Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information
Abstract
:1. Introduction
1.1. A Brief Introduction to the Concept of Rough Sets
1.2. A Brief Historical Overview of Dombi Aggregation Operators
1.3. A Comprehensive Overview of the TOPSIS Method
1.4. A Short Introduction of HFSs
1.5. The Motivations of the Manuscript
- (1)
- To compile a list of numerous AOPs based on Dombi t-norm and t-conorm, namely, IHFR Dombi weighted averaging aggregation operator (IHFRDWAAO), IHFR ordered weighted averaging aggregation operator (IHFRDOWAAO), and IHFR Dombi hybrid weighted averaging aggregation operator (IHFRDHWAAO), and investigate their key operating laws. Additionally, describe their related properties.
- (2)
- To establish the score and accuracy functions employing IHFRSs.
- (3)
- To provide a DM technique for combining vague information employing the prescribed AOPs.
- (4)
- By using the demonstrated AOPs, an empirical analysis using numerical information from a real-world DM problem involving the selection of a suitable multinational partnership is initiated.
- (5)
- The findings are also assessed using comparisons to the IHFR-TOPSIS approach.
1.6. Structure of the Article
2. Basic Concepts
- (1)
- is reflexive if and
- (2)
- is symmetric if , and
- (3)
- is transitive if
- (1)
- If then
- (2)
- If then
- (3)
- If then
- (a)
- If then
- (b)
- If then
- (c)
- If then
3. Dombi Aggregation Operators Based on Intuitionistic Hesitant Fuzzy Rough Sets
3.1. Dombi t-Norm and t-Conorm
3.2. Dombi Operations of IHFR Information
3.3. Aggregation Operators
3.4. Intuitionistic Hesitant Fuzzy Rough Dombi Weighted Arithmetic Averaging (IHFRDWAA) Operator
3.5. Intuitionistic Hesitant Fuzzy Rough Dombi Ordered Weighted Arithmetic Averaging (IHFRDOWAA) Operator
3.6. Intuitionistic Hesitant Fuzzy Rough Dombi Hybrid Weighted Arithmetic Averaging (IHFRDHWAA) Operator
4. Multiple Attribute Group Decision-Making Method under IHRFR Information
- Step-1
- Let be the set of alternatives, be the set of criteria, and be the set of decision-makers with the weight vector where such that . The MADM method comprises the following procedures:
- Step-2
- The assessment of the alternative based on criteria by decision makers can be written as . Consequently, the IHFR decision matrix DMAi may be established as follows:
- Step-3
- Assess the normalised expert matrices as
- Step-4
- Construct the collected IHFR information using IHFRDWAA related to , denoted by , as follows:
- Step-5
- To use the aforementioned aggregation information, assess the combined IHFR values for each alternative that has been investigated in accordance with the specified list of attributes/criteria.
- Step-6
- Compute the score values for
- Step-7
- Assemble the numerical values of all score values in a specific sequence.
- Step-8
- Select the option retaining the highest scoring value. Figure 1 illustrates the diagrammatic chart of the algorithm for the implied MADM technique.
5. Numerical Application
- (i)
- Science, technology, and innovation (STI) (): Science, technology, and innovation have long been recognised as a fundamental resource in productivity growth and a significant, long-term strategy for increasing economic development and living standards. If developing countries are to be capable of participating in international STI activities, humanitarian assistance should collaborate more intimately with research and innovation stakeholders to strengthen STI capability. As a consequence, it is essential to promote more production capacities by both governments and corporations, particularly via public–private partnerships. Moreover, it is critical to collaborate in order to build the skills required to capitalise on the opportunities given by STI in the pursuit of sustainable development. Because of the interaction of science, technology, innovation, and digitalisation, tremendous upheavals are feasible. Until now, it has been probable that these changes would not immediately alleviate social and environmental challenges. Essentially, changing global development onto a more sustainable route will need not only the extension of currently appropriate technology but also radical breakthroughs (including social ones) and paradigm transformations. The capacity to innovate is important because desired adjustments in attitudes and practises need (social) innovation. Ultimately, STI may become a common goal of the public and private sectors, mobilising all investments in the direction of sustainable development, and it may be structured towards industries that cause economic and social changes, all of which minimise transformation costs.
