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Some new product operations of T-spherical fuzzy graphs and an application of T-spherical fuzzy graphs in MCGDM

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Abstract

A T-spherical fuzzy (T-SF) graph (T-SFG) structure is a generalization of the spherical fuzzy graphs (SFGs) and other extensions of the fuzzy graphs (FGs). In this paper, we define the strong product, cross product, lexicographic product, modular product, and homomorphic product operations between two T-SFGs and investigate some of their properties. We give examples to make the defined operations more understandable. We also propose a multi-criteria group decision-making (MCGDM) method under the T-SF-environment. Besides, a numerical example is given to show the progress of the proposed method.

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References

  • Akram M (2021) Decision making method based on spherical fuzzy graphs. In: Kahraman C, Kutlu Gündoğdu F (eds) Decision making with spherical fuzzy sets. Studies in fuzziness and soft computing, vol 392. Springer, Cham

    Google Scholar 

  • Akram M, Saleem D (2020) Spherical fuzzy graphs with application to decision-making. Math Comput Appl 25(8):1–32

    MathSciNet  Google Scholar 

  • Akram M, Sitara M (2022) Decision-making with q-rung orthopair fuzzy graph structures. Granul Comput 7:505–526

    Article  Google Scholar 

  • Akram M, Ilyas F, Borumand SA (2019) Certain notions of pythagorean fuzzy Graphs. J Intell Fuzzy Syst 36:5857–5874

    Article  Google Scholar 

  • Ali Z, Mahmood T, Yang MS (2020) Complex T-spherical fuzzy aggregation operators with application to multi-attribute decision making. Symmetry 12:1311

    Article  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K, Gabriella P, Yager R, Atanassova V (2003) Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making, pp 177–182

  • Borzooei RA, Rashmanlou H (2015) Ring sum in product intuitionistic fuzzy graphs. J Adv Res Pure Math 7(1):16–31

    Article  MathSciNet  Google Scholar 

  • Borzooei R, Rashmanlou H (2015) Degree of vertices in vague graphs. J Appl Math Inform 33:545–557

    Article  MathSciNet  MATH  Google Scholar 

  • Chellamani P, Ajay D, Broumi S et al (2022) An approach to decision-making via picture fuzzy soft graphs. Granul Comput 7:527–548

    Article  Google Scholar 

  • Cuong BC (2013) Picture fuzzy sets first results. Part 1, in Preprint of Seminar on neuro-fuzzy systems with applications. Institute of Mathematics, Hanoi

  • Garg H, Munir M, Ullah K, Mahmood T, Jan N (2018) Algorithm for T-spherical fuzzy multi-attribute decision making based on improved interactive aggregation operators. Symmetry 10(12):1–23

    Article  Google Scholar 

  • Garg H, Ullah K, Mahmood T et al (2021) T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making. J Ambient Intell Human Comput 12:9067–9080

    Article  Google Scholar 

  • Guleria A, Bajaj RK (2020) T-spherical fuzzy graphs: operations and applications in various selection processes. Arab J Sci Eng 45:2177–2193

    Article  Google Scholar 

  • Guleria A, Bajaj R (2021) T-spherical fuzzy soft sets and its aggregation operators with application in decision-making. Scientia Iran 28(2):1014–1029

    Google Scholar 

  • Gündoğdu FK, Kahraman C (2018) Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell Fuzzy Syst 36:1–16

    Google Scholar 

  • Habib A, Akram M, Farooq A (2019) q-Rung orthopair fuzzy competition graphs with application in the soil ecosystem. Mathematics 7:91

    Article  Google Scholar 

  • Kaufmann A (1973) Introduction a la Theorie des Sour-Ensembles Flous. Paris, France, Masson et Cie

  • Koam AN, Akram M, Liu P (2020) Decision-making analysis based on fuzzy graph structures. Math Probl Eng 2020:30

    Article  MathSciNet  MATH  Google Scholar 

  • Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7(1):48–50

    Article  MathSciNet  MATH  Google Scholar 

  • Mahmood T, Ullah K, Khan Q, Jan N (2019) An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 31(11):7041–7053

    Article  Google Scholar 

  • Mordeson JN, Peng CS (1994) Operations on fuzzy graphs. Inf Sci 79:159–170

    Article  MathSciNet  MATH  Google Scholar 

  • Naz S, Ashraf S, Akram M (2018) A novel approach to decisionmaking with Pythagorean fuzzy information. Mathematics 6(6):1–28

    Article  MATH  Google Scholar 

  • Özlü Ş, Karaaslan F (2022) Correlation coefficient of T-spherical type-2 hesitant fuzzy sets and their applications in clustering analysis. J Ambient Intell Hum Comput 13:329–357

    Article  Google Scholar 

  • Parvathi R, Karunambigai MG (2006) Intuitionistic fuzzy graphs. In: Reusch B (ed) Computational intelligence, theory and applications. Springer, Berlin, pp 139–150

    Chapter  Google Scholar 

  • Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36(6):1389–1401

    Article  Google Scholar 

  • Rashmanlou H, Pal M (2013) Some properties of highly irregular interval valued fuzzy Graphs. World Appl Sci J 27:1756–1773

    Google Scholar 

  • Rashmanlou H, Muhiuddin G, Amanathulla SK, Mofidnakhaei F, Pal M (2020) A study on cubic graphs with novel application. J Intell Fuzzy Syst 40:1–13

    Google Scholar 

  • Rosenfeld A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M (eds) Fuzzy sets and their applications. Academic Press, New York, pp 77–95

    Google Scholar 

  • Shoaib M, Mahmood W, Xin Q, Tchier F (2021) Certain operations on picture fuzzy graph with application. Symmetry 13:2400

    Article  Google Scholar 

  • Thilagavathi S, Parvathi R, Karunambigai MG (2009) Operations on intuitionistic fuzzy graphs. Int J Comput Appl 51:1396–1401

    Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp 57-61

  • Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Article  Google Scholar 

  • Yin S, Li H, Yang Y (2019) Product operations on q-rung orthopair fuzzy graphs. Symmetry 11:588

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zedam L, Jan N, Rak E et al (2020) An approach towards decision-making and shortest path problems based on T-spherical fuzzy information. Int J Fuzzy Syst 22:1521–1534

    Article  Google Scholar 

  • Zeng S, Shoaib M, Ali S, Smarandache F, Rashmanlou H, Mofidnakhaei F (2021) Certain properties of single-valued neutrosophic graph with application in food and agriculture organization. Int J Comput Intell Syst 14(1):1516

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Çankırı Karatekin University, 18100, Çankırı, Turkey

    Faruk Karaaslan & Fatih Karamaz

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  1. Faruk Karaaslan
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  2. Fatih Karamaz
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Correspondence to Fatih Karamaz.

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Karaaslan, F., Karamaz, F. Some new product operations of T-spherical fuzzy graphs and an application of T-spherical fuzzy graphs in MCGDM. Artif Intell Rev 56, 13663–13689 (2023). https://doi.org/10.1007/s10462-023-10477-5

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