Integration of Bayesian Decision Theory and Computing with Words: A Novel Approach to Decision Support Using Z-numbers

Decision support systems have emerged over five decades ago to serve decision makers in uncertain conditions and usually rapidly changing and unstructured problems. Most decision support approaches, such as Bayesian decision theory and computing with words, compare and analyze the consequences of different decision alternatives. Bayesian decision methods use probabilities to handle uncertainty and have been widely used in different areas for estimating, predicting, and offering decision supports. On the other hand, computing with words (CW) and approximate reasoning apply fuzzy set theory to deal with imprecise measurements and inexact information and are most concerned with propositions stated in natural language. The concept of a Z-number [69] has been recently introduced to represent propositions and their reliability in natural language. This work proposes a methodology that integrates Z-numbers and Bayesian decision theory to provide decision support when precise measurements and exact values of parameters and probabilities are not available. The relationships and computing methods required for such integration are derived and mathematically proved. The proposed hybrid methodology benefits from both approaches and combines them to model the expert knowledge and its certainty (reliability) in natural language and apply such model to provide decision support. To the best of our knowledge, so far there has been no other decision support methodology capable of using the reliability of propositions in natural language. In order to demonstrate the proof of concept, the proposed methodology has been applied to a realistic case study on breast cancer diagnosis and a daily life example of choosing means of transportation