Non-additive multi-attribute fuzzy target-oriented decision analysis

Abstract

As an emerging area considering behavioral aspects of decision making, target-oriented decision model lies in the philosophical root of bounded rationality as well as represents the S-shaped value function. This paper deals with multi-attribute decision analysis from target-oriented viewpoint. First, the basic (random) target-oriented decision model is extended to involve three types of target preferences: benefit target, cost target, and equal target. Next, since applying fuzzy set theory in decision analysis allows the decision maker to specify imprecise aspiration levels, fuzzy target-oriented decision analysis is formulated to model three typical types of fuzzy targets: fuzzy min, fuzzy max, and fuzzy equal. Also, different attitudes are used to derive target achievement functions, which can be viewed as a support for “probability as psychological distance”. Furthermore, we have proved that multi-attribute target-oriented decision analysis has a similar structure with discrete fuzzy measure and Choquet integral. Hence, we propose using discrete fuzzy measure and Choquet integral to model non-additive multi-attribute target-oriented decision analysis. In particular, the λ-measure is applied to reduce the difficulty of collecting information via a designed bisection search algorithm. Finally, a new product development example is used to illustrate the effectiveness and advantages of our model. The main advantages of our target-oriented decision model are its abilities to model the fuzzy uncertainty of targets as well as capture the non-additive behaviors among targets by means of discrete fuzzy measure and Choquet integral.