{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T11:46:27Z","timestamp":1770032787377,"version":"3.49.0"},"reference-count":32,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,8,11]]},"abstract":"<jats:p>In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan\u2019s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan\u2019s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.<\/jats:p>","DOI":"10.3233\/jifs-202717","type":"journal-article","created":{"date-parts":[[2021,7,7]],"date-time":"2021-07-07T05:24:57Z","timestamp":1625635497000},"page":"819-839","source":"Crossref","is-referenced-by-count":6,"title":["An algebraic approach to N-soft sets with application in decision-making using TOPSIS"],"prefix":"10.1177","volume":"41","author":[{"given":"Muhammad","family":"Shabir","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid i Azam University Islamabad"}]},{"given":"Rimsha","family":"Mushtaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid i Azam University Islamabad"}]},{"given":"Munazza","family":"Naz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Fatima Jinnah Women 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