An Algorithm for Fuzzy Negations Based-Intuitionistic Fuzzy Copula Aggregation Operators in Multiple Attribute Decision Making

Abstract

In this paper, we develop a novel computation model of Intuitionistic Fuzzy Values with the usage of fuzzy negations and Archimedean copulas. This novel computation model’s structure is based on the extension of the existing operations of intuitionistic fuzzy values with some classes of fuzzy negations. Many properties of the proposed operations are investigated and proved. Additionally, in this paper we introduce the concepts of intuitionistic fuzzy Archimedean copula weighted arithmetic and geometric aggregation operators based on fuzzy negations, including a further analysis of their properties. Finally, using a case study from an already published paper we found that our method has many advantages.

Generator of Fuzzy Implications

“…In step 1, in Case 1-Isosceles trapezium, a large number of temperature (39) and humidity (21) values received membership degree values greater than 0.9 or equal to 1.…”

“…Giakoumakis and Papadopoulos [21] developed a novel computation model of Intuitionistic Fuzzy Values with the use of fuzzy negations and Archimedean copulas. This novel computation model's structure is based on the extension of the existing operations of intuitionistic fuzzy values with some classes of fuzzy negations.…”

Novel Construction of Copulas Based on ( α , β ) Transformation for Fuzzy Random Variables

“…On the other hand, the case in which these construction methods could possibly be defined in more than four subrectangles of the unit square may be examined. In addition, the extension of those methods for Intuitionistic fuzzy sets [16,18] and Pythagorean fuzzy sets [31] could be possibly achieved, in order to develop aggregation operators for multiple attribute decision making algorithms. ese topics are the basis for our future investigations.…”

“…e second is to present a new fuzzy copula construction between two fuzzy random variables, via the construction mentioned before. e investigation of fuzzy copulas is of great importance, as in many circumstances, researchers need to fuse or aggregate probabilistic and fuzzy information [16][17][18]. In the present paper, we aim to provide a novel construction method of copulas, in order to produce a construction procedure of fuzzy copulas that no attempt has been made since the concept of fuzzy copulas was recently developed.…”