- (ii)
- Business operation level (): Business operations are the ordinary activities that a corporation performs in order to increase its value and produce revenue. It is conceivable to optimise operations to the point that they produce greater profits than they consume. Employees contribute to a company’s success by performing crucial duties such as advertising, accounting, and production. As a firm grows, it must alter its operating procedures to keep things running smoothly, which requires meticulous planning on the part of senior management. A growing organisation must be equipped to confront new challenges such as those connected to the law, marketing, and growth. A corporation should develop effective and quantifiable measures to monitor its success. Establishing goals is the first step towards generating a foundation for performance assessment. Management should strive for clear, quantifiable results. Keeping up with industry advances is essential for discovering cost-cutting and productivity-boosting possibilities, as well as satisfying the needs of evolving policies. Another strategy for improving the efficiency of company operations is to keep up with industry advances. Management should constantly be looking for alternative techniques to streamline and improve critical operations.
- (iii)
- International cooperation level (): The International cooperation level for the GP is the major multi-stakeholder vehicle for enhancing development effectiveness by increasing the efficacy of all types of development cooperation for the shared tangible benefits for individuals, the environment, prosperity, and harmony. It brings together groups devoted to improving the effectiveness of their development relationships, including governmental institutions, non-governmental organisations, businesses, parliamentarians, and labour organisations. A binding contract is formed between two or more parties to share resources and collaborate to accomplish a common goal. National stakeholders and external partners (such as international development organisations) must take part in the establishment, implementation, and assessment of a country’s own development strategy under the guidance of the government. Commitment is reflected when public or private institutions work together to achieve mutual goals or adopt common procedures, such as in scientific endeavours or the establishment of mandatory industry standards.
- (iv)
- Credit level (): In numerous countries, the principle of economic growth has been elevated to the level of a national policy priority. Private enterprises are intensifying their efforts to reach previously unserved or undeserved aspects as a consequence of decision makers’ and regulators’ attempts to improve the level of financial inclusion in their countries. Formerly, conceptions of financial inclusion have differed significantly among countries; however, there has been significant convergence in recent years. There is accessibility to a diverse choice of appropriate financial services (i.e., individuals, firms and government entities). These criteria include the desire to purchase and pay, as well as the usage of credit, credit cards, savings, investment, and insurance products and services. The quality of financial merchandise and services, when paired with consumer protection and financial knowledge, maximises a user’s capacity to realise the advantages when employing these products and services on a regular basis.
The Evaluation Procedure for Selecting an Appropriate Global Partnership
- Step-1
- Step-2
- There is no need for normalisation because all of the expert information is of the benefit type.
- Step-3
- Step-4
- Ascertain the aggregate IHFR values for each of the assessed alternatives using the specified set of criteria/attributes utilising the aggregation information. Table 7 and Table 8 visualised the aggregated information for IHFRDWA and IHFRODWA, respectively. The hybrid collected expert information is presented in Table 9, and their score values are displayed in Table 10. The results of IHFRHDWA are presented in Table 11.
- Step-5
- The score values determined for the information acquired via IHFRDWA, IHFRODWA, and IHFRHDWA are presented in Table 12. Ranking alternatives accordingly to their score, we observed that is the optimal alternative. The ranking of the score values of the acquired information through IHFRDWA, IHFRODWA, and IHFRHDWA is depicted in Figure 2.
6. Sensitivity Analysis
7. Comparative Analysis
- Step-1
- Let the set of alternatives be and the set of criteria be , and the information obtained from the professionals is provided as follows:
- Step-2
- First, we assemble information from DMs using IHFR numbers.
- Step-3
- Second, normalise the DM information, owing to the fact that the decision matrix contains cost and benefit criteria, which is demonstrated as follows:
- Step-4
- Analyse the normalised information obtained from professionals as
- Step-5
- The PIS and NIS are determined by the score values. are the PIS and are the NIS. The algorithm that yields the PIS is as follows:In a comparable way, the formula used to determine the negative ideal solution is as follows:Based on the aforementioned information, calculate the geometric distance between each alternative and the PIS using the subsequent algorithm:Likewise, the geometric distance between each alternative and the NIS, represented as , can be expressed in the following mathematical manner:
- Step-6
- Here is the procedure employed for determining the relative closeness indices for each DM alternative:
- Step-7
- In the context of decision making, the alternative with the minimum distance is deemed the most preferable.
