Abstract
Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decision-making processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relative-closeness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.
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Arora R, Garg H (2017) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Scientia Iranica p inpress
Arora R, Garg H (2017) A robust intuitionistic fuzzy soft aggregation operators and its application to decision making process. Scientia Iranica p inpress
Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349
Atanassov K, Pasi G, Yager RR (2005) Intuitionistic fuzzy interpretations of multi criteria multi person and multi-measurement tool decision making. Int J Syst Sci 36(14):859–868
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Bustince H, Burillo P (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 74:237–244
Cagman N, Deli I (2013) Similarity measures of intuitionistic fuzzy soft sets and their decision making. arXiv:1301.0456
Chen TY (2015) The inclusion-based TOPSIS method with interval -valued intuitionistic fuzzy sets for multiple criteria group decision making. Appl Soft Comput 26:57–73
Garg H (2016) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999. https://doi.org/10.1016/j.asoc.2015.10.040
Garg H (2016) A new generalized pythagorean fuzzy information aggregation using einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920
Garg H (2017) Confidence levels based pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory:1–26. https://doi.org/10.1007/s10588-017-9242-8
Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174
Garg H, Agarwal N, Tripathi A (2016) Fuzzy number intuitionistic fuzzy soft sets and its properties. J Fuzzy Set Valued Anal 2016(3):196–213. https://doi.org/10.5899/2016/jfsva-00332
Garg H, Arora R (2017) Distance and similarity measures for dual hesistant fuzzy soft sets and their applications in multi criteria decision-making problem. Int. J. Uncertain. Quantif. in press. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2017019801
Garg H, Arora R (2017) Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Intell 1–13. doi:https://doi.org/10.1007/s10489-017-0981-5
Guh YY, Hon CC, Lee ES (2001) Fuzzy weighted average: The linear programming approach via charnes and cooper’s rule. Fuzzy Sets Syst 117(1):157–160
Hwang CL, Yoon K (1981) Multiple attribute decision making methods and applications a state-of-the-art survey. Springer, Berlin
Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval - valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60(3):906–918
Jiang Y, Tang Y, Liu H, Chen Z (2013) Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Inf Sci 240:95–114
Khalid A, Abbas M (2015) Distance measures and operations in intuitionistic and interval-valued intuitionistic fuzzy soft set theory. Int J Fuzzy Syst 17(3):490–497
Kumar K, Garg H (2016) TOPSIS Method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math:1–11. https://doi.org/10.1007/s40314-016-0402-0
Li DF (2010) TOPSIS- Based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18:299–311
Li DF (2011) Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Appl Soft Comput 11(4):3402–3418
Li DF, Wan SP (2013) Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information. Appl Soft Comput 13(11):4333–4348
Liu Y, Qin K (2015) Entropy on interval-valued intuitionistic fuzzy soft set, pp 1360–1365
Maji PK, Biswas R, Roy A (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4-5):555–562
Molodtsov D (1999) Soft set theory - first results. Comput Math Appl 27(4-5):19–31
Mukherjee A, Sarkar S (2014) Similarity measures for interval-valued intuitionistic fuzzy soft sets and its application in medical diagnosis problem. New Trends Math Sci 2(3):159–165
Muthukumar P, Krishnan GSS (2016) A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis. Appl Soft Comput 41:148–156
Park DG, Kwun YC, Park JH, Park IY (2009) Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multi attribute group decision making problems. Math Comput Model 50:1279–1293
Park JH, Lim KM, Park JS, Kwun YC (2008) Distances between interval-valued intuitionistic fuzzy sets. In: Journal of physics: Conference series, vol 96. IOP Publishing, p 012089
Park JH, Park IY, Kwun YC, Tan X (2011) Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy sets. Appl Math Model 35(5):2544– 2556
Peng X, Yang Y (2017) Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Appl Soft Comput 54:415–430
Rajarajeswari P, Dhanalakshmi P (2014) Similarity measures of intuitionistic fuzzy soft sets and its application in medical diagnosis. Int J Math Arch 5(5):143–149
Sarala N, Suganya B (2016) An application of similarity measure of intuitionistic fuzzy soft set based on distance in medical diagnosis. Int J Sci Res 5(3):559–563
Shanthi SA, Thillaigovindan N, Naidu JV (2016) Application of interval valued intuitionistic fuzzy soft sets of root type in decision making. ICTACT J Soft Comput 6(3):1224–1230
Shui XZ, Li DQ (2003) A possibility based method for priorities of interval judgment matrix. Chinese J Manag Sci 11(1):63–65
Singh P (2012) A new method on measure of similarity between interval-valued intuitionistic fuzzy sets for pattern recognition. J Appl Comput Math 1(1):101
Wang LL, Li DF, Zhang SS (2013) Mathematical programming methodology for multiattribute decision making using interval-valued intuitionistic fuzzy sets. J Intell Fuzzy Syst 24(4):755–763
Wang Z, Li KW, Wang W (2009) An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf Sci 179:3026–3040
Wei G, Wang X (2007) Some geometric aggregation operators based on interval - valued intuitionistic fuzzy sets and their application to group decision making. In: Proceedings of the IEEE international conference on computational intelligence and security, pp 495–499
Xu ZS, Jian C (2007) Approach to group decision making based on interval-valued intuitionistic judgment matrices. Syst Eng Theory Pract 27(4):126–133
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zhang H, Yu L (2012) MADM Method based on cross-entropy and extended TOPSIS with interval-valued intuitionistic fuzzy sets. Knowl-Based Syst 30:115–120
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The author would like to thank the Editor-in-Chief and referees for providing very helpful comments and suggestions.
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Garg, H., Arora, R. A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information. Appl Intell 48, 2031–2046 (2018). https://doi.org/10.1007/s10489-017-1035-8
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DOI: https://doi.org/10.1007/s10489-017-1035-8