×

zbMATH — the first resource for mathematics

\(N\)-soft sets and their decision making algorithms. (English) Zbl 1398.03176
Summary: In this paper, we motivate and introduce the concept of \(N\)-soft set as an extended soft set model. Some useful algebraic definitions and properties are given. We cite real examples that prove that \(N\)-soft sets are a cogent model for binary and non-binary evaluations in numerous kinds of decision making problems. Finally, we propose decision making procedures for \(N\)-soft sets.

MSC:
03E72 Theory of fuzzy sets, etc.
91B06 Decision theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abbas SE, Ibedou I (2016) Fuzzy soft uniform spaces. Soft Comput (in press) · Zbl 1384.54003
[2] Akram, M; Nawaz, S, Operations on soft graphs, Fuzzy Inf Eng, 7, 423-449, (2015) · Zbl 1329.05248
[3] Akram M, Shahzadi S (2016) Novel intuitionistic fuzzy soft multiple-attribute decision-making methods. Neural Comput Appl (in press) · Zbl 1366.05086
[4] Alcantud JCR (2015) Fuzzy soft set based decision making: a novel alternative approach. In: IFSA-EUSFLAT conference 2015, Atlantic Press, pp 106-111
[5] Alcantud JCR (2016a) Fuzzy soft set decision making algorithms: some clarifications and reinterpretations. In: et al OL (ed) Advances in artificial intelligence. 17th Conference of the Spanish association for artificial intelligence, CAEPIA 2016, Springer-Verlag, pp 479-488
[6] Alcantud, JCR, A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set, Inf Fus, 29, 142-148, (2016)
[7] Alcantud, JCR, Some formal relationships among soft sets, fuzzy sets, and their extensions, Int J Approx Reason, 68, 45-53, (2016) · Zbl 1346.03046
[8] Alcantud, JCR; Laruelle, A, Dis and approval voting: a characterization, Soc Choice Welf, 43, 1-10, (2014) · Zbl 1302.91073
[9] Alcantud JCR, Santos-García G (2016) Incomplete soft sets: new solutions for decision making problems. Springer, Cham, pp 9-17
[10] Alcantud JCR, Santos-García G (2017) A new criterion for soft set based decision making problems under incomplete information. Int J Comput Intell Syst 10:394-404
[11] Alcantud, JCR; Andrés, Calle R; Cascón, JM, On measures of cohesiveness under dichotomous opinions: some characterizations of approval consensus measures, Inf Sci, 240, 45-55, (2013) · Zbl 1406.91098
[12] Alcantud JCR, Santos-García G, Hernández-Galilea E (2015) Glaucoma diagnosis: a soft set based decision making procedure. Springer, Cham, pp 49-60
[13] Aleskerov, F; Chistyakov, VV; Kalyagin, V, The threshold aggregation, Econ Lett, 107, 261-262, (2010) · Zbl 1203.91068
[14] Ali, MI; Feng, F; Liu, X; Min, WK; Shabir, M, On some new operations in soft set theory, Comput Math Appl, 57, 1547-1553, (2009) · Zbl 1186.03068
[15] Ali MI, Mahmood T, Rehman MMU, Aslam MF (2015) On lattice ordered soft sets. Appl Soft Comput 36:499-505
[16] Alkhazaleh, S; Salleh, AR; Hassan, N, Soft multisets theory, Appl Math Sci, 5, 3561-3573, (2011) · Zbl 1257.03081
[17] Babitha KV, John SJ (2013) Hesitant fuzzy soft sets. J New Results Sci 3:98-107
[18] Bakanic, V; McPhail, C; Simon, RJ, The manuscript review and decision-making process, Am Sociol Rev, 52, 631-642, (1987)
[19] Basu, K; Deb, R; Pattanaik, PK, Soft sets: an ordinal formulation of vagueness with some applications to the theory of choice, Fuzzy Sets Syst, 45, 45-58, (1992) · Zbl 0749.90006
[20] Brunelli, M; Fedrizzi, M; Fedrizzi, M, Fuzzy m-ary adjacency relations in social network analysis: optimization and consensus evaluation, Inf Fus, 17, 36-45, (2014)
[21] Çetkin, V; Aygün, H, On l-soft merotopies, Soft Comput, 20, 4779-4790, (2016) · Zbl 1379.54006
[22] Chen, S; Liu, J; Wang, H; Augusto, JC, Ordering based decision making a survey, Inf Fus, 14, 521-531, (2013)
[23] Deli, I; Broumi, S, Neutrosophic soft matrices and nsm-decision making, J Intell Fuzzy Syst, 28, 2233-2241, (2015) · Zbl 1321.03063
