Abstract
Multi-attribute decision-making approach is a widely used algorithm that needs some aggregation tools and several such aggregation operators have been developed in past decades to serve the purpose. Hamacher aggregation operator is one such operator which is based on Hamacher t-norm and t-conorm. It is observed that the Hamacher aggregation operators of intuitionistic fuzzy set, Pythagorean fuzzy set and that of picture fuzzy set has some limitations in their applicability. To serve the purpose, in this paper, some Hamacher aggregation operators based on T-spherical fuzzy numbers are introduced. The concepts of T-spherical fuzzy Hamacher-weighted averaging and T-spherical fuzzy Hamacher-weighted geometric aggregation operators are proposed which described four aspects of human opinion including yes, no, abstinence and refusal with no limitations. Such type of aggregation operators efficiently describes the cases that left unsolved by the existing aggregation operators. The validity of the proposed aggregation operators is examined, and some basic properties are discussed. The proposed new Hamacher aggregation operators are used to analyze the performance of search and rescue robots using a multi-attribute decision-making approach as their performance in an emergency is eminent. The proposed Hamacher aggregation operators have two variable parameters, namely q and \(\gamma \) which affects the decision-making process and their sensitivity towards decision-making results is analyzed. A comparative analysis of the results obtained using proposed Hamacher aggregation operators in view of the variable parameters q and \(\gamma \) is established to discuss any advantages or disadvantages.
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Yager, R.R.: Pythagorean fuzzy subsets. In: IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013 Joint. IEEE. (2013) https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25(5), 1222–1230 (2017)
Cường, B.C.: Picture fuzzy sets. J. Comput. Sci. Cybern. 30(4), 409–420 (2014)
Mahmood, T., Ullah, K., Khan, Q., Jan, N.: An approach towards decision making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput. Appl. 31, 7041–7053 (2019)
Xu, Z.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)
Xu, Z., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)
Garg, H.: Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng. Appl. Artif. Intell. 60, 164–174 (2017)
Peng, X., Yang, Y.: Some results for Pythagorean fuzzy sets. Int. J. Intell. Syst. 30(5), 1133–1160 (2015)
Liu, P., Wang, P.: Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int. J. Intell. Syst. 33(2), 259–280 (2018)
Garg, H.: Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. Arab. J. Sci. Eng. 42(12), 5275–5290 (2017)
Wang, C., Zhou, X., Tu, H., Tao, S.: Some geometric aggregation operators based on picture fuzzy sets and their application in multiple attribute decision making. Italian J. Pure Appl. Math. 37, 477–492 (2017)
Wang, W., Liu, X.: Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int. J. Intell. Syst. 26(5), 1049–1075 (2011)
Zhao, X., Wei, G.: Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowl. Based Syst. 37, 472–479 (2013)
Garg, H.: Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int. J. Intell. Syst. 32(6), 597–630 (2017)
Garg, H.: A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int. J. Intell. Syst. 31(4), 886–920 (2016)
Kaur, G., Garg, H.: Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arab. J. Sci. Eng. 44(3), 2775–2794 (2019)
Liu, P., Khan, Q., Mahmood, T., Hassan, N.: T-spherical fuzzy power Muirhead mean operator based on novel operational laws and their application in multi-attribute group decision making. IEEE Access 7, 22613–22632 (2019)
Garg, H., Munir, M., Ullah, K., Mahmood, T., Jan, N.: Algorithm for T-spherical fuzzy multi-attribute decision making based on improved interactive aggregation operators. Symmetry 10(12), 670 (2018). https://doi.org/10.3390/sym10120670
