Decision-making approach based on Pythagorean Dombi fuzzy soft graphs
Tóm tắt
A Pythagorean fuzzy set model is more useful than intuitionistic fuzzy set model to handle the imprecise information involving both membership and nonmembership degrees, and a soft set is an other parameterized point of view for handling the vagueness. A Pythagorean fuzzy soft graph is considered more capable than intuitionistic fuzzy soft graph for representing the parametric relationships between objects, and the Dombi operators with operational parameters have creditable extensibility. Based on these two notions, we propose the concept of Pythagorean Dombi fuzzy soft graph (PDFSG). We describe certain concepts of graph theory under Pythagorean Dombi fuzzy soft environment. Further, we define the degree sequence and degree set in PDFSG, and the concept of edge regular PDFSG with consequential properties. Moreover, we illustrate the examples in decision making including selection of suitable ETL software for a business intelligence project and evaluation of electronics companies. Finally, we present the comparison analysis of our proposed model to show the superiority than existing model.
Tài liệu tham khảo
Akram M, Ali G (2019) Group decision making approach under multi \((Q, N)\)-soft multi granulation rough model. Granul Comput. https://doi.org/10.1007/s41066-019-00190-6
Akram M, Ali G (2020) Hybrid models for decision making based on rough Pythagorean fuzzy bipolar soft information. Granul Comput 5(1):1–15
Akram M, Dudek WA, Dar JM (2019) Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision making. Int J Intell Syst 34(11):3000–3019
Akram M, Dar JM, Naz S (2020) Pythagorean Dombi fuzzy graphs. Complex Intell Syst 6:29–54
Akram M, Davvaz B (2012) Strong intuitionistic fuzzy graphs. Filomat 26(1):177–196
Akram M, Nawaz S (2016) Fuzzy soft graphs with applications. J Intell Fuzzy Syst 30(6):3619–3632
Ali MI (2011) A note on soft sets, rough soft sets and fuzzy soft sets. Appl Soft Comput 11(4):3329–3332
Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553
Ashraf S, Naz S, Kerre EE (2018) Dombi fuzzy graphs. Fuzzy Inf Eng 10(1):58–79
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Bai SM, Chen SM (2008a) Automatically constructing grade membership functions of fuzzy rules for students evaluation. Expert Syst Appl 35(3):1408–1414
Bai SM, Chen SM (2008b) Automatically constructing concept maps based on fuzzy rules for adapting learning systems. Expert Syst Appl 35(1–2):41–49
Chen SM (1996) A fuzzy reasoning approach for rule-based systems based on fuzzy logics. IEEE Trans Syst Man Cybern B (Cybern) 26(5):769–778
Chen SM, Cheng SH (2016) Fuzzy multi-attribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators. Inf Sci 352:133–149
Chen SM, Cheng SH, Lan TC (2016a) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40
Chen SM, Cheng SH, Lan TC (2016b) Multi-criteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values. Inf Sci 367:279–295
Chen SM, Manalu GMT, Pan JS, Liu HC (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43(3):1102–1117
Chen J, Ye J (2017) Some single-valued neutrosophic Dombi weighted aggregation operators for multiple attribute decision making. Symmetry 9(6):82
Dombi J (1982) A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst 8(2):149–163
Dubois D, Ostasiewicz W, Prade H (2000) Fuzzy sets: history and basic notions. Handbook of fuzzy sets and possibility theory. Springer, New York, pp 121–124
Feng F, Li C, Davvaz B, Ali MI (2011a) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911
Feng F, Liu X, Fotea VL, Jun YB (2011b) Soft sets and soft rough sets. Inf Sci 181(6):1125–1137
Hamacher H (1978) On logical aggregations of non-binar explicit decision criteria. Rita G. Fischer Verlag, Frankfurt
Jana C, Pal M, Wang JQ (2019) Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision making process. J Ambient Intell Human Comput 10(9):3533–3549
Klement EP, Mesiar R, Pap E (2013) Triangular norms, vol 8. Springer Science and Business Media, Berlin
Kuwagaki A (1952) On the rational functional equation of function unknown of two variables. Mem Coll Sci 28(2)
Liu P, Liu J, Chen SM (2018) Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J Oper Res Soc 69(1):1–24
Liu P, Chen SM, Liu J (2017) Multiple-attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators. Inf Sci 411:98–121
Liu X, Wang L (2020) An extension approach of TOPSIS method with OWAD operator for multiple criteria decision making. Granul Comput 5(1):135–148
Maji PK, Biswas R, Roy AR (2001a) Fuzzy soft sets. J Fuzzy Math 9(3):589–602
Maji PK, Biswas R, Roy AR (2001b) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692
Menger K (1942) Statistical metrics. Proc Natl Acad Sci U S A 28(12):535–537
Mishra AR, Chandel A, Motwani D (2020) Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets. Granul Comput 5(1):97–117
Molodtsov DA (1999) Soft set theory-first results. Comput Math Appl 37:19–31
Naz S, Ashraf S, Akram M (2018) A novel approach to decision making with Pythagorean fuzzy information. Mathematics 6:1–28
Parvathi R, Karunambigai MG (2006) Intuitionistic fuzzy graphs. Computational intelligence, theory and applications. Springer, Berlin, pp 139–150
Peng X, Yang Y, Song J, Jiang Y (2015) Pythagorean fuzzy soft set and its application. Comput Eng 41(7):224–229
Rosenfeld A (1975) Fuzzy graphs, fuzzy sets and their applications. Academic Press, New York, pp 77–95
Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):461–472
Schweizer B, Sklar S (1983) Probabilistic metric spaces. Probab Appl Math
Shahzadi S, Akram M (2017) Intuitionistic fuzzy soft graphs with applications. J Appl Math Comput 55(12):369–392
Shi L, Ye J (2018) Dombi Aggregation operators of neutrosophic cubic sets for multiple attribute decision making. Algorithms. https://doi.org/10.3390/a11030029
Som T (2006) On the theory of soft sets, soft relations and fuzzy soft relation. In: Proceedings of the national conference on uncertainty: a mathematical approach, UAMA-06, Burdwan, pp 1–9
Thumbakara RK, George B (2014) Soft graphs. Gen Math Notes 21(2):75–86
Yager RR (2013) Pythagorean fuzzy subsets. In: 2013 Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS). IEEE, pp 57–61
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078