Development of Estimation Procedure of Population Mean in Two-Phase Stratified Sampling

This article describes the problem of estimation of finite population mean in two-phase stratified random sampling. Using information on two auxiliary variables, a class of product to regression chain type estimators has been proposed and its characteristic is discussed. The unbiased version of the proposed class of estimators has been constructed and the optimality condition for the proposed class of estimators is derived. The efficacy of the proposed methodology has been justified through empirical investigations carried over the data set of natural population as well as the data set of artificially generated population. The survey statistician may be suggested to use it

Hypercomplex Neutrosophic Similarity Measure & Its Application in Multicriteria Decision Making Problem

Neutrosophic set is very useful to express uncertainty, impreciseness, incompleteness and inconsistency in a more general way. It is prevalent in real life application problems to express both indeterminate and inconsistent information. This paper focuses on introducing a new similarity measure in the neutrosophic environment. Similarity measure approach can be used in ranking the alternatives and determining the best among them. It is useful to find the optimum alternative for multi criteria decision making (MCDM) problems from similar alternatives in neutrosophic form. We define a function based on hypercomplex number system in this paper to determine the degree of similarity between single valued neutrosophic sets and thus a new approach to rank the alternatives in MCDM problems has been introduced. The approach of using hypercomplex number system in formulating the similarity measure in neutrosophic set is new and is not available in literature so far. Finally, a numerical example demonstrates how this function determines the degree of similarity between single valued neutrosohic sets and thereby solves the MCDM problem

Application of Extended Fuzzy Programming Technique to a real life Transportation Problem in Neutrosophic environment

This paper focuses on solving the transportation problems with neutrosophic data for the first time. The indeterminacy factor has been considered in Transportation Problems (TP). The two methods of linear programming – Fuzzy Linear Programming (FLP) and Crisp Linear Programming (CLP) are discussed with reference to neutrosophic transportation problems. The first method uses the membership, non-membership and indeterminacy degrees separately to find the crisp solution using the Fuzzy Programming Technique and then the optimal solution is calculated in terms of neutrosophic data with the help of defined cost membership functions. The satisfaction degree is then calculated to check the better solution

Selection of Transportation Companies and Their Mode of Transportation for Interval Valued Data

The paper presents selection of transportation companies and their mode of transportation for interval valued neutrosophic data. The paper focuses on the application of distance measures to select mode of transportation for transportation companies. The paper also presents the application of multi-criteria decision making method using weighted correlation coefficient and extended TOPSIS for transportation companies. The multi-criteria decision making problem (MCDM) is taken in which there are different criteria and different modes. The selection is done among different modes and then it is done among four transportation companies in which data is taken as Interval Valued Neutrosophic Set (IVNS)

Application of Neutrosophic Set Theory in Generalized Assignment Problem

This paper presents the application of Neutrosophic Set Theory (NST) in solving Generalized Assignment Problem (GAP). GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author. The problem has been solved by evaluating score function matrix and then solving it by Extremum Difference Method (EDM) [1] to get the optimal assignment. The method has been demonstrated by a suitable numerical example

Solution of Multi-Criteria Assignment Problem using Neutrosophic Set Theory

Assignment Problem (AP) is a very well-known and also useful decision making problem in real life situations. It becomes more effective when different criteria are added. To solve Multi-Criteria Assignment Problem (MCAP), the different criteria have been considered as neutrosophic elements because Neutrosophic Set Theory (NST) is a generalization of the classical sets, conventional fuzzy sets, Intuitionistic Fuzzy Sets (IFS) and Interval Valued Fuzzy Sets (IVFS). In this paper two different methods have been proposed for solving MCAP. In the first method, we have calculated evaluation matrix, score function matrix, accuracy matrix and ranking matrix of the MCAP. The rows represent the alternatives and columns represent the projects of the MCAP. From the ranking matrix, the ranking order of the alternatives and the projects are determined separately. From the above two matrices, composite matrix is formed and it is solved by Hungarian Method to get the optimal assignment