Abstract In general, a fuzzy set can’t handle situations of inconsistencies and inexact data, however, the Neutrosophic Set (NS) has been used to address such types of issues in all real world problems. The neutrosophic set is an extension of the fuzzy set and the intuitionistic fuzzy set, that can deal with imperfect, inconsistent, and indeterminate data in all the related problems. This article proposed a conventional neutrosophic approach using a ranking function for the transportation problem. This approach has considered a single-valued neutrosophic set for the entire transportation problem with the numerical illustration. Single valued trapezoidal neutrosophic numbers are well-known and used in solving the transportation problem and its extension. Besides, a novel ranking function is proposed with the help of membership functions, which gives the best optimal solution. Moreover, the obtained optimal solution has been compared with recent new approaches. This research will help to get the best optimal solution for the transportation problem under uncertainty.

ABSTRACT Digital watermarking has emerged as major technique for ensuring security for various types of data like medical data, digital copyright protection, transaction tracing and so on. With the advancement in digital data distribution over the network there has been increase in the need for protection of such data from unauthorized copying or usages. Watermarking helps in providing the security to some extent. Robustness against any sort of unauthenticated attack is the major requirement of watermarking. In this paper we proposed an efficient watermarking technique for medical data security with the aid of neural network. Usage of neural network is generally used to create and control watermarking strength automatically. This method provides better watermarked data which can be highly secured to unauthorized usage. It is observed that the proposed method provides better security for the multimedia data when compared with other data security methods.