Some aggregation operators of credibility trapezoidal fuzzy neutrosophic values and their decision-making application in the selection of slope design schemes

Abstract

Modern decision-making (DM) systems are becoming more and more complex and sophisticated in their demands for information expressions and credibility levels. In the existing literature, a trapezoidal fuzzy neutrosophic value (TFNV) that combines trapezoidal fuzzy numbers with neutrosophic values can be better depicted by truth, indeterminacy, and falsity membership functions. Unfortunately, TFNV implies its defect since it lacks a measure of credibility. To make TFNV more creditable, TFNV should be related to its credibility level. Regarding the motivation for combining TFNV with its credibility level, this paper first proposes the concept of a credibility TFNV (C-TFNV) as a new framework of TFNV associated with the measure of credibility. The advantage of its information expression is that C-TFNV has a more creditable ability to describe indeterminate and inconsistent knowledge and judgments of human beings by the mixed information of a TFNV and a related credibility level (an ordered pair of TFNVs). Next, we propose the operational laws of C-TFNVs and the score function of C-TFNV. Furthermore, we present a C-TFNV weighted arithmetic averaging (C-TFNVWAA) and a C-TFNV weighted geometric averaging (C-TFNVWGA) operators and their properties. Then, a multicriteria DM model based on the C-TFNVWAA and C-TFNVWGA operators and the score function is established in the case of C-TFNVs. Finally, an actual DM example of slope decision schemes is provided to show the applicability and efficiency of the established DM model in the case of C-TFNVs.