Membership function

Extension (predicate logic)

Discrete mathematics

Similarity (geometry)

Similarity measure

Set (abstract data type)

Data mining

Computer science

Counterexample

Fuzzy set

Fuzzy number

Pattern recognition (psychology)

Mathematics

Image (mathematics)

Axiom

Fuzzy logic

Artificial intelligence

Geometry

Measure (data warehouse)

Programming language

A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets ( SFS ) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries.

Distance and Similarity Measures for Spherical Fuzzy Sets and Their Applications in Selecting Mega Projects