Research Article
BibTex RIS Cite

Year 2025, Volume: 15 Issue: 9, 2313 - 2330, 01.09.2025

Abstract

References

  • Reference1 Akram, M., Adeel, A., (2023), Aggregation operators for decision making with multi-polar fuzzy sets, in: Multiple criteria decision making methods with multi-polar fuzzy information, Studies in Fuzziness and Soft Comput., 403.
  • Reference2 Akram, M., Noreen, U., Al-Shamiri, M. M. A., (2022), Decision analysis approach based on 2-tuple linguistic m-polar fuzzy hamacher aggregation operators. Discre. Dynam. in Nature and Socie., 6269115. K. R. MAITY, M. PAL: M-POLAR FUZZY SET WITH DOMBI POWER AGGREGATION. . . 2329
  • Reference3 Akram, M., Noreen, U., Al-Shamiri, M. M. A., Pamucar, D., (2022), Integrated decision-making meth- ods based on 2-tuple linguistic m-polar fuzzy information, AIMS Maths., 7(8), pp. 14557–14594.
  • Reference4 Akram, M., Yaqoob, N., Ali, G. and Chammam, W., (2020), Extensions of Dombi aggregation operators for decision-making under m-polar fuzzy information, J. of Maths., 4739567.
  • Reference5 Akram, M., Adeel, A., Alcantud, J. C. R., (2019), Multi-criteria group decision-making using an m- polar hesitant fuzzy TOPSIS approach, Symmetry, 11(6), 795.
  • Reference6 Akram, M., Waseem, N. and Liu, P., (2019), Novel Approach in Decision Making with m–Polar Fuzzy ELECTRE-I, Int. J. Fuzzy Syst., https://doi.org/10.1007/s40815-019-00608-y.
  • Reference7 Atanassov, K., (1986), Intuitionistic fuzzy sets, Fuzzy Sets and syst., 20, pp. 87-96.
  • Reference8 Beliakov, G., James, S., Mordelova, J., Ruckschlossova, T. and Yager, R. R., (2010), Generalised Bonferroni mean operators in multi-criteria aggregation, Fuzzy Set. and Syst., 161, pp. 2227-2242.
  • Reference9 Chen, J., Li, S., Ma, S., Wang, X., (2014), m-polar fuzzy sets: an extension of bipolar fuzzy sets, Scientific World J., 416530.
  • Reference10 Deschrijver, G., Cornelis, C., Kerre, E. E., (2004), On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEETrans Fuzzy Syst, 12, pp. 45–61.
  • Reference11 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 and Systems, 8, pp. 149-163.
  • Reference12 Garg, H., (2017), Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t- norm and t-conorm for multicriteria decision-making process, Inter. J. of Intelli. Syst., 33(6), pp. 1197-1233.
  • Reference13 He, X., (2018), Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators, Nat Hazards, 90(3), pp. 1153–1175.
  • Reference14 Jana, C. and Hezam, I. M., (2024), Multi-attribute group decision making method for sponge iron factory location selection problem using multi-polar fuzzy EDAS approach, Heliyon, https://doi.org/10.1016/j.heliyon.2024.e27712.
  • Reference15 Jana, C., Garg, H., Pal, M., (2023), Multi-attribute decision-making for power Dombi operators under Pythagorean fuzzy information with MABAC method, J. of Ambient Intelli. and Humani. Comput., 14(8), pp. 10761-10778.
  • Reference16 Jana, C., Dobrodolac, M., Simic, V., Pal, M., Sarkar, B. and Stevic, Z., (2023), Evaluation of sustain- able strategies for urban parcel delivery: linguistic q-rung orthopair fuzzy Choquet integral approach, Eng. Appl. Artif. Intell., 126, 106811.
  • Reference17 Jana, C., Pal, M., (2021), Multi-criteria decision making process based on some single-valued neutro- sophic Dombi power aggregation operators, Soft Comput., 25(7), pp. 5055–5072.
  • Reference18 Jana, C., Muhiuddin, G., Pal, M., (2021), Multi-criteria decision-making approach based on SVTrN Dombi aggregation functions, Artifi. Intelli. Review, 54(5), pp. 3685-3723.
