In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.

In the present paper, a new accuracy function is provided to overcome the limitations of the existing score/accuracy functions for interval-valued Pythagorean Fuzzy Sets (PFSs). The proposed accuracy function is validated and discussed in detail through illustrative examples. Furthermore, a new distance measure for interval-valued Pythagorean fuzzy numbers is proposed and used in terms of the existing weighted averaging operators. Finally, with regard to the proposed accuracy function, distance measure, and weighted averaging operators, a numerical example of Multi-Criteria Decision Making (MCDM) process is presented to validate the methodology.