{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T10:43:49Z","timestamp":1784889829874,"version":"3.55.0"},"reference-count":45,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,12,10]],"date-time":"2019-12-10T00:00:00Z","timestamp":1575936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.<\/jats:p>","DOI":"10.3390\/sym11121498","type":"journal-article","created":{"date-parts":[[2019,12,10]],"date-time":"2019-12-10T10:52:41Z","timestamp":1575975161000},"page":"1498","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":59,"title":["Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators"],"prefix":"10.3390","volume":"11","author":[{"given":"Neha","family":"Waseem","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7217-7962","authenticated-orcid":false,"given":"Muhammad","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4533-9281","authenticated-orcid":false,"given":"Jos\u00e9 Carlos R.","family":"Alcantud","sequence":"additional","affiliation":[{"name":"BORDA Research Unit and IME, University of Salamanca, 37007 Salamanca, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,10]]},"reference":[{"key":"ref_1","first-page":"29","article-title":"Improving early OSV design robustness by applying \u2018Multivariate Big Data Analytics\u2019 on a ship\u2019s life cycle","volume":"10","author":"Abbasian","year":"2018","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_2","first-page":"49","article-title":"An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem","volume":"8","author":"Pourhassan","year":"2017","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_3","first-page":"116","article-title":"Classification methodology for spare parts management combining maintenance and logistics perspectives","volume":"5","author":"Teixeira","year":"2018","journal-title":"J. Manag. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inform. Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1109\/21.87068","article-title":"On ordered weighted averaging Aggregation operators in multi-criteria decision-making","volume":"18","author":"Yager","year":"1988","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","article-title":"Intuitionistic fuzzy Aggregation operators","volume":"15","author":"Xu","year":"2007","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/03081070600574353","article-title":"Some geometric Aggregation operators based on intuitionistic fuzzy sets","volume":"35","author":"Xu","year":"2006","journal-title":"Int. J. Gener. Syst."},{"key":"ref_9","unstructured":"Zhang, W.R. (1998, January 4\u20139). Bipolar fuzzy sets. Proceedings of the IEEE International Conference on Fuzzy Systems Proceedings, IEEE World Congress on Computational Intelligence, Anchorage, AK, USA."},{"key":"ref_10","unstructured":"Zhang, W.R. (1994, January 18\u201321). Bipolar fuzzy sets and relations. A computational framework for cognitive modeling and multiagent decision analysis. Proceedings of the First International Joint Conference of the North American Fuzzy Information Processing Society Biannual Conference, The Industrial Fuzzy Control and Intellige, San Antonio, TX, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1142\/S0218339009002958","article-title":"Bipolar linear algebra and YinYang-N-element cellular networks for equilibrium-based biosystem simulation and regulation","volume":"17","author":"Zhang","year":"2009","journal-title":"J. Biol. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1108\/CCSM-10-2015-0137","article-title":"Global implications of the indigenous epistemological system from the East: How to apply Yin-Yang balancing to paradox management","volume":"23","author":"Li","year":"2016","journal-title":"Cross Cult. Strateg. Manag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.3233\/JIFS-16612","article-title":"Hesitant bipolar fuzzy aggregation operators in multiple attribute decision making","volume":"33","author":"Wei","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_14","first-page":"155","article-title":"Dual hesitant bipolar fuzzy Aggregation operators in multiple attribute decision making","volume":"21","author":"Xu","year":"2017","journal-title":"Int. J. Knowl.-Based Intell. Eng. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1007\/s12652-018-0723-5","article-title":"Linguistic single-valued neutrosophic prioritized Aggregation operators and their applications to multiple-attribute group decision-making","volume":"9","author":"Garg","year":"2018","journal-title":"J. Ambient Intell. Hum. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"181","DOI":"10.5391\/IJFIS.2014.14.3.181","article-title":"Group decision making using intuitionistic hesitant fuzzy sets","volume":"14","author":"Beg","year":"2014","journal-title":"Int. J. Fuzzy Log. Intell. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"137","DOI":"10.5391\/IJFIS.2017.17.3.137","article-title":"On separability of fuzzy relations","volume":"17","author":"Grzegorzewski","year":"2017","journal-title":"Int. J. Fuzzy Log. Intell. Syst."},{"key":"ref_18","unstructured":"Alcantud, J.C.R., Khameneh, A.Z., and Kilicman, A. Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Inform. Sci., in press."},{"key":"ref_19","first-page":"276","article-title":"Uber Logische Verknunpfungenn Unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione","volume":"Volume 3","author":"Trappl","year":"1978","journal-title":"Progress in Cybernatics and Systems Research"},{"key":"ref_20","unstructured":"Beliakov, G., Pradera, A., and Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners, Springer."