Complex T-Spherical Fuzzy Frank Aggregation Operators With Application in the Assessment of Soil Fertility

Abstract

Complex T-spherical fuzzy set (CTSF) is the extended form of complex spherical fuzzy set (CSFs). CTSF can extract the maximum information from real-life phenomena with the help of a membership degree (MD), abstinence degree (AD), and non-membership degree (NMD). Due to this nature, CTSF can describe every human opinion’s phenomenon with less uncertainty. The major contribution of this article is to develop an interesting approach to aggregate the information in the form of the CTSFS. To do this, first, we develop the operational laws for CTSF values (CTSFVs) based on Frank’s operational laws. Then two types of aggregation operators (AOs), CTSF Frank weighted averaging (CTSFWA) and CTSF Frank weighted geometric (CTSFFWG) operators are introduced based on the Frank t-norm (FTNM). Further, some basic properties of the CTSFFWA and CTSFFWG operators are studied. The developed approach is also applied to the real-life problem of multi-attribute decision-making (MADM) where the soil fertility is assessed based on some factors affecting the soil fertility. The sensitivity of the developed approach is observed with the variation of the involved parameter graphically. The comparison of the developed approach is also studied and as well as graphed.

Keywords

• Fuzzy set
• complex T-spherical fuzzy set
• aggregation operators
• multi-attribute decision-making problems