Decision-making approach based on Pythagorean Dombi fuzzy soft graphs

Granular Computing - Tập 6 - Trang 671-689 - 2020
Muhammad Akram1, Gulfam Shahzadi1
1Department of Mathematics, University of the Punjab, Lahore, Pakistan

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