Combinatorics

Computational intelligence

Fuzzy set operations

Defuzzification

Type-2 fuzzy sets and systems

Mathematics

Multiple-criteria decision analysis

Data mining

Mathematical optimization

Fuzzy classification

Rank (graph theory)

Artificial intelligence

Set (abstract data type)

Fuzzy number

Programming language

Computer science

Fuzzy set

Membership function

Fuzzy logic

Complex & Intelligent Systems

Orthopair fuzzy sets are fuzzy sets in which every element is represented by a pair of values in the unit interval, one of which refers to membership and the other refers to non-membership. The different types of orthopair fuzzy sets given in the literature are distinguished according to the proposed constrain for membership and non-membership grades. The aim of writing this manuscript is to familiarize a new class of orthopair fuzzy sets called “(2,1)-Fuzzy sets” which are good enough to control some real-life situations. We compare (2,1)-Fuzzy sets with IFSs and some of their celebrated extensions. Then, we put forward the fundamental set of operations for (2,1)-Fuzzy sets and investigate main properties. Also, we define score and accuracy functions which we apply to rank (2,1)-Fuzzy sets. Moreover, we reformulate aggregation operators to be used with (2,1)-Fuzzy sets. Finally, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making (MCDM) problems in the environment of (2,1)-Fuzzy sets. To show the effectiveness and usability of the proposed technique in MCDM problems, an illustrative example is provided.

(2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods