{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:34:19Z","timestamp":1760236459879,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T00:00:00Z","timestamp":1638144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Science Foundation of China","award":["62162055"],"award-info":[{"award-number":["62162055"]}]},{"name":"the Science Foundation of Gansu province","award":["21JR7RA115"],"award-info":[{"award-number":["21JR7RA115"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Interval-valued fuzzy soft set theory is a powerful tool that can provide the uncertain data processing capacity in an imprecise environment. The two existing methods for decision making based on this model were proposed. However, when there are some extreme values or outliers on the datasets based on interval-valued fuzzy soft set for making decisions, the existing methods are not reasonable and efficient, which may ignore some excellent candidates. In order to solve this problem, we give a novel approach to decision making based on interval-valued fuzzy soft set by means of the contrast table. Here, the contrast table has symmetry between the objects. Our proposed algorithm makes decisions based on the number of superior parameter values rather than score values, which is a new perspective to make decisions. The comparison results of three methods on two real-life cases show that, the proposed algorithm has superiority to the existing algorithms for the feasibility and efficiency when we face up to the extreme values of the uncertain datasets. Our proposed algorithm can also examine some extreme or unbalanced values for decision making if we regard this method as supplement of the existing algorithms.<\/jats:p>","DOI":"10.3390\/sym13122274","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T03:12:40Z","timestamp":1638328360000},"page":"2274","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Novel Approach to Decision Making Based on Interval-Valued Fuzzy Soft Set"],"prefix":"10.3390","volume":"13","author":[{"given":"Hongwu","family":"Qin","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1569-460X","authenticated-orcid":false,"given":"Xiuqin","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.31181\/dmame2003070r","article-title":"Certain properties of soft multi-set topology with applications in multi-criteria decision making","volume":"3","author":"Riaz","year":"2020","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105","DOI":"10.31181\/rme2001020105t","article-title":"Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management","volume":"2","author":"Ali","year":"2021","journal-title":"Rep. Mech. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"104","DOI":"10.31181\/dmame2104104s","article-title":"Career selection of students using hybridized distance measure based on picture fuzzy set and rough set theory","volume":"4","author":"Sahu","year":"2021","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","article-title":"Soft set theory-First results","volume":"37","author":"Molodtsov","year":"1999","journal-title":"Comput. Math. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103248","DOI":"10.1016\/j.engappai.2019.103248","article-title":"Integrating the 2-tuple linguistic representation and soft set to solve supplier selection problems with incomplete information","volume":"87","author":"Wen","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.asoc.2016.08.052","article-title":"0\u20131 Linear programmingmethods for optimal normal and pseudo parameter reductions of soft sets","volume":"54","author":"Han","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4808","DOI":"10.1016\/j.apm.2015.03.055","article-title":"Normal parameter reduction in soft set based on particle swarm optimization algorithm","volume":"39","author":"Kong","year":"2015","journal-title":"Appl. Math. Model."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"35499","DOI":"10.1109\/ACCESS.2019.2905140","article-title":"Soft Set Based Parameter Value Reduction for Decision Making Application","volume":"7","author":"Ma","year":"2019","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.knosys.2016.08.020","article-title":"Soft set based association rule mining","volume":"111","author":"Feng","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113557","DOI":"10.1016\/j.eswa.2020.113557","article-title":"Maximal association analysis using logical formulas over soft sets","volume":"159","author":"Feng","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.asoc.2017.12.037","article-title":"Screening alternatives considering different evaluation index sets: A method based on soft set theory","volume":"64","author":"Li","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.future.2017.05.024","article-title":"Soft sets based symbiotic organisms search algorithm for resource discovery in cloud computing environment","volume":"76","author":"Ezugwu","year":"2017","journal-title":"Futur. Gener. Comput. