FITradeoff Method (Flexible and Interactive Tradeoff)

1. FITradeoffMethod(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 ofki. • 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 behavioralstudies (Borcherding et al, 1991): • 30% using the ratio • 50% using the swing • 67% using the tradeoff

6. Tradeoff Elicitation Procedure First step: intracriteriaevaluation 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. 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) Tradeoff Elicitation Procedure If there is indifference – v(A) = v(C) – v(A) = k1v1(b1) = k1; v(C) = k2v2(x2) – k1 = k2v2(x2)

8. Elicitation Methods in MAVT Context Methods using the additive model for aggregation: SMART; SMARTER Swing Procedure AHP Ratio Procedure MACBETH Swing Procedure TOPSIS No Clear Procedure FITradeoff Tradeoff Procedure Several Others

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

10. Partial Information Methods Additives in the context of MAVTusing 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 swingprocedure, 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 tradeoffprocedure

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. FITRADEOFF TRADEOFF Informação completa Informação parcial • High cognitive effort • 67% of inconsistencies • Reduced cognitive effort • Less inconsistency is expected

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 Weights Space If x = x2’ APB k2v2(x’2) > k3 If x = x2’’ BPA k2v2(x’’2) < k3 • Declaration of strict preference between consequences - easier than finding relationships of indifference

17. FITradeoff Collecting the preferences of the decision maker:

18. FITradeoff – choice problematic

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

20. 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. FITradeoff - Ranking Problematic

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. Graphicsofweightspace

25. Conclusions 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. 179-191. doi: 10.1016/j.ejor.2015.08.058. • Frej, E.A.; de Almeida, A.T.; Costa, A.P.C.S (2019) Using Data Visualization for Ranking Alternatives with Partial Information and Interactive TradeoffElicitation. Operational Research, pp 1–23. doi.org/10.1007/s12351-018-00444-2 • FITradeoff: Softwares available for download atwww.fitradeoff.org