FITradeoff Method (Flexible and Interactive Tradeoff)

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

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)

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

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

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

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

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

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

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.

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.

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

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

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).

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.

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

FITradeoff Collecting the preferences of the decision maker:

FITradeoff – choice problematic

FITradeoff – choice problematic Graphical display of potentially optimal alternatives

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.

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.

FITradeoff - Ranking Problematic

FITradeoff - Ranking Problematic Hasse diagram for ranking visualization

Graphics of weight space

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

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 Tradeoff Elicitation. Operational Research, pp 1–23. doi.org/10.1007/s12351-018-00444-2 FITradeoff: Softwares available for download at www.fitradeoff.org