An Application of Neutrosophic Set to Relative Importance Assignment in AHP

Napat Harnpornchai and Wiriyaporn Wonggattaleekam
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Napat Harnpornchai: Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 50200, Thailand
Wiriyaporn Wonggattaleekam: Department of Agricultural Economy and Development, Faculty of Agriculture, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2021, vol. 9, issue 20, 1-14

Abstract: The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market.

Keywords: fuzzy and neutrosophic AHP; neutrosophic set; relative importance assignment; discrete single valued neutrosophic number (DSVNN); deneutrosophication; similarity measure; comparison matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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