In this paper, several new algebraic mathematics for positive fuzzy numbers of type (a,a,a,a) are devised and do not need the computation of α-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type (a,a,a,a) are obtained using the basic analytical principles of algebraic mathematics an...

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

After introducing and developing fuzzy set theory, a lot of studies have been done in this field and then a result appeared as a Fuzzy Graph (Combination of graph theory and fuzzy set theory). This is now known as Fuzzy graph theory. In this article we review essential works on different types of fuzzy graph and fuzzy hyper graph. Mathematics Subject Classification (2010): 03E72, 05C72

Numerous investigations have been directed toward aspects of rational life insurance purch&es and optimal coverage levels under differing conditions. Most of these studies have taken as "given" the design of life insurance contracts and have focused on optimal consumer responses to available insurance opportunities.' However, in works by Borch (1960, 1983), Arrow (1963, 1974) and Raviv (1979), ...

This model presents the invention scheduling difficulty in industry with different operational constraints, as well as strategic plan of the business, revenue purpose, and limit on finishing. In this article, we have studied an inventory model for deteriorating items with shortages under partially backlogging. The aim of present study is to minimize the total cost function in fuzzy environment....