Abstract
Similarity measure plays an important role in fuzzy environment. Motivating from usual Euclidean distance measure, it introduces a new distance-similarity approach to get a solution of a fuzzy sets and fuzzy soft sets based maximization decision-making problems. Also, three algorithms have been proposed connected to fuzzy sets and fuzzy soft sets. Then using these algorithms, different types of decision-making problems can be solved. To check the efficiency of our approach, we consider an example and solve it by different existing methods, and the results are compared.
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Balopoulos V, Hatzimichailidis AG, Papadopoulos BK (2007) Distance and similarity measures for fuzzy operators. Inf Sci 177:2336–2348. https://doi.org/10.1016/j.ins.2007.01.005
Basu TM, Mahapatra NK, Mondal SK (2012) A balanced solution of medical science. Appl Soft Comput 12:3260–3275
Basu TM, Mahapatra NK, Mondal SK (2014) Intuitionistic fuzzy soft matrix and its application in decision making problems. Ann Fuzzy Math Inform 7:109–131
Basu TM, Mondal SK (2015) A new solution approach using intuitionistic fuzzy cognitive map to solve intuitionistic fuzzy multi-criteria ranking problems in medical science. J Fuzzy Math 23:431–442
Basu TM, Mondal SK (2017) Multi-criteria assignment techniques in multi-dimensional neutrosophic soft set theory. Neutrosophic Sets Syst 15:49–59
Bosteels K, Kerre EE (2007) A triparametric family of cardinality-based fuzzy similarity measures. Fuzzy Sets Syst 158:2466–2479. https://doi.org/10.1016/j.fss.2007.05.006
Bouchon-Meunier B, Coletti G, Lesot MJ, Rifqi M (2010) Towards a conscious choice of a fuzzy similarity measure: a qualitative point of view. In: Hullermeier E, Kruse R, Hoffmann F (eds) Computational intelligence for knowledge-based systems design IPMU 2010, vol 6178. Lecture notes in computer science. Springer, Berlin, pp 1–10. https://doi.org/10.1007/978-3-642-14049-51
Chen SM (1995) Measures of Similarity between vague sets. Fuzzy Sets Syst 74:217–223. https://doi.org/10.1016/0165-0114(94)00339-9
Couso I, Garrido L, Sanchez L (2013) Similarity and dissimilarity measures between fuzzy sets: a formal relational study. Inf Sci 229:122–141. https://doi.org/10.1016/j.ins.2012.11.012
Deng T, Wang X (2013) An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets. Appl Math Model 37:4139–4146. https://doi.org/10.1016/j.apm.2012.09.010
Fan J, Xie W (1999) Some notes on similarity measure and proximity measure. Fuzzy Sets Syst 101:403–412. https://doi.org/10.1016/S0165-0114(97)00108-5
Feng F, Jun YB, Liu X, Li L (2009) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math. https://doi.org/10.1016/j.com.2009.11.055
Feng F, Jun YB, Liu X, Li L (2010) An adjustable approach to fuzzy sets based decision making. J Comput Appl Math 234:10–20. https://doi.org/10.1016/j.cam.2009.11.055
Kehagis A, Konstantinidou M (2003) L-fuzzy valued inclusion measure, L-fuzzy similarity and L-fuzzy distance. Fuzzy Sets Syst 136:313–332. https://doi.org/10.1016/S0165-0114(02)00407-4
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9:589–602
Manna S, Mahapatra NK, Mondal SK (2017) Some properties of fuzzy soft groups. Ann Fuzzy Math Inform 13:47–61
Manna S, Basu TM, Mondal SK (2018) Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making. Granul comput. https://doi.org/10.1007/s41066-018-0119-0
Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31. https://doi.org/10.1016/S0898-1221(99)00056-5
Pappis CP, Karacapilidis NI (1993) A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Syst 56:171–174. https://doi.org/10.1016/0165-0114(93)90141-4
Patra K, Mondal SK (2012) Risk analysis in diabetes prediction based on a new approach of ranking of generalized trapezoidal numbers. Cybern Syst Int J 43:623–650. https://doi.org/10.1080/01969722.2012.707572
Patra K, Mondal SK (2015a) Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application. Appl Soft Comput 28:276–284. https://doi.org/10.1016/j.asoc.2014.11.042
Patra K, Mondal SK (2015b) Risk analysis in a production inventory model with fuzzy demand, variable production rate and production time dependent selling price. Opsearch 52:505–529. https://doi.org/10.1007/s12597-014-0189-y
Patra K, Mondal SK (2016) A supplier selection model with fuzzy risk analysis using the balanced solution technique with a soft set. Pac Sci Rev A Nat Sci Eng 18:162–168. https://doi.org/10.1016/j.psra.2016.09.004
Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. Comput Appl Math 203:412–418
Wang X, De Baets B, Kerre E (1995) A comparative study of similarity measures. Fuzzy Sets Syst 73:259–268. https://doi.org/10.1016/0165-0114(94)00308-T
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356. https://doi.org/10.1016/S0019-9958(65)90241-X
Zimmermann HJ (1991) Fuzzy set theory and its applications. Kluwer Academic Publishers, Dordrecht
Zwick R, Carlstein E, Budescu DV (1987) Measures of similarity among fuzzy concepts: a comparative analysis. Int J Approx Reason 1:221–242. https://doi.org/10.1016/0888-613X(87)90015-6
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Paik, B., Mondal, S.K. A distance-similarity method to solve fuzzy sets and fuzzy soft sets based decision-making problems. Soft Comput 24, 5217–5229 (2020). https://doi.org/10.1007/s00500-019-04273-z
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DOI: https://doi.org/10.1007/s00500-019-04273-z