Evidence Theory in Picture Fuzzy Set Environment

Abstract

Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the low conflict. Keeping the advantages of these, in the present paper, we present the concept of the evidence theory for the picture fuzzy set environment using DST. Under this, we define the concept of interval probability distribution and discuss its properties. Finally, an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.

Generalized Heronian Mean Operators Based on Archimedean T‐Norms of the Complex Picture Fuzzy Information and Their Application to Decision‐Making

“…By using the TN and TCN in the shape of equations ( 9) and (10), then equations (19) to (22) are changed to equations (2) to (5), which invented the algebraic operational laws. Additionally, if we chose the TN and TCN in the shape of equations ( 11) and (12), then equations (19) to (22) are changed to equations (23) to (26), which invented the Einstein operational laws.…”

“…For the value of 􏽣 δ SC � 1, equations ( 27) to ( 30) are changed to equations (2) to ( 5) and if we choose the value of 􏽣 δ SC � 2, equations ( 27) to (30) are changed to equations (23) to (26). When we chose the TN and TCN in the shape of equations ( 13) and ( 14), then equations (19) to (22) are changed to equations ( 31) to (34), which invented the Frank operational laws.…”

“…For this, the principle of picture FS (PFS) was initiated by Cuong [15,16] which covers the TG M, abstinence grade (AG) A and FG N with a well-known principle of 0 ≤ M + A + N ≤ 1. IFS and FS are the specifc cases of the PFS, and several persons have employed them in the region of distinct areas such as geometric aggregation operators [17], aggregation operators [18], Dombi aggregation operators [19], weighted aggregation operators [20], Hamacher aggregation operators [21], evidence theory [22], picture fuzzy soft set [23], analytical hierarchy processes [24], and distance measures [25].…”

A Type-2 Fuzzy Logic Approach for Forecasting of Effluent Quality Parameters of Wastewater Treatment

“…ese vulnerabilities can be presented by utilizing of T2FSs. e likelihood of a T2-fuzzy system can be calculated as a stipend of the likelihood of a Type 1 system [26,27]. A T1FS's enrollment grade is a new number in the range [0, 1].…”

Retracted: Evidence Theory in Picture Fuzzy Set Environment

“…Tis article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. Tis investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”