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"115358","DOI":"10.1016\/j.eswa.2021.115358","article-title":"A new data filling approach based on probability analysis in incomplete soft sets","volume":"184","author":"Kong","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2478\/v10006-012-0060-3","article-title":"A Novel Data Filling Approach For An Incomplete Soft Set","volume":"22","author":"Qin","year":"2012","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_15","first-page":"589","article-title":"Fuzzy soft sets","volume":"9","author":"Maji","year":"2001","journal-title":"J. Fuzzy Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10530","DOI":"10.1109\/ACCESS.2018.2800017","article-title":"A Distance-Based Parameter Reduction Algorithm of Fuzzy Soft Sets","volume":"6","author":"Ma","year":"2018","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105889","DOI":"10.1016\/j.asoc.2019.105889","article-title":"Chest X-ray enhancement to interpret pneumonia malformation based on fuzzy soft set and Dempster\u2013Shafer theory of evidence","volume":"86","author":"Biswajit","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.asoc.2019.01.041","article-title":"A group medical diagnosis model based on intuitionistic fuzzy soft sets","volume":"77","author":"Hu","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/TFUZZ.2018.2860967","article-title":"Another View on Generalized Intuitionistic Fuzzy Soft Sets and Related Multiattribute Decision Making Methods","volume":"27","author":"Feng","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.eswa.2018.10.054","article-title":"Belief interval-valued soft set","volume":"119","author":"Vijayabalaji","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.camwa.2010.05.036","article-title":"Interval-valued intuitionistic fuzzy soft sets and their properties","volume":"60","author":"Jiang","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.eswa.2018.07.060","article-title":"Group decision-making methods based on hesitant N-soft sets","volume":"115","author":"Muhammad","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.cie.2018.11.005","article-title":"Confidence soft sets and applications in supplier selection","volume":"127","author":"Aggarwal","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.asoc.2016.06.009","article-title":"Fault-tolerant enhanced bijective soft set with applications","volume":"54","author":"Gong","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4948","DOI":"10.1016\/j.apm.2012.10.006","article-title":"A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets","volume":"37","author":"Zhang","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.asoc.2016.09.012","article-title":"A novel soft rough set: Soft rough hemirings and its multicriteria group decision making","volume":"54","author":"Zhan","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.asoc.2017.03.038","article-title":"On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods","volume":"56","author":"Zhan","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1007\/s00500-016-2119-9","article-title":"A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making","volume":"21","author":"Zhan","year":"2017","journal-title":"Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.camwa.2009.04.019","article-title":"Combination of interval-valued fuzzy set and soft set","volume":"58","author":"Yang","year":"2009","journal-title":"Comput. Math. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3561","DOI":"10.1109\/ACCESS.2018.2886215","article-title":"Data Analysis Approaches of Interval-Valued Fuzzy Soft Sets Under Incomplete Information","volume":"7","author":"Qin","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1109\/TFUZZ.2013.2246571","article-title":"The parameter reduction of the interval-valued fuzzy soft sets and its related algorithms","volume":"22","author":"Ma","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"35012","DOI":"10.1109\/ACCESS.2018.2846586","article-title":"A Complete Model for Evaluation System Based on Interval-Valued Fuzzy Soft Set","volume":"6","author":"Qin","year":"2018","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1016\/j.camwa.2010.07.006","article-title":"Application of level soft sets in decision making based on interval-valued fuzzy soft sets","volume":"60","author":"Feng","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.cie.2018.04.001","article-title":"Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure","volume":"119","author":"Peng","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.asoc.2016.06.036","article-title":"Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight","volume":"54","author":"Peng","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_36","first-page":"3226","article-title":"A new efficient decision making algorithm based on interval-valued fuzzy soft set","volume":"51","author":"Ma","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/S0898-1221(02)00216-X","article-title":"An application of soft sets in a decision making problem","volume":"44","author":"Maji","year":"2002","journal-title":"Comput. Math. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.inffus.2015.08.007","article-title":"A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set","volume":"29","author":"Alcantud","year":"2016","journal-title":"Inf. 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