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/TFUZZ.2013.2248736","article-title":"Some Hamacher Aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making","volume":"22","author":"Liu","year":"2013","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40815-017-0338-6","article-title":"Bipolar fuzzy Hamacher Aggregation operators in multiple attribute decision making","volume":"20","author":"Wei","year":"2018","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"11508","DOI":"10.1109\/ACCESS.2017.2784963","article-title":"Dual hesitant bipolar fuzzy Hamacher prioritized Aggregation operators in multiple attribute decision making","volume":"6","author":"Gao","year":"2017","journal-title":"IEEE Access"},{"key":"ref_24","first-page":"416530","article-title":"m-polar fuzzy sets: An extension of bipolar fuzzy sets","volume":"2014","author":"Chen","year":"2014","journal-title":"Sci. World J."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Akram, M., and Adeel, A. (2019). Novel TOPSIS Method for Group Decision Making Based on Hesitant m-Polar Fuzzy Model. J. Intell. Fuzzy Syst.","DOI":"10.3233\/JIFS-190551"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ali, G., Akram, M., and Alcantud, J.C.R. (2019). Attributes reductions of bipolar fuzzy relation decision systems. Neural Comput. Appl.","DOI":"10.1007\/s00521-019-04536-8"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"9955","DOI":"10.1007\/s00500-018-3552-8","article-title":"Novel decision-making method based on bipolar neutrosophic information","volume":"23","author":"Zhan","year":"2019","journal-title":"Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Akram, M., Ilyas, F., and Garg, H. (2019). Multi-criteria group decision-making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput., 1\u201329.","DOI":"10.1007\/s00500-019-04105-0"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1007\/s40815-019-00608-y","article-title":"Novel approach in decision-making with m-polar fuzzy ELECTRE-I","volume":"21","author":"Akram","year":"2019","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Akram, M. (2019). Springer m-polar fuzzy graphs. Studies in Fuzziness and Soft Computing, Springer.","DOI":"10.1007\/978-3-030-03751-2"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3000","DOI":"10.1002\/int.22183","article-title":"Pythagorean Dombi fuzzy Aggregation operators with application in multicriteria decision-making","volume":"34","author":"Akram","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_32","first-page":"1","article-title":"Hesitant fuzzy linguistic arithmetic Aggregation operators in multiple attribute decision making","volume":"13","author":"Wei","year":"2016","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1002\/int.21911","article-title":"Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making","volume":"33","author":"Wei","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1002\/int.21985","article-title":"Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making","volume":"33","author":"Wei","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Khameneh, A.Z., and Kilicman, A. (2018). m-polar fuzzy soft weighted Aggregation operators and their applications in group decision-making. Symmetry, 10.","DOI":"10.3390\/sym10110636"},{"key":"ref_36","first-page":"173","article-title":"The ordered weighted geometric operator: Properties and application in MCDM problems","volume":"Volume 2","author":"Chiclana","year":"2002","journal-title":"Technologies for Constructing Intelligent Systems"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1080\/0952813X.2018.1467497","article-title":"Generalised Pythagorean fuzzy geometric interactive Aggregation operators using Einstein operations and their application to decision making","volume":"30","author":"Garg","year":"2018","journal-title":"J. Exp. Theor. Artif. Intell."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Jana, C., Pal, M., and Wang, J. (2019). Bipolar fuzzy Dombi prioritized Aggregation operators in multiple attribute decision making. Soft Comput.","DOI":"10.1007\/s00500-019-04130-z"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3233\/IFS-130973","article-title":"Approaches to decision making with interval-valued intuitionistic fuzzy information and their application to enterprise financial performance assessment","volume":"27","author":"Li","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1002\/int.21960","article-title":"Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading","volume":"33","author":"Liang","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.1002\/int.22155","article-title":"Some q-rung orthopair fuzzy Hamy mean operators in multiple attribute decision-making and their application to enterprise resource planning systems selection","volume":"34","author":"Wang","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"527","DOI":"10.3233\/IFS-131021","article-title":"Induced interval-valued intuitionistic fuzzy Hamacher ordered weighted geometric operator and their application to multiple attribute decision making","volume":"27","author":"Xiao","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/j.knosys.2011.01.011","article-title":"Approaches to multiple attribute group decision making based on intuitionistic fuzzy power Aggregation operators","volume":"24","author":"Xu","year":"2011","journal-title":"Knowl.-Based Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2689","DOI":"10.3233\/IFS-130939","article-title":"Hesitant fuzzy Hamacher Aggregation operators and their application to multiple attribute decision making","volume":"26","author":"Zhou","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Alcantud, J.C.R., Cruz, S., and Torrecillas, M.J.M. (2017). Valuation fuzzy soft sets: A flexible fuzzy soft set based decision making procedure for the valuation of assets. 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