7.1. A Numerical Illustration
- Step-1
- Step-2
- The collected expert information obtained using the IHFR Dombi weighted arithmetic averaging aggregation operator are presented in Table 4.
- Step-3
- There is no need to normalise the information since it is the benefit type.
- Step-4
- The PIS and NIS can be determined by referencing the score value, as displayed in Table 15.
- Step-5
- In order to determine the distance, measure between PIS and NIS as follows:
Distance measures of PIS 0.0483 0.0369 0.0311 0.0334 andDistance measures of NIS 0.0411 0.0539 0.0122 0.0419
- Step-6
- The procedure for determining the relative closeness indices for all DMs of the alternatives is as follows:
The relative closeness indices for each DMs of the alternatives. 0.5403 0.4064 0.7182 0.4436 - Step-7
- The alternatives are ranked in descending order, as presented in Table 16. The minimum distance can be observed in . Therefore, based on the given information, it can be determined that is the most suitable selection among the alternatives. The geometrical representation of ranking order using the TOPSIS approach is illustrated in Figure 4.
7.2. Characteristic and Analytical Comparison
8. Conclusions and Future Recommendations
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
- When , we obtain the following findings based on Dombi operations as
- Suppose the result is true for ; that is,So, the result is true for all Hence, the theorem is proven for all
References
- Zadeh, L. Fuzzy sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef]
- Atanassov, K. Intuitionistic fuzzy sets. Int. J. Bioautomation 2016, 20, 1. [Google Scholar]
- Yager, R.R. Pythagorean fuzzy subsets. In Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, AB, Canada, 24–28 June 2013; pp. 57–61. [Google Scholar]
- Pawlak, Z. Rough sets. Int. J. Comput. Inf. Sci. 1982, 11, 341–356. [Google Scholar] [CrossRef]
- Li, T.; Nguyen, H.S.; Wang, G.; Grzymala-Busse, J.W.; Janicki, R.; Hassanien, A.E.; Yu, H. Rough Sets and Knowledge Technology; Springer: Berlin/Heidelberg, Germany, 2012. [Google Scholar]
- Pawlak, Z. Rough sets and intelligent data analysis. Inf. Sci. 2002, 147, 1–12. [Google Scholar] [CrossRef]
- Dubois, D.; Prade, H. Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 1990, 17, 191–209. [Google Scholar] [CrossRef]
- Cornelis, C.; DeCock, M.; Kerre, E.E. Intuitionistic fuzzy rough sets: At the crossroads of imperfect knowledge. Expert Syst. 2003, 20, 260–270. [Google Scholar] [CrossRef]
- Samanta, S.; Mondal, T. Intuitionistic fuzzy rough sets and rough intuitionistic fuzzy sets. J. Fuzzy Math. 2001, 9, 561–582. [Google Scholar]
- Zhou, L.; Wu, W.-Z. On generalized intuitionistic fuzzy rough approximation operators. Inf. Sci. 2008, 178, 2448–2465. [Google Scholar] [CrossRef]
- Huang, B.; Li, H.; Wei, D. Dominance-based rough set model in intuitionistic fuzzy information systems. Knowl.-Based Syst. 2012, 28, 115–123. [Google Scholar] [CrossRef]
- Huang, B.; Wei, D.; Li, H.; Zhuang, Y. Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems. Inf. Sci. 2013, 221, 215–229. [Google Scholar] [CrossRef]
- Zhou, L.; Wu, W.-Z.; Zhang, W.-X. On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Inf. Sci. 2009, 179, 883–898. [Google Scholar] [CrossRef]
- Feng, F.; Li, C.; Davvaz, B.; Ali, M.I. Soft sets combined with fuzzy sets and rough sets: A tentative approach. Soft Comput. 2010, 14, 899–911. [Google Scholar] [CrossRef]
