Abstract
Fuzzy soft multiset (FSMS) is a substantial and important fuzzy generalization of soft set and multiset (also called bag). In this paper, we have presented the idea of weighted fuzzy soft multiset (WFSMS) as a generalization of FSMS and its basic properties are to be studied. Also, we introduce a new adjustable approach to WFSMS based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed WFSMS based decision-making procedure in practical application is read by a mathematical example.
Similar content being viewed by others
References
Alhazaymeh K, Hassan N (2014) Vague soft multiset theory. Int J Pure Appl Math 93:511–523
Ali MI, Feng F, Liu X, Minc WK, Shabir M (2009) On some new operations in soft set theory. Comp Math Appl 57:1547–1553
Alkhazaleh S (2012) Salleh AR (2012) Fuzzy soft multi sets theory. Abstr Appl Anal 350603:20 pages. doi:10.1155/2012/350603 (Hindawi Publishing Corporation)
Alkhazaleh S, Salleh AR, Hassan N (2011) Soft multisets theory. Appl Math Sci 5:3561–3573
Babitha KV, John SJ (2013) On soft multi sets. Ann Fuzzy Math Inform 5:35–44
Balami HM, Ibrahim AM (2013) Soft multiset and its application in information system. Int J Sci Res Manag 1:471–482
Blizard WD (1989) Multiset Theory. Notre Dame J Form Log 30:36–65
Broumi S (2015) Q-intuitionistic fuzzy soft sets. J New Theory 5:80–91
Das AK (2015) Fuzzy soft multi relation and its properties. Int J Comput Sci Theor App 4:47–53
Das AK (2016) On partially included intuitionistic fuzzy rough relations. Afrika Matematika 27:993–1001
Farhadinia B (2016) Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl-Based Syst 93:135–144
Feng F, Jun YB, Liu X, Li L (2010) An adjustable approach to fuzzy soft set based decision making. J Comp Appl Math 234:10–20
Girish KP, John SJ (2009) Relations and functions in multiset context. Inf Sci 179:758–768
Girish KP, John SJ (2012) Multiset topologies induced by multiset relations. Inf Sci 188:298–313
Jena SP, Ghosh SK, Tripathy BK (2001) On the theory of bags and lists. Inf Sci 132:241–254
Kong Z, Gao LQ, Wang LF (2009) Comment on a fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 223:540–542
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9:589–602
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562
Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083
Massanet S, Riera JV, Torrens J, Herrera-Viedma E (2014) A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf Sci 258:277–290
Miyamoto S (2001) Fuzzy multisets and their generalizations. Multiset Process LNCS 2235:225–235
Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31
Morente-Molinera JA, Pérez IJ, Ureña MR, Herrera-Viedma E (2015) Building and managing fuzzy ontologies with heterogeneous linguistic information. Knowl-Based Syst 88:154–164
Mukherjee A, Das AK (2015) Application of fuzzy soft multi sets in decision making problems. Smart Innovation Systems and Technologies, Springer Verlag, 43(1) 21–28
Mukherjee A, Das AK (2013) Topological structure formed by fuzzy soft multi sets. Rev Bull Cal Math Soc 21:193–212
Mukherjee A, Das AK (2014) Topological structure formed by soft multi sets and soft multi compact space. Ann Fuzzy Math Inform 7:919–933
Mukherjee A, Das AK (2015) Interval valued intuitionistic fuzzy soft multi set theoretic approach to decision making problems. In: Proceedings of the 2015 IEEE Int. Conf. on Comp. Comm. Cont., IEEE Xplore Digital Library, 1–5 (2015), doi: 10.1109/IC4.2015.7375640
Mukherjee A, Das AK (2015) Application of interval valued intuitionistic fuzzy soft set in investment decision making. In: Proceedings of the 2015 IEEE 5th Int. Conf. on Advances in Computing and Communications, 61–64, doi: 10.1109/ICACC.2015.37
Mukherjee A, Das AK (2015) Relations on intuitionistic fuzzy soft multi sets. Inf Sci Appl Lect Notes Electr Eng Springer 339:607–614
Pérez IJ, Cabrerizo FJ, Alonso S, Herrera-Viedma E (2014) A new consensus model for group decision making problems with non homogeneous experts. IEEE Trans Syst Man Cybern Syst 44(4):494–498
Rocacher D (2003) On fuzzy bags and their application to flexible querying. Fuzzy Sets Syst 140(1):93–110
Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203:412–418
Yager RR (1986) On the theory of bags. Int J Gen Syst 13:23–37
Yager RR, Alajlan N (2016) Some issues on the OWA aggregation with importance weighted arguments. Knowl-Based Syst. doi:10.1016/j.knosys.2016.02.009
Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Das, A.K. Weighted fuzzy soft multiset and decision-making. Int. J. Mach. Learn. & Cyber. 9, 787–794 (2018). https://doi.org/10.1007/s13042-016-0607-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-016-0607-y
Keywords
- Decision-making
- Soft set
- Level soft set
- Fuzzy soft multiset
- Weighted fuzzy soft multi set
- Weighted fuzzy soft multiset part