Here a novel idea to handle imprecise or vague set viz. Pseudo fuzzy set has been proposed. Pseudo fuzzy set is a triplet of element and its two membership functions. Both the membership functions may or may not be dependent. The hypothesis is that every positive sense has some negative sense. So, one membership function has been considered as positive and another as negative. Considering this ...

Let A be any nonrecursive set. For each k 0, we show that there are functions (k + 1)-truth-table reducible to A that are not k-weak-truth-table reducible to A; and we show that there are functions (k + 1)-Turing reducible to A that are not k-Turing reducible to A. Intuitively, this means that k + 1 queries to a nonrecursive oracle are strictly more useful than k queries to the same oracle (for...

We present an entirely new approach for the representation of intensifying and weakening linguistic hedges in fuzzy set theory, which is primarily based on a crisp ordering relation associated with the term that is modified, as well as on a fuzzy quantifier. With this technique we can generate membership functions for both atomic and modified linguistic terms. We prove that our model respects s...

Utilities and probabilities in decision theory are usually assessed by asking individuals to indicate their preferences between various uncertain choices. In this paper, we argue that (1) The utility of a consequence can be assessed as the membership function of the consequence in the fuzzy set ‘satisfactory’. (2) The probability of an event, instead of being directly assessed, should be inferr...

Confidence sets are generally interpreted in terms of replications of an experiment. However, this interpretation is only valid before observing the sample. After observing the sample, any confidence sets have probability zero or one to contain the parameter value. In this paper, we provide a confidence set analysis for an observed sample based on fuzzy set theory by using the concept of member...

Fuzzy sets refer to the datasets which do not have separate, distinct clusters, and they contain data elements whose membership values are between 0 and 1. Often each element belongs to several groups. We design a disk diagram with an augmented frequency graph to visualize elements in a fuzzy set. It shows the distribution of the elements within the set with respect to the membership function v...