- Feng, F.; Liu, X.; Leoreanu-Fotea, V.; Jun, Y.B. Soft sets and soft rough sets. Inf. Sci. 2011, 181, 1125–1137. [Google Scholar] [CrossRef]
- Shabir, M.; Ali, M.I.; Shaheen, T. Another approach to soft rough sets. Knowl.-Based Syst. 2013, 40, 72–80. [Google Scholar] [CrossRef]
- Sun, B.; Ma, W. Soft fuzzy rough sets and its application in decision making. Artif. Intell. Rev. 2014, 41, 67–80. [Google Scholar] [CrossRef]
- Zhang, Z. Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings. Inf. Sci. 2012, 198, 186–206. [Google Scholar] [CrossRef]
- Hussain, A.; Ali, M.I.; Mahmood, T. Pythagorean fuzzy soft rough sets and their applications in decision-making. J. Taibah Univ. Sci. 2020, 14, 101–113. [Google Scholar] [CrossRef]
- Hussain, A.; IrfanAli, M.; Mahmood, T. Covering based q-rung orthopair fuzzy rough set model hybrid with topsis for multi-attribute decision making. J. Intell. Fuzzy Syst. 2019, 37, 981–993. [Google Scholar] [CrossRef]
- Hussain, A.; Mahmood, T.; Ali, M.I. Rough pythagorean fuzzy ideals in semigroups. Comput. Appl. Math. 2019, 38, 1–15. [Google Scholar] [CrossRef]
- Wan, S.-P.; Yi, Z.-H. Power average of trapezoidal intuitionistic fuzzy numbers using strict t-norms and t-conorms. IEEE Trans. Fuzzy Syst. 2015, 24, 1035–1047. [Google Scholar] [CrossRef]
- Wan, S.-P.; Wang, F.; Lin, L.-L.; Dong, J.-Y. Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision making. Comput. Ind. Eng. 2016, 93, 286–301. [Google Scholar] [CrossRef]
- Ahmmad, J.; Mahmood, T.; Mehmood, N.; Urawong, K.; Chinram, R. Intuitionistic fuzzy rough aczel-alsina average aggregation operators and their applications in medical diagnoses. Symmetry 2022, 14, 2537. [Google Scholar] [CrossRef]
- Zheng, L.; Mahmood, T.; Ahmmad, J.; Rehman, U.U.; Zeng, S. Spherical fuzzy soft rough average aggregation operators and their applications to multi-criteria decision making. IEEE Access 2022, 10, 27832–27852. [Google Scholar] [CrossRef]
- Cornelis, C.; Verbiest, N.; Jensen, R. Ordered weighted average based fuzzy rough sets. In Rough Set and Knowledge Technology; Springer: Berlin/Heidelberg, Germany, 2010; pp. 78–85. [Google Scholar]
- Liu, H.B.; Liu, Y.; Xu, L. Dombi interval-valued hesitant fuzzy aggregation operators for information security risk assessment. Math. Probl. Eng. 2020, 2020, 3198645. [Google Scholar] [CrossRef]
- Akram, M.; Yaqoob, N.; Ali, G.; Chammam, W. Extensions of dombi aggregation operators for decision making under m-polar fuzzy information. J. Math. 2020, 2020, 4739567. [Google Scholar] [CrossRef]
- Tehreem; Hussain, A.; Alsanad, A. Novel dombi aggregation operators in spherical cubic fuzzy information with applications in multiple attribute decision-making. Math. Probl. Eng. 2021, 2021, 9921553. [Google Scholar]
- Ashraf, S.; Abdullah, S.; Mahmood, T. Spherical fuzzy dombi aggregation operators and their application in group decision making problems. J. Ambient Intell. Humaniz. Comput. 2020, 11, 2731–2749. [Google Scholar] [CrossRef]
- Chen, J.; Ye, J. Some single-valued neutrosophic dombi weighted aggregation operators for multiple attribute decision-making. Symmetry 2017, 9, 82. [Google Scholar] [CrossRef]
- Shi, L.; Ye, J. Dombi aggregation operators of neutrosophic cubic sets for multiple attribute decision-making. Algorithms 2018, 11, 29. [Google Scholar] [CrossRef]
