The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators
Open accessAbstract
In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with interval-valued Pythagorean fuzzy sets (IVPFSs). First, the concept, operational laws, score function, and accuracy function of IVPFSs are defined. Then, based on the operational laws, two interval-valued Pythagorean fuzzy aggregation operators are developed for aggregating the interval-valued Pythagorean fuzzy information, such as interval-valued Pythagorean fuzzy weighted average (IVPFWA) operator and interval-valued Pythagorean fuzzy weighted geometric (IVPFWG) operator. A series of inequalities of aggregation operators are studied. Later, we develop some interval-valued Pythagorean fuzzy point operators. Moreover, combining the interval-valued Pythagorean fuzzy point operators with IVPFWA operator, we present some interval-valued Pythagorean fuzzy point weighted averaging (IVPFPWA) operators, which can adjust the degree of the aggregated arguments with some parameters. Then, we propose an interval-valued Pythagorean fuzzy ELECTRE method to solve uncertainty MAGDM problem. Finally, an illustrative example for evaluating the software developments is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Zadeh, L. A. (1965) · Information and Control · doi:10.1016/s0019-9958(65)90241-x · Cited by 67,855
Atanassov, K. T. (1986) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(86)80034-3 · Cited by 16,465
Interval valued intuitionistic fuzzy sets
Atanassov, K., & Gargov, G. (1989) · Fuzzy Sets and Systems · doi:10.1016/0165-0114(89)90205-4 · Cited by 2,916
Pythagorean Membership Grades in Multicriteria Decision Making
Yager, R. R. (2014) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2013.2278989 · Cited by 2,847
Yager, R. R. (2013) · 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS) · doi:10.1109/ifsa-nafips.2013.6608375 · Cited by 2,703
Intuitionistic Fuzzy Aggregation Operators
Xu, Z. (2007) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2006.890678 · Cited by 2,678
Some geometric aggregation operators based on intuitionistic fuzzy sets
Xu, Z., & Yager, R. R. (2006) · International Journal of General Systems · doi:10.1080/03081070600574353 · Cited by 2,356
Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets
Zhang, X., & Xu, Z. (2014) · International Journal of Intelligent Systems · doi:10.1002/int.21676 · Cited by 1,506
Yager, R. R., & Abbasov, A. M. (2013) · International Journal of Intelligent Systems · doi:10.1002/int.21584 · Cited by 1,430
Classement et choix en présence de points de vue multiples
Roy, B. (1968) · Revue française d'informatique et de recherche opérationnelle · doi:10.1051/ro/196802v100571 · Cited by 944
Cited by
Senapati, T., & Yager, R. R. (2019) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2019.05.012 · Cited by 451
Optimization of PFMEA Team Composition in the Automotive Industry Using the IPF-RADAR Approach
Komatina, N., & Marinković, D. (2025) · Algorithms · doi:10.3390/a18060342 · Cited by 13
Aleksić, A., Tadić, D., Komatina, N., & Nestić, S. (2025) · Mathematics · doi:10.3390/math13132216 · Cited by 11
Metadata
- Authors
- Peng, X., & Yang, Y.
- Venue
- International Journal of Intelligent Systems
- Publisher
- Hindawi Limited
- Published
- 2015-10-19
- Volume
- 31
- Issue
- 5
- Pages
- 444-487
- ISSN
- 0884-8173 (ISSN-L)
- OpenAlex
- W1765570948
- Cited by
- 537
- References
- 24
- FWCI
- 26.19
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators. https://app.cochat.ai/papers/10.1002/int.21790
- The paper
- Peng, X., & Yang, Y. (2016). Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators. International Journal of Intelligent Systems. https://doi.org/10.1002/int.21790
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