  • Reference19 Jana, C., Pal, M., (2021), Some m-polar fuzzy operators and their application in multiple-attribute decision-making process, S¯adhan¯a, 46(2), pp. 1–15.
  • Reference20 Jana, C., Pal, M., (2021), Multi-criteria decision making process based on some single-valued neutro- sophic Dombi power aggregation operators, Soft Comput., 25(7), pp. 5055-5072.
  • Reference21 Jana, C., Muhiuddin, G., Pal, M., (2020), Multiple-attribute decision-making problems based on SVTNH methods, J. of Ambi. Intelli. and Humani. Comput., 11(9), pp. 3717-3733.
  • Reference22 Jana, C., Senapati, T., Yager, R. R., (2019), Picture fuzzy Dombi aggregation operators: application to MADM process, Applied Soft Comput. J., 74(1), pp. 99-109.
  • Reference23 Liu, P. D., (2017), Multiple attribute group decision making method based on interval-valued intu- itionistic fuzzy power Heronian aggregation operators, Comput Ind Eng, 108, pp. 199–212.
  • Reference24 Mandal, P., Samanta, S., Pal, M., and Ranadive, A. S., (2023), Regret theory based three-way con- flict analysis model under q-rung orthopair fuzzy information: studies with parameter and three-way decision-making-based approaches, Artifi. Intelli. Review, 56, pp. 3417-3469.
  • Reference25 Ruan, C., Chen, X., Zeng, S., Ali, S., Almutairi, B., (2024), Fermatean fuzzy power Bonferroni aggregation operators and their applications to multi-attribute decision-making, Soft computing, 28, pp. 191-203.
  • Reference26 Sarkar, A., Biswas, A., (2019), Multicriteria decision-making using Archimedean aggregation operators in Pythagorean hesitant fuzzy environment, Inter. J. of Intelli. Syst., 34(7), pp. 1361-1386.
  • Reference27 Taherdoost, H., Madanchian, M., (2023), Multi-criteria decision making(MCDM) methods and con- cepts, Encyclopedia, 3, pp. 77-87.
  • Reference28 Wang, L., Li, N., (2020), Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 35(1), pp. 150–183.
  • Reference29 Waseem, N., Akram, M., Alcantud, J. C. R., (2019), Multi-Attribute decision-making based on m- polar fuzzy Hamachar aggregation operators, Symmetry, 11, 1498.
  • Reference30 Wei, G., Lu, M., (2018), Pythagorean fuzzy power aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 33(1), pp. 169–186.
  • Reference31 Xia, M. M., Xu, Z. S., Zhu, B., (2012), Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and tnorm, Knowl. Based. Syst., 31(1), pp. 78–88.
  • Reference32 Xiao, S., (2014), Induced interval-valued intuitionistic fuzzy Hamachar ordered weighted geometric operator and their application to multiple attribute decision making, J. of Intelli. Fuzzy Syst., 27, pp. 527-534.
  • Reference33 Xing, Y., Zhang, R., Wang, J., Zhu, X., (2018), Some new Pythagorean fuzzy Choquet-Frank aggre- gation operators for multi-attribute decision-making, Inter. J. of Intelli. Syst., 33(11), pp. 1-27.
  • Reference34 Xu, Y., Merigo, J. M., Wang, H., (2012), Linguistic power aggregation operators and their application to multiple attribute group decision making, Appl. Math. Model, 36, pp. 5427–5444.
  • Reference35 Xu, Z. S., Yager, R. R., (2010), Power-Geometric operators and their use in group decision making, IEEE Trans. Fuzzy Syst., 18(1), pp. 94–105.
  • Reference36 Yager, R. R., (1998), On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cybern., 18(1), pp. 183–190.
  • Reference37 Yager, R. R., (2001), The power average operator, IEEE Trans. Syst. Man Cybern. Part A, 31, pp. 724–731.
  • Reference38 Zadeh, L. A., (1965), Fuzzy sets, Information Control, 8, pp. 338-353.