- Lu, X.; Ye, J. Dombi aggregation operators of linguistic cubic variables for multiple attribute decision making. Information 2018, 9, 188. [Google Scholar] [CrossRef]
- He, X. Typhoon disaster assessment based on dombi hesitant fuzzy information aggregation operators. Nat. Hazards 2018, 90, 1153–1175. [Google Scholar] [CrossRef]
- Jana, C.; Senapati, T.; Pal, M.; Yager, R.R. Picture fuzzy Dombi aggregation operators: Application to MADM process. Appl. Soft Comput. 2019, 74, 99–109. [Google Scholar] [CrossRef]
- Hwang, C.-L.; Masud, A.S.M. Multiple Objective Decision Making Methods and Applications: A State-of-the-Art Survey; Springer: Berlin/Heidelberg, Germany, 2012; Volume 164. [Google Scholar]
- Umer, R.; Touqeer, M.; Omar, A.H.; Ahmadian, A.; Salahshour, S.; Ferrara, M. Selection of solar tracking system using extended topsis technique with interval type-2 pythagorean fuzzy numbers. Optim. Eng. 2021, 22, 2205–2231. [Google Scholar] [CrossRef]
- Pishyar, S.; Khosravi, H.; Tavili, A.; Malekian, A.; Sabourirad, S. A combined ahp-and topsis-based approach in the assessment of desertification disaster risk. Environ. Model. Assess. 2020, 25, 219–229. [Google Scholar] [CrossRef]
- Kacprzak, D. An extended topsis method based on ordered fuzzy numbers for group decision making. Artif. Intell. Rev. 2020, 53, 2099–2129. [Google Scholar] [CrossRef]
- Rani, P.; Mishra, A.R.; Rezaei, G.; Liao, H.; Mardani, A. Extended pythagorean fuzzy topsis method based on similarity measure for sustainable recycling partner selection. Int. J. Fuzzy Syst. 2020, 22, 735–747. [Google Scholar] [CrossRef]
- Jun, H.; Junmin, W.; Jie, W. Topsis hybrid multiattribute group decision-making based on interval pythagorean fuzzy numbers. Math. Probl. Eng. 2021, 2021, 5735272. [Google Scholar] [CrossRef]
- Zhao, H.; Xu, Z.; Ni, M.; Cui, F. Hybrid fuzzy multiple attribute decision making. Inf. Int. Interdiscip. J. 2009, 12, 1033–1044. [Google Scholar]
- Zhang, K.; Dai, J. A novel topsis method with decision-theoretic rough fuzzy sets. Inf. Sci. 2022, 608, 1221–1244. [Google Scholar] [CrossRef]
- Torra, V. Hesitant fuzzy sets. Int. J. Intell. Syst. 2010, 25, 529–539. [Google Scholar] [CrossRef]
- Liao, H.; Xu, Z.; Xia, M. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int. J. Inf. Technol. Decis. Mak. 2014, 13, 47–76. [Google Scholar] [CrossRef]
- Ebrahimpour, M.K.; Eftekhari, M. Ensemble of feature selection methods: A hesitant fuzzy sets approach. Appl. Soft Comput. 2017, 50, 300–312. [Google Scholar] [CrossRef]
- Sun, G.; Guan, X.; Yi, X.; Zhou, Z. Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition. Expert Syst. Appl. 2018, 92, 521–532. [Google Scholar] [CrossRef]
- Xu, Z.; Zhang, X. Hesitant fuzzy multi-attribute decision making based on topsis with incomplete weight information. Knowl.-Based Syst. 2013, 52, 53–64. [Google Scholar] [CrossRef]
- Feng, X.; Tan, Q.; Wei, C. Hesitant fuzzy linguistic multi-criteria decision making based on possibility theory. Int. J. Mach. Learn. Cybern. 2018, 9, 1505–1517. [Google Scholar] [CrossRef]
- Qian, Y.; Liang, J.; Yao, Y.; Dang, C. Mgrs: A multi-granulation rough set. Inf. Sci. 2010, 180, 949–970. [Google Scholar] [CrossRef]
- Qian, Y.; Liang, X.; Wang, Q.; Liang, J.; Liu, B.; Skowron, A.; Yao, Y.; Ma, J.; Dang, C. Local rough set: A solution to rough data analysis in big data. Int. J. Approx. Reason. 2018, 97, 38–63. [Google Scholar] [CrossRef]
