A UTILITY FUNCTION is an important tool for representing a DM’s preference. We adjoin UTILITY FUNCTIONs tomulti objective optimization problems. In current studies, usually one UTILITY FUNCTION is used for each objective FUNCTION. Situations may arise for a goal to have multiple UTILITY FUNCTIONs. Here, we consider a constrained MULTI-OBJECTIVE problem with each objective having multiple UTILITY FUNCTIONs. We induce the probability of the utilities for each objective FUNCTION using BAYESIAN THEORY. Illustrative examples considering dependence and independence of variables are worked through to demonstrate the usefulness of the proposed model.

The nonlinear Black-Scholes equation has been increasingly attracting interest over the last two decades, because it provides more accurate values by considering trans-action costs as a viable assumption. In this paper we review the fully nonlinear Black-Scholes equation with an adjusted volatility which is a FUNCTION of the second derivative of the price and then we prove two new theorems in this realistic model.

Background: Hypothyroidism, a preventable cause of mental retardation, is one of the most common diseases of the endocrine gland in children. The disorder can be corrected if it is identified and treated within the first few days of birth. In Iran, hypothyroidism is estimated to affect one out of 400 to 900 neonates, which is much higher than the global average.Objectives: This article is conducted to investigate the most cost–UTILITY option i.e. whether to implement the neonatal screening of genetic hypothyroidism or to merely treat such patients in the absence of the screening process.Patients and Methods: The present research is a cross-sectional, descriptive and analytical study. The provider perspective was employed to calculate the direct costs imposed on Shiraz University of Medical Sciences, insurance organizations, charities and patients concerning the implementation of screening PROGRAM and the treatment of detected cases along with the direct costs related to patients treated in the absence of the screening process; costs related to death were excluded. The statistical population of the study consisted of all 81837 newborns referred to university laboratory in Shiraz in 2010. In order to measure the UTILITY, time-trade-off method was employed to determine the life quality of patients.Results: The incremental cost-effectiveness ratios (ICER) of hypothyroidism, calculated through dividing the cost difference (ΔC) by UTILITY difference (ΔQALY), indicated that screening saved a total of 13413 US. $.Conclusions: The economic evaluation (cost-UTILITY analysis) resulted from the comparison of the above choices revealed that implementing the screening plan can actually be better and more cost-effective.