A NOVEL APPROACH ON m-POLAR FUZZY SET WITH DOMBI POWER AGGREGATION OPERATORS TO SOLVE MULTI-ATTRIBUTE DECISION-MAKING PROBLEMS

Year 2025, Volume: 15 Issue: 9, 2313 - 2330, 01.09.2025

Abstract

This article introduces new aggregation operators by combining Dombi and power operators, resulting in m-polar fuzzy Dombi power averaging and geometric operators, with several key properties analyzed. A novel approach is then developed using these combined operators to assist in selecting the best company for stock market investments. Unlike existing research, which primarily utilizes homogeneous sub-characteristics for each attribute in the mPF environment, this study emphasizes the use of heterogeneous sub-characteristic collections in our application to address complex, uncertain decision making challenges. Finally, the proposed approach is compared to various established operators and the MABAC method, with an analysis of its advantages and limitations.

References

  • Reference1 Akram, M., Adeel, A., (2023), Aggregation operators for decision making with multi-polar fuzzy sets, in: Multiple criteria decision making methods with multi-polar fuzzy information, Studies in Fuzziness and Soft Comput., 403.
  • Reference2 Akram, M., Noreen, U., Al-Shamiri, M. M. A., (2022), Decision analysis approach based on 2-tuple linguistic m-polar fuzzy hamacher aggregation operators. Discre. Dynam. in Nature and Socie., 6269115. K. R. MAITY, M. PAL: M-POLAR FUZZY SET WITH DOMBI POWER AGGREGATION. . . 2329
  • Reference3 Akram, M., Noreen, U., Al-Shamiri, M. M. A., Pamucar, D., (2022), Integrated decision-making meth- ods based on 2-tuple linguistic m-polar fuzzy information, AIMS Maths., 7(8), pp. 14557–14594.
  • Reference4 Akram, M., Yaqoob, N., Ali, G. and Chammam, W., (2020), Extensions of Dombi aggregation operators for decision-making under m-polar fuzzy information, J. of Maths., 4739567.
  • Reference5 Akram, M., Adeel, A., Alcantud, J. C. R., (2019), Multi-criteria group decision-making using an m- polar hesitant fuzzy TOPSIS approach, Symmetry, 11(6), 795.
  • Reference6 Akram, M., Waseem, N. and Liu, P., (2019), Novel Approach in Decision Making with m–Polar Fuzzy ELECTRE-I, Int. J. Fuzzy Syst., https://doi.org/10.1007/s40815-019-00608-y.
  • Reference7 Atanassov, K., (1986), Intuitionistic fuzzy sets, Fuzzy Sets and syst., 20, pp. 87-96.
  • Reference8 Beliakov, G., James, S., Mordelova, J., Ruckschlossova, T. and Yager, R. R., (2010), Generalised Bonferroni mean operators in multi-criteria aggregation, Fuzzy Set. and Syst., 161, pp. 2227-2242.
  • Reference9 Chen, J., Li, S., Ma, S., Wang, X., (2014), m-polar fuzzy sets: an extension of bipolar fuzzy sets, Scientific World J., 416530.
  • Reference10 Deschrijver, G., Cornelis, C., Kerre, E. E., (2004), On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEETrans Fuzzy Syst, 12, pp. 45–61.
  • Reference11 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 and Systems, 8, pp. 149-163.
  • Reference12 Garg, H., (2017), Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t- norm and t-conorm for multicriteria decision-making process, Inter. J. of Intelli. Syst., 33(6), pp. 1197-1233.
  • Reference13 He, X., (2018), Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators, Nat Hazards, 90(3), pp. 1153–1175.
  • Reference14 Jana, C. and Hezam, I. M., (2024), Multi-attribute group decision making method for sponge iron factory location selection problem using multi-polar fuzzy EDAS approach, Heliyon, https://doi.org/10.1016/j.heliyon.2024.e27712.
  • Reference15 Jana, C., Garg, H., Pal, M., (2023), Multi-attribute decision-making for power Dombi operators under Pythagorean fuzzy information with MABAC method, J. of Ambient Intelli. and Humani. Comput., 14(8), pp. 10761-10778.
  • Reference16 Jana, C., Dobrodolac, M., Simic, V., Pal, M., Sarkar, B. and Stevic, Z., (2023), Evaluation of sustain- able strategies for urban parcel delivery: linguistic q-rung orthopair fuzzy Choquet integral approach, Eng. Appl. Artif. Intell., 126, 106811.
  • Reference17 Jana, C., Pal, M., (2021), Multi-criteria decision making process based on some single-valued neutro- sophic Dombi power aggregation operators, Soft Comput., 25(7), pp. 5055–5072.