- Yang, X.; Song, X.; Qi, Y.; Yang, J. Constructive and axiomatic approaches to hesitant fuzzy rough set. Soft Comput. 2014, 18, 1067–1077. [Google Scholar] [CrossRef]
- Zhang, H.; Shu, L.; Liao, S. Hesitant fuzzy rough set over two universes and its application in decision making. Soft Comput. 2017, 21, 1803–1816. [Google Scholar] [CrossRef]
- Torra, V.; Narukawa, Y. On hesitant fuzzy sets and decision. In Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, Jeju, Republic of Korea, 20–24 August 2009; pp. 1378–1382. [Google Scholar]
- Beg, I.; Rashid, T. Group decision making using intuitionistic hesitant fuzzy sets. Int. J. Fuzzy Log. Intell. Syst. 2014, 14, 181–187. [Google Scholar] [CrossRef]
- Chinram, R.; Hussain, A.; Mahmood, T.; Ali, M.I. Edas method for multi-criteria group decision making based on intuitionistic fuzzy rough aggregation operators. IEEE Access 2021, 9, 10199–10216. [Google Scholar] [CrossRef]
- Dombi, J. A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst. 1982, 8, 149–163. [Google Scholar] [CrossRef]
- Hsu, P.-F.; Hsu, M.-G. Optimizing the information outsourcing practices of primary care medical organizations using entropy and topsis. Qual. Quant. 2008, 42, 181–201. [Google Scholar] [CrossRef]
- Tzeng, G.-H.; Huang, J.-J. Multiple Attribute Decision Making: Methods and Applications; CRC Press: Boca Raton, FL, USA, 2011. [Google Scholar]
- Yu, C.; Shao, Y.; Wang, K.; Zhang, L. A group decision making sustainable supplier selection approach using extended topsis under interval-valued pythagorean fuzzy environment. Expert Syst. Appl. 2019, 121, 1–17. [Google Scholar] [CrossRef]
- Chakraborty, S. Applications of the moora method for decision making in manufacturing environment. Int. J. Adv. Manuf. Technol. 2011, 54, 1155–1166. [Google Scholar] [CrossRef]
- Bolturk, E.; Kahraman, C. A novel interval-valued neutrosophic ahp with cosine similarity measure. Soft Comput. 2018, 22, 4941–4958. [Google Scholar] [CrossRef]
- Mir, M.A.; Ghazvinei, P.T.; Sulaiman, N.; Basri, N.; Saheri, S.; Mahmood, N.; Jahan, A.; Begum, R.; Aghamohammadi, N. Application of topsis and vikor improved versions in a multi criteria decision analysis to develop an optimized municipal solid waste management model. J. Environ. Manag. 2016, 166, 109–115. [Google Scholar]
- Akram, M.; Shumaiza; Arshad, M. Bipolar fuzzy topsis and bipolar fuzzy electre-i methods to diagnosis. Comput. Appl. Math. 2020, 39, 1–21. [Google Scholar] [CrossRef]
- Behzadian, M.; Kazemzadeh, R.B.; Albadvi, A.; Aghdasi, M. Promethee: A comprehensive literature review on methodologies and applications. Eur. J. Oper. Res. 2010, 200, 198–215. [Google Scholar] [CrossRef]
- Akram, M.; Adeel, A.; Alcantud, J.C.R. Group decision-making methods based on hesitant n-soft sets. Expert Syst. Appl. 2019, 115, 95–105. [Google Scholar] [CrossRef]
- Akram, M.; Adeel, A.; Alcantud, J.C.R. Hesitant fuzzy n-soft sets: A new model with applications in decision-making. J. Intell. Fuzzy Syst. 2019, 36, 6113–6127. [Google Scholar] [CrossRef]
- Ashraf, S.; Kousar, M.; Hameed, M.S. Early infectious diseases identification based on complex probabilistic hesitant fuzzy n-soft information. Soft Comput. 2023, 27, 18285–18310. [Google Scholar] [CrossRef] [PubMed]
- Garg, H.; Mahmood, T.; Rehman, U.; Ali, Z. Chfs: Complex hesitant fuzzy sets-their applications to decision making with different and innovative distance measures. CAAI Trans. Intell. Technol. 2021, 6, 93–122. [Google Scholar] [CrossRef]