Ullah, K., Mahmood, T., Jan, N.: Similarity measures for T-spherical fuzzy sets with applications in pattern recognition. Symmetry 10(6), 193 (2018). https://doi.org/10.3390/sym10060193
Quek, S.G., Selvachandran, G., Munir, M., Mahmood, T., Ullah, K., Son, L.H., Thong, P.H., Kumar, R., Priyadarshini, I.: Multi-attribute multi-perception decision-making based on generalized T-spherical fuzzy weighted aggregation operators on neutrosophic sets. Mathematics 7(4), 780 (2019). https://doi.org/10.3390/math7090780
Ullah, K., Garg, H., Mahmood, T., Jan, N., Ali, Z.: Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making. Soft Comput 24(3), 1647–1659 (2020). https://doi.org/10.1007/s00500-019-03993-6
Oussalah, M.: On the use of Hamacher’s t-norms family for information aggregation. Inf. Sci. 153, 107–154 (2003)
Huang, J.Y.: Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst. 27(1), 505–513 (2014)
Liu, P.: Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans. Fuzzy Syst. 22(1), 83–97 (2013)
Garg, H.: Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems. Iran. J. Sci. Technol. Trans. Electr. Eng. 43(3), 597–613 (2019)
Wu, S.J., Wei, G.W.: Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int. J. Knowl. Based Intell. Eng. Syst. 21(3), 189–201 (2017)
Gao, H.: Pythagorean fuzzy hamacher prioritized aggregation operators in multiple attribute decision making. J. Intell. Fuzzy Syst. 35(2), 2229–2245 (2018)
Wei, G.W.: Pythagorean fuzzy Hamacher power aggregation operators in multiple attribute decision making. Fundam. Inf. 166(1), 57–85 (2019)
Darko, A.P., Liang, D.: Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Eng. Appl. Artif. Intell. 87, 103259 (2020)
Wei, G.: Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fundam. Inf. 157(3), 271–320 (2018)
Jana, C., Pal, M.: Assessment of enterprise performance based on picture fuzzy hamacher aggregation operators. Symmetry 11(1), 75 (2019)
Murphy, R.R., Tadokoro, S., Nardi, D., Jacoff, A., Fiorini, P., Choset, H., Erkmen, A.M.: Search and rescue robotics. Springer handbook of Robotics pp. 1151–1173 (2008). https://doi.org/10.1007/978-3-540-30301-5_51
Zhou, J., Baležentis, T., Streimikiene, D.: Normalized weighted Bonferroni Harmonic mean-based intuitionistic fuzzy operators and their application to the sustainable selection of search and rescue robots. Symmetry 11(2), 218 (2019). https://doi.org/10.3390/sym11020218
Ullah, K., Hassan, N., Mahmood, T., Jan, N., Hassan, M.: Evaluation of investment policy based on multi-attribute decision-making using interval valued T-spherical fuzzy aggregation operators. Symmetry 11(3), 357 (2019). https://doi.org/10.3390/sym11030357
Garg, H., Kumar, K.: A novel possibility measure to interval-valued intuitionistic fuzzy set using connection number of set pair analysis and their applications. Neural Comput. Appl. (2019). https://doi.org/10.1007/s00521-019-04291-w
Wang, L., Garg, H., Li, N.: Interval-valued q-rung orthopair 2-tuple linguistic aggregation operators and their applications to decision making process. IEEE Access 7(1), 131962–131977 (2019)
Garg, H.: Nancy, linguistic single-valued neutrosophic power aggregation operators and their applications to group decision-making problems. IEEE CAA J. Autom. Sin. (2019). https://doi.org/10.1109/JAS.2019.1911522
Garg, H., Kaur, G.: Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Comput. Ind. Eng. 140, 106211 (2020). https://doi.org/10.1016/j.cie.2019.106211
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of Interest
The authors declare that they have no conflict of interests.
Ethical Approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Rights and permissions
About this article
Cite this article
Ullah, K., Mahmood, T. & Garg, H. Evaluation of the Performance of Search and Rescue Robots Using T-spherical Fuzzy Hamacher Aggregation Operators. Int. J. Fuzzy Syst. 22, 570–582 (2020). https://doi.org/10.1007/s40815-020-00803-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-020-00803-2