  • Reference18 Jana, C., Muhiuddin, G., Pal, M., (2021), Multi-criteria decision-making approach based on SVTrN Dombi aggregation functions, Artifi. Intelli. Review, 54(5), pp. 3685-3723.
  • Reference19 Jana, C., Pal, M., (2021), Some m-polar fuzzy operators and their application in multiple-attribute decision-making process, S¯adhan¯a, 46(2), pp. 1–15.
  • Reference20 Jana, C., Pal, M., (2021), Multi-criteria decision making process based on some single-valued neutro- sophic Dombi power aggregation operators, Soft Comput., 25(7), pp. 5055-5072.
  • Reference21 Jana, C., Muhiuddin, G., Pal, M., (2020), Multiple-attribute decision-making problems based on SVTNH methods, J. of Ambi. Intelli. and Humani. Comput., 11(9), pp. 3717-3733.
  • Reference22 Jana, C., Senapati, T., Yager, R. R., (2019), Picture fuzzy Dombi aggregation operators: application to MADM process, Applied Soft Comput. J., 74(1), pp. 99-109.
  • Reference23 Liu, P. D., (2017), Multiple attribute group decision making method based on interval-valued intu- itionistic fuzzy power Heronian aggregation operators, Comput Ind Eng, 108, pp. 199–212.
  • Reference24 Mandal, P., Samanta, S., Pal, M., and Ranadive, A. S., (2023), Regret theory based three-way con- flict analysis model under q-rung orthopair fuzzy information: studies with parameter and three-way decision-making-based approaches, Artifi. Intelli. Review, 56, pp. 3417-3469.
  • Reference25 Ruan, C., Chen, X., Zeng, S., Ali, S., Almutairi, B., (2024), Fermatean fuzzy power Bonferroni aggregation operators and their applications to multi-attribute decision-making, Soft computing, 28, pp. 191-203.
  • Reference26 Sarkar, A., Biswas, A., (2019), Multicriteria decision-making using Archimedean aggregation operators in Pythagorean hesitant fuzzy environment, Inter. J. of Intelli. Syst., 34(7), pp. 1361-1386.
  • Reference27 Taherdoost, H., Madanchian, M., (2023), Multi-criteria decision making(MCDM) methods and con- cepts, Encyclopedia, 3, pp. 77-87.
  • Reference28 Wang, L., Li, N., (2020), Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 35(1), pp. 150–183.
  • Reference29 Waseem, N., Akram, M., Alcantud, J. C. R., (2019), Multi-Attribute decision-making based on m- polar fuzzy Hamachar aggregation operators, Symmetry, 11, 1498.
  • Reference30 Wei, G., Lu, M., (2018), Pythagorean fuzzy power aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 33(1), pp. 169–186.
  • Reference31 Xia, M. M., Xu, Z. S., Zhu, B., (2012), Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and tnorm, Knowl. Based. Syst., 31(1), pp. 78–88.
  • Reference32 Xiao, S., (2014), Induced interval-valued intuitionistic fuzzy Hamachar ordered weighted geometric operator and their application to multiple attribute decision making, J. of Intelli. Fuzzy Syst., 27, pp. 527-534.
  • Reference33 Xing, Y., Zhang, R., Wang, J., Zhu, X., (2018), Some new Pythagorean fuzzy Choquet-Frank aggre- gation operators for multi-attribute decision-making, Inter. J. of Intelli. Syst., 33(11), pp. 1-27.
  • Reference34 Xu, Y., Merigo, J. M., Wang, H., (2012), Linguistic power aggregation operators and their application to multiple attribute group decision making, Appl. Math. Model, 36, pp. 5427–5444.
  • Reference35 Xu, Z. S., Yager, R. R., (2010), Power-Geometric operators and their use in group decision making, IEEE Trans. Fuzzy Syst., 18(1), pp. 94–105.
  • Reference36 Yager, R. R., (1998), On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cybern., 18(1), pp. 183–190.
  • Reference37 Yager, R. R., (2001), The power average operator, IEEE Trans. Syst. Man Cybern. Part A, 31, pp. 724–731.
  • Reference38 Zadeh, L. A., (1965), Fuzzy sets, Information Control, 8, pp. 338-353.
There are 38 citations in total.

Details

Primary Language English
Subjects Operations Research İn Mathematics
Journal Section Research Articles
Authors

Krishna Rani Maity This is me

Madhumangal Pal

Publication Date September 1, 2025
Submission Date August 5, 2024
Acceptance Date December 2, 2024
Published in Issue Year 2025 Volume: 15 Issue: 9

Cite