Discrete mathematics

Fuzzy set operations

Applied mathematics

Computer science

Fuzzy set

Minkowski space

Geology

Paleontology

Fuzzy number

Type (biology)

Mathematics

Fuzzy logic

Artificial intelligence

Geometry

International Journal of Intelligent Systems

The generalized orthopair fuzzy set inherits the virtues of intuitionistic fuzzy set and Pythagorean fuzzy set in relaxing the restriction on the support for and support against. The very lax requirement provides decision makers great freedom in expressing their beliefs about membership grades, which makes generalized orthopair fuzzy sets having a wide scope of application in practice. In this paper, we present the Minkowski-type distance measures, including Hamming, Euclidean, and Chebyshev distances, for q-rung orthopair fuzzy sets. First, we introduce the Minkowski-type distances of q-rung orthopair membership grades, based on which we can rank orthopairs. Second, we propose several distances over q-rung orthopair fuzzy sets on a finite discrete universe and subsequently discuss their applications to multiattribute decision-making problems. Then we extend these results to a continuous universe, both bounded and unbounded cases are considered. Some illustrative examples are employed to substantiate the conceptual arguments.

Minkowski-type distance measures for generalized orthopair fuzzy sets