{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T09:25:20Z","timestamp":1769851520011,"version":"3.49.0"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:p> Interval-valued Pythagorean fuzzy set is one of the successful extensions of the interval-valued intuitionistic fuzzy set for handling the uncertainties in the data. Under this environment, in this paper, we introduce the notion of induced interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (I-IVPFEOWA) aggregation operator. Some of its desirable properties namely, idempotency, boundedness, commutatively, monotonicity have also been proved. The main advantage of using the proposed operator is that this operator gives a more complete view of the problem to the decision-makers. The method proposed in this paper provides more general, more accurate and precise results as compared to the existing methods. Therefore this method play a vital role in real world problems. Finally, we apply the proposed operator to deal with multi-attribute group decision- making problems under interval-valued Pythagorean fuzzy information. The approach has been illustrated with a numerical example from the field of the decision-making problems to show the validity, practicality and effectiveness of the new approach. <\/jats:p>","DOI":"10.1142\/s1793005718500217","type":"journal-article","created":{"date-parts":[[2018,5,9]],"date-time":"2018-05-09T02:34:04Z","timestamp":1525833244000},"page":"343-361","source":"Crossref","is-referenced-by-count":44,"title":["Approaches to Multi-Attribute Group Decision Making Based on Induced Interval-Valued Pythagorean Fuzzy Einstein Aggregation Operator"],"prefix":"10.1142","volume":"14","author":[{"given":"K.","family":"Rahman","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}]},{"given":"A.","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}]},{"given":"S.","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of 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