[24] Deli, I; Çağman, N, Intuitionistic fuzzy parameterized soft set theory and its decision making, Appl Soft Comput, 28, 109-113, (2015)
[25] Deli I, Eraslan S, Çağman N (2016) ivnpiv-neutrosophic soft sets and their decision making based on similarity measure. Neural Comput Appl (in press)
[26] Deng, T; Wang, X, An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets, Appl Math Model, 37, 4139-4146, (2013)
[27] Dokow, E; Holzman, R, Aggregation of non-binary evaluations, Adv Appl Math, 45, 487-504, (2010) · Zbl 1195.91033
[28] Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2017a) Probabilistic soft sets and dual probabilistic soft sets in decision-making. Neural Comput Appl (in press)
[29] Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2017b) A social choice approach to graded soft sets. 2017 IEEE Int Conf Fuzzy Syst (FUZZ-IEEE). doi:10.1109/FUZZIEEE.2017.8015428
[30] Feng, F; Jun, YB; Liu, X; Li, L, An adjustable approach to fuzzy soft set based decision making, J Comput Appl Math, 234, 10-20, (2010) · Zbl 1274.03082
[31] Feng, F; Liu, X; Leoreanu-Fotea, V; Jun, YB, Soft sets and soft rough sets, Inf Sci, 181, 1125-1137, (2011) · Zbl 1211.68436
[32] Hakim RBF, Saari EN, Herawan T (2014a) On if-then multi soft sets-based decision making. In: et al L (ed) Information and communication technology, Springer Berlin Heidelberg, Berlin, No. 8407 in Lecture Notes in Computer Science, pp 306-315
[33] Hakim RBF, Saari EN, Herawan T (2014b) Soft solution of soft set theory for recommendation in decision making. In: et al TH (ed) Recent advances on soft computing and data mining, Springer International Publishing, Switzerland, No. 287 in Advances in Intelligent Systems and Computing, pp 313-324 · Zbl 1298.90048
[34] Han, BH; Li, YM; Liu, J; Geng, SL; Li, HY, Elicitation criterions for restricted intersection of two incomplete soft sets, Knowl-Based Syst, 59, 121-131, (2014)
[35] Handaga B, Deris MM (2012) Text categorization based on fuzzy soft set theory. Springer, Berlin, pp 340-352
[36] Herawan T, Deris MM (2009) On multi-soft sets construction in information systems. Springer, Berlin, pp 101-110 · Zbl 1226.68111
[37] Jiang, Y; Tang, Y; Chen, Q; Liu, H; Tang, J, Interval-valued intuitionistic fuzzy soft sets and their properties, Comput Math Appl, 60, 906-918, (2010) · Zbl 1201.03047
[38] Jiang, Y; Tang, Y; Chen, Q; Wang, J; Tang, S, Extending soft sets with description logics, Comput Math Appl, 59, 2087-2096, (2010) · Zbl 1189.68140
[39] Kong, Z; Zhang, G; Wang, L; Wu, Z; Qi, S; Wang, H, An efficient decision making approach in incomplete soft set, Appl Math Model, 38, 2141-2150, (2014) · Zbl 1427.91089
[40] Li, Z; Wen, G; Xie, N, An approach to fuzzy soft sets in decision making based on greyrelational analysis and Dempster Shafer theory of evidence: an application in medical diagnosis, Artif Intell Med, 64, 161-171, (2015)
[41] Li, Z; Xie, N; Gao, N, Rough approximations based on soft binary relations and knowledge bases, Soft Comput, 21, 839-852, (2017) · Zbl 1381.68289
[42] Liu, Y; Qin, K; Rao, C; Mahamadu, MA, Object parameter approaches to predicting unknown data in an incomplete fuzzy soft set, Int J Appl Math Comput Sci, 27, 157-167, (2017) · Zbl 1368.68297
[43] Ma, X; Liu, Q; Zhan, J, A survey of decision making methods based on certain hybrid soft set models, Artif Intell Rev, 47, 507-530, (2017)
[44] Maji, PK; Biswas, R; Roy, AR, No article title, Fuzzy soft sets. J Fuzzy Math, 9, 589-602, (2001)
[45] Maji, PK; Biswas, R; Roy, AR, Intuitionistic fuzzy soft sets, J Fuzzy Math, 9, 677-692, (2001) · Zbl 1004.03042
[46] Maji, PK; Roy, AR; Biswas, R, An application of soft sets in a decision making problem, Comput Math Appl, 44, 1077-1083, (2002) · Zbl 1044.90042
[47] Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555-562 · Zbl 1032.03525