- Zhang, S.; Xu, Z.; He, Y. Operations and integrations of probabilistic hesitant fuzzy information in decision making. Inf. Fusion 2017, 38, 1–11. [Google Scholar] [CrossRef]
- Mahmood, T.; UrRehman, U.; Ali, Z. A novel complex fuzzy n-soft sets and their decision-making algorithm. Complex Intell. Syst. 2021, 7, 2255–2280. [Google Scholar] [CrossRef]
- Saha, A.; Senapati, T. Yager, R.R. Hybridizations of generalized dombi operators and bonferroni mean operators under dual probabilistic linguistic environment for group decision-making. Int. J. Intell. Syst. 2021, 36, 6645–6679. [Google Scholar] [CrossRef]
- Su, Y.; Zhao, M.; Wei, G.; Wei, C.; Chen, X. Probabilistic uncertain linguistic edas method based on prospect theory for multiple attribute group decision-making and its application to green finance. Int. J. Fuzzy Syst. 2022, 24, 1318–1331. [Google Scholar] [CrossRef]
- Wei, G.; Lin, R.; Lu, J.; Wu, J.; Wei, C. The generalized dice similarity measures for probabilistic uncertain linguistic magdm and its application to location planning of electric vehicle charging stations. Int. J. Fuzzy Syst. 2022, 24, 933–948. [Google Scholar] [CrossRef]
- Zhao, M.; Wei, G.; Wei, C.; Wu, J. Pythagorean fuzzy todim method based on the cumulative prospect theory for magdm and its application on risk assessment of science and technology projects. Int. J. Fuzzy Syst. 2021, 23, 1027–1041. [Google Scholar] [CrossRef]
- Romero, Á.L.; Rodríguez, R.M.; Martínez, L. Computing with comparative linguistic expressions and symbolic translation for decision making: Elicit information. IEEE Trans. Fuzzy Syst. 2019, 28, 2510–2522. [Google Scholar] [CrossRef]
- García-Zamora, D.; Labella, Á.; Ding, W.; Rodríguez, R.M.; Martínez, L. Large-scale group decision making: A systematic review and a critical analysis. IEEE/CAA J. Autom. Sin. 2022, 9, 949–966. [Google Scholar] [CrossRef]
- Labella, Á.; Liu, H.; Rodríguez, R.M.; Martínez, L. A cost consensus metric for consensus reaching processes based on a comprehensive minimum cost model. Eur. J. Oper. Res. 2020, 281, 316–331. [Google Scholar] [CrossRef]
- Labella, Á.; Liu, Y.; Rodríguez, R.; Martínez, L. Analyzing the performance of classical consensus models in large scale group decision making: A comparative study. Appl. Soft Comput. 2018, 67, 677–690. [Google Scholar] [CrossRef]
- Lei, W.; Ma, W.; Li, X.; Sun, B. Three-way group decision based on regret theory under dual hesitant fuzzy environment: An application in water supply alternatives selection. Expert Syst. Appl. 2024, 237, 121249. [Google Scholar] [CrossRef]
- Ransikarbum, K.; Pitakaso, R. Multi-objective optimization design of sustainable biofuel network with integrated fuzzy analytic hierarchy process. Expert Syst. Appl. 2024, 240, 122586. [Google Scholar] [CrossRef]
- Rodríguez, R.M.; Labella, Á.; DeTré, G.; Martínez, L. A large scale consensus reaching process managing group hesitation. Knowl.-Based Syst. 2018, 159, 86–97. [Google Scholar] [CrossRef]
- Xu, L.; Hu, X.; Zhang, Y.; Feng, J.; Luo, S. A fuzzy multiobjective team decision model for codp and supplier selection in customized logistics service supply chain. Expert Syst. Appl. 2024, 237, 121387. [Google Scholar] [CrossRef]
- Zhou, X.; Tan, W.; Sun, Y.; Huang, T.; Yang, C. Multi-objective optimization and decