Hamming code

Algorithm

Fuzzy classification

Division (mathematics)

Pure mathematics

Discrete mathematics

Defuzzification

Fuzzy set operations

Degree (music)

Computer science

Subtraction

Acoustics

Fuzzy set

Fuzzy number

Decoding methods

Physics

Hamming distance

Mathematics

Fuzzy logic

Type-2 fuzzy sets and systems

Artificial intelligence

Block code

Algebra over a field

Arithmetic

Information Sciences

Intuitionistic fuzzy values, each characterized by a membership degree and a nonmembership degree, are the basic components of intuitionistic fuzzy sets. Arithmetic operations on intuitionistic fuzzy values/sets are of importance in practical problem solving. In this paper, the subtraction and division operations over intuitionistic fuzzy values/sets are derived from the Hamming distance between them by the optimization method. Compared with the existing operations, the developed operations are complete, that is, any two intuitionistic fuzzy values/sets can be performed by these two operations. Then, fundamental properties of the modified arithmetic operations are extensively investigated for intuitionistic fuzzy values/sets. Finally, the continuity and the derivative operation of intuitionistic fuzzy functions are introduced based on the proposed operations, which provides a novel basis for the intuitionistic fuzzy differential calculus.

Subtraction and division operations on intuitionistic fuzzy sets derived from the Hamming distance