[48] Molodtsov, D, Soft set theory-first results, Comput Math Appl, 37, 19-31, (1999) · Zbl 0936.03049
[49] Muthukumar, P; Krishnan, GSS, A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis, Appl Soft Comput, 41, 148-156, (2016)
[50] Pawlak Z (1994) Hard and soft sets. Springer, London, pp 130-135 · Zbl 0819.04008
[51] Peng, X; Yang, Y, Approaches to interval-valued intuitionistic hesitant fuzzy soft sets based decision making, Ann Fuzzy Math Inform, 10, 657-680, (2015) · Zbl 1334.68222
[52] Peng, X; Yang, Y, Interval-valued hesitant fuzzy soft sets and their application in decision making, Fundam Inform, 141, 71-93, (2015) · Zbl 1342.68316
[53] Peng, X; Liu, C, Algorithms for neutrosophic soft decision making based on edas, new similarity measure and level soft set, J Intell Fuzzy Syst, 32, 955-968, (2017) · Zbl 1366.91058
[54] Qin, H; Ma, X; Herawan, T; Zain, JM; Nguyen, NT (ed.); Kim, CG (ed.); Janiak, A (ed.), Data filling approach of soft sets under incomplete information, No. 6592, 302-311, (2011), Berlin
[55] Sezgın, A; Atagün, AO, On operations of soft sets, Comput Math Appl, 61, 1457-1467, (2011) · Zbl 1217.03040
[56] Sun, B; Ma, W; Li, X, Linguistic value soft set-based approach to multiple criteria group decision-making, Appl Soft Comput, 58, 285-296, (2017)
[57] Sutoyo, E; Mungad, M; Hamid, S; Herawan, T, An efficient soft set-based approach for conflict analysis, PLoS ONE, 13, 1-31, (2016)
[58] Wang, C; Aj, Qu, The applications of vague soft sets and generalized vague soft sets, Acta Mathematicae Applicatae Sinica, English Series, 31, 977-990, (2015) · Zbl 1335.03057
[59] Wang, F; Li, X; Chen, X, Hesitant fuzzy soft set and its applications in multicriteria decision making, J Appl Math, (2014)
[60] Xiao, Z; Gong, K; Zou, Y, A combined forecasting approach based on fuzzy soft sets, J Comput Appl Math, 228, 326-333, (2009) · Zbl 1161.91472
[61] Xu, W; Ma, J; Wang, S; Hao, G, Vague soft sets and their properties, Comput Math Appl, 59, 787-794, (2010) · Zbl 1189.03063
[62] Yang, X; Lin, TY; Yang, J; Li, Y; Yu, D, Combination of interval-valued fuzzy set and soft set, Comput Math Appl, 58, 521-527, (2009) · Zbl 1189.03064
[63] Yang Y, Song J, Peng X, (2015) Comments on “An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets” [Appl. Math. Modell. 37, (2013) 4139-4146]. Appl Math Model 39(23):7746-7748
[64] Zhan, J; Zhu, K, Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets, J Intell Fuzzy Syst, 29, 1169-1176, (2015) · Zbl 1361.91037
[65] Zhan, J; Zhu, K, A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Comput, 21, 1923-1936, (2017) · Zbl 1386.03069
[66] Zhan J, Ali MI, Mehmood N (2017a) On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods. Appl Soft Comput 56:446-457
[67] Zhan, J; Liu, Q; Herawan, T, A novel soft rough set: soft rough hemirings and corresponding multicriteria group decision making, Appl Soft Comput, 54, 393-402, (2017)
[68] Zhan, J; Liu, Q; Zhu, W, Another approach to rough soft hemirings and corresponding decision making, Soft Comput, 21, 3769-3780, (2017) · Zbl 1381.16047
[69] Zhan J, Dudek WA, Neggers J (2017d) A new soft union set: characterizations of hemirings. Int J Mach Learn Cybern 8:525-535
[70] Zhang, X, On interval soft sets with applications, Int J Comput Intell Syst, 7, 186-196, (2014)
[71] Zhang, Z; Wang, C; Tian, D; Li, K, A novel approach to interval-valued intuitionistic fuzzy soft set based decision making, Appl Math Model, 38, 1255-1270, (2014) · Zbl 1427.91114
[72] Zhou W, Xu ZS (2017) Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Trans Fuzzy Syst PP(99):1-1
[73] Zhu, P; Wen, Q, Probabilistic soft sets, IEEE Int Conf Granul Comput, 51, 635-638, (2010)
[74] Zou, Y; Xiao, Z, Data analysis approaches of soft sets under incomplete information, Knowl-Based Syst, 21, 941-945, (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.