Development of fully intuitionistic fuzzy data envelopment analysis model with missing data: an application to Indian police sector

Data Envelopment Analysis (DEA) is a technique used to measure the efficiency of decision-making units (DMUs). In order to measure the efficiency of DMUs, the essential requirement is input-output data. Data is usually collected by humans, machines, or both. Due to human/machine errors, there are chances of having some missing values or inaccuracy, such as vagueness/uncertainty/hesitation in the collected data. In this situation, it will be difficult to measure the efficiencies of DMUs accurately. To overcome these shortcomings, a method is presented that can deal with missing values and inaccuracy in the data. To measure the performance efficiencies of DMUs, an input minimization BCC (IMBCC) model in a fully intuitionistic fuzzy (IF) environment is proposed. To validate the efficacy of the proposed fully intuitionistic fuzzy input minimization BCC (FIFIMBCC) model and the technique to deal with missing values in the data, a real-life application to measure the performance efficiencies of Indian police stations is presented

A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones