In this chapter, we proposed two methods to model the target-oriented decision analy-sis with different target preferences: cdf based method and level set based method. Both of these two methods can induce four shaped value functions: S-shaped, inverseS-shaped, convex, and concave, which represent DM’s psychological preference. The main difference between these two methods is that the value function induced by the level set based method model is steeper than that induced by the cdf based method.
Target-oriented decision analysis presumes that target has a random probability dis-tribution. In some cases, it is not so easy for the DM to specify a suitable pdf for the uncertain target. Furthermore, it is well known that all facets of uncertainty cannot be captured by a single probability distribution. In many applications, fuzzy subsets provide a very convenient object for the representation of uncertain information. In the next chapter, we shall discuss target-oriented decision analysis with fuzzy targets.
Chapter 4
Fuzzy Target-Oriented Decision Analysis with Different Target Preferences
Abstract: Simon proposed a behavioral model for rational choice, by enunciating the so-called theory of bounded rationality implying that the decision maker (DM) simply looks for the first “satisfactory” act that meets some predefined target. Target-oriented decision model has relaxed the assumption of a known target by considering a random consequence T instead. Then the target-oriented decision model prescribes that the DM should choose an act a that maximizes the probability of meeting the random target.
However, in many situations, it is not so easy to specify a probability function for the uncertain target. Moreover, it is widely acknowledged that all facets of uncertainty cannot be captured by a single probability distribution. Fuzzy subset provides a very convenient object for representing uncertain information.
Toward this end, the main focus of this chapter is to discuss the issue of how to use fuzzy targets in the target-oriented decision model with different target preferences.
To do so, we firstly analysis different fuzzy-probability transformation techniques, then the proportional transformation method is chosen to transform the fuzzy targets into probabilistic targets. Secondly, based on the probabilistic target-oriented decision model discussed in Chapter 3, we can finally obtain the fuzzy target-oriented decision model with different target preferences.
4.1 Introduction
Simon [120] proposed a behavioral model for rational choice, by enunciating the so-called theory of bounded rationality implying that due to the cost or the practical im-possibility of searching among all possible acts for the optimal, the decision maker (DM) simply looks for the first “satisfactory” act that meets some predefined targets. Although simple and appealing from this satisficing-oriented point of view, its resulted model is still not complete because there may be uncertainty about the target itself. Target-oriented decision model has relaxed the assumption of a known target by considering a random consequence T instead. Then the target-based decision model prescribes that the agent should choose an act a that maximizes the probability of meeting an uncertain target T, assuming that the target T is stochastically independent of the random consequences to be evaluated.
However, it is now more and more widely acknowledged that all facets of uncertainty cannot be captured by a single probability distribution. Moreover, it is usually not easy for a DM to specify the probability distribution of the uncertain target. In many applica-tions, fuzzy subsets provide a very convenient object for the representation of uncertain information. The subjective assessments provides by DMs are usually conceptually vague, with uncertainty that is frequently represented in linguistic forms. To help people easily express their subjective assessments, the linguistic variables are used to linguistically ex-press requirements. Fuzzy numbers are usually used in decision analysis problems. Thus it is necessary to consider the fuzzy targets in target-oriented decision model. Toward this end, Huynh et al. [61, 62] have discussed the problem of decision analysis under uncer-tainty (DAUU) with a payoff variable. There are three drawbacks in their work. Firstly, only one target preference is considered. As we mentioned in Chapter 3, the DM can have three types of target preferences. Secondly, a thorough analysis of the possibility-probability conversion problems is ignored. In the literature, there are many techniques to transform a possibility into its associated probability. Thirdly, in fact, fuzzy decision analysis has received a lot of attraction since the pioneering work on fuzzy decision anal-ysis by Bellman and Zadeh [12] in 1970. Bellman and Zadeh’s paradigm is still widely used in most literature of fuzzy decision analysis, comparing fuzzy target-oriented decision model with Bellman and Zadeh paradigm will be of great help to fuzzy decision analysis.
However, a complete analysis with Bellman and Zadeh is missed in their research.
Based on the above-mentioned observations, the main focus of this chapter is to revisit fuzzy targets in target-oriented decision model based on the probabilistic target-oriented decision model discussed in Chapter 3. To do so, firstly a through analysis of differ-ent possibility-probability transformation techniques is given and then the proportional transformation method is properly chosen. Secondly, we extend the probabilistic target-oriented decision model into fuzzy target case. Thirdly, we use several fuzzy targets, commonly used in Bellman and Zadeh paradigm, to illustrate the proposed fuzzy target-oriented decision model. Finally, we compare our work with Bellman and Zadeh in terms of three aspects.
The rest of this chapter is organized as follows. In Section 4.2 we introduce some concepts of possibility distribution and fuzzy subsets. Section 4.3 analyzes different possibility-probability conversion methods. Section 4.4 revisits fuzzy target-oriented de-cision model with different target preferences. In Section 4.5, four commonly used fuzzy targets in Bellman and Zadeh paradigm, are selected to illustrate our proposed models.
Section 4.6 gives a comparative analysis with Bellman and Zadeh paradigm from three aspects. Finally, some concluding remarks are given in Section 4.7.