A Novel Neutrosophic Interpretive Structural Modeling Approach: Hierarchical Visual Graphs of Indeterminate Causalities

Introduction

Interpretive Structural Modeling (ISM) is defined as a process of interpreting systems with well-defined factors. It models the relationships that appear in mind and transforms them into visual forms (Sage, 1977). The method summarizes the relationship between certain variables in defining a problem (Warfield, 1974). Thus, the hierarchical structure or the order between these variables is also modeled. ISM provides a decision support to present undesired factors / risks / barriers visually in a system in hierarchical graphics and clarifies the relationships between these obstacles. It is used to identify the root causes of a problem with a graph of directed relationships. For this purpose, the factors causing a problem are clarified and mutual relationships are shown based on their power of influence (Mandal & Deshmukh, 1994).

ISM requires expert opinions to evaluate the causal relationships of identified variables. However, in many cases experts cannot determine a relationship, or can be doubtful about stating an idea. This is a well-known problem which is not well-discussed in determining the relationships. The analysis of indeterminate concepts is one of the difficult way for individualts to provide mathematical expressions. Therefore, neutrosophy is introduced by Smarandache as an extension / combination of the fuzzy logic by including the indeterminacy (Smarandache., 1999). While, fuzzy logic only measures the existence or non-existence membership grades, the neutrosophic sets can attribute the concepts when the relations between indeterminate concepts (Kandasamy & Smarandache, 2003).

The ISM and cognitive mapping have common relationship matrices and similar prodecures. For instance, the connection matrix transforms to reachability matrix in ISM, while it is called adjacency matrix in cognitive mapping. Or as another example, the indirect relationships are detected via transitivity rules in ISM, while the neutrosophic cognitive maps implements the hidden pattern determination rules. Therefore, the well-known neutrosophic cognitive mapping steps (Kandasamy & Smarandache, 2003) can be applied to transform the traditional ISM to propose the neutrosophic ISM. The neutrosophic cognitive mapping is a fundamental technique by providing a step-by-step guidance to deal with the indeterminate relationships of ISM.

Hence, this study aims to propose a neutrosophic ISM approach, and to implement it for the medical tourism services’ barriers during the COVID-19 Pandemic as an illustrative example. In order to that, text mining was conducted to the medical tourism related tweets written in English from January to December 2020 via RapidMiner software, and the barriers in medical tourism were identified. Next, the relationships between these barriers were examined via expert evaluations, and the proposed neutrosophic ISM was applied to construct a structural model by presenting how the barriers are related with a hierarchy between them. In addition, the relationships between the barriers of this study were evaluated by the owner of a Dental Hospital, an Eye Hospital partner, and an academician working on health tourism operations management. ISM studies are generally applied by referring to less than 6 industry experts and less than 3 academicians (Dwivedi et al., 2017). In addition, it is emphasized that at least 3 expert evaluations are sufficient for validation in studies using ISM (Yudatama et al., 2018).

In the following sections, the background section includes neutrosophic sets, hidden pattern determination procedure, medical tourism services network, and the related literature. Next, the steps of the proposed methodology are presented. Then, the barriers were identified via text mining, and these barriers were analyzed with neutrosophic Interpretative Structural Modeling. Findings, future research directions and conclusion are stated.