics of weight space

25. Conclusions More reliable elicitation procedure
Use of the flexible elititation concept to implement a decision process in the tradeoff procedure used in the additive model.
More reliable elicitation procedure
since the cognitive effort required of the decision-maker is lower
This results in a reduction of the elicitation error
Possibility of various applications

26. Thank You!
References:
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
Frej, E.A.; de Almeida, A.T.; Costa, A.P.C.S (2019) Using Data Visualization for Ranking Alternatives with Partial Information and Interactive Tradeoff Elicitation. Operational Research, pp 1–23. doi.org/ /s
FITradeoff: Softwares available for download at