Neutrosophic Analysis of the Experimental Data using Neutrosophic Latin Square Design

Abstract

While dealing with the observed or measured data in surveys or experiments, it is not uncommon to deal with vague, incomplete, and imprecise information for whatever reasons. In this regard, researchers have proposed various emerging approaches such as fuzzy, intuitionistic fuzzy and neutrosophic logic and analysis, which provide better understanding, analysis and interpretations of the data. Neutrosophic logic is an extension of fuzzy logic where a variable x is described by triplet values, i.e., x ti f = , , ( ) , where t is the degree of “truth”, f is the degree of “false” and i is the level of “indeterminacy” AlAita, Abdulrahmanand Aslam, Muhammad (2023). A neutrosophic data x can be expressed as x = d + i, where d is the determinate (sure) part of x, and i is the indeterminate (unsure) part of x. Experimental design and analysis is a systematic, rigorous approach to problem solving that applies principles and techniques at the data collection stage so as to ensure the generation of valid, defensible, and supportable conclusions. Latin square designs (LSDs) are used to compare treatment factor levels represented by the Latin letters and using two blocking factors in rows and columns to simultaneously control two sources of nuisance variability. In this paper, we will define a neutrosophic Latin square design (NLSD), neutrosophic LSD model and consider the neutrosophic analysis of the NLSD experimental data for testing the abrasion resistance of rubber-coated fabric in a Martindale wear tester.