Dempster–Shafer theory of evidence is one of the important tools for decision making under uncertainty. It is more useful in situations when cost of technical difficulties is involved or uniqueness of the situation under study makes it difficult/impossible to cover enough observations to quantify the models with real data. Consequently, experts provide opinions in terms of basic probability assignment for focal elements. Usually, it is seen that experts provide basic probability assignment for interval (or crisp) focal elements. However, due to presence of uncertainty focal elements can sometimes be treated as normal/generalized triangular fuzzy number (TFN in short) instead of intervals or crisp sets. TFN encodes only most likely value (mode) and the spread. This paper presents an attempt to combine Dempster–Shafer structures (DSS in short) with generalized/normal fuzzy focal elements using possibilistic sampling technique. To this end, human health risk assessment is carried out under such setting

This article describes how most frequently uncertainty arises due to vagueness, imprecision, partial information, etc., are encountered in medical diagnosis. To deal with this type of uncertainty, initially fuzzy set theory (FST) was explored and accordingly, medical decision making became one of the most important and interesting areas of applications of FST. Interval valued fuzzy sets (IVFSs) and intuitionistic fuzzy sets (IFS's) were developed and successfully applied in different areas including medical diagnosis. Although, IFS forms a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one, but one of the important and integral part i.e., degree of neutrality is not taken into consideration in IFS, which is generally occurred in medical diagnosis. In such circumstances, picture fuzzy set (PFS) can be considered as a strong mathematical tool, which adequate in situations when human opinions involved more answers of type: yes, abstain, no. For this purpose, this article, proposes some distance measures on PFS and studies some of its properties. Also, an attempt has been made to carry out medical diagnosis via the proposed distance measures on PFSs and exhibit the technique with a suitable case study. It is found that the distance measures make it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

Health risk assessments have been carried out worldwide to examine potential health risk due to exposure to toxic contaminants in various environments. In risk assessment, it is most important to know the nature of all available information, data or model parameters. It is observed that available information/data are tainted with uncertainty and variability in the same time, i.e., uncertainty and variability co-exist. In such situation it is important to devise method for processing both uncertainty and variability into same framework and which is an open issue. In this regards, this paper presents an algorithm to combined approach to propagate variability and uncertainty in the same framework. The differences and advantages of this algorithm over the existing methods are presented below: •The representation of uncertain model parameters are probabilistic together with generalized fuzzy numbers and normal interval valued fuzzy numbers.•The results obtained are then interpreted in terms of p-box and fuzzy numbers.•The advantage of this approach over the existing methods is that this approach gives an accurate resultant fuzzy number which is of trapezoidal type generalized fuzzy number that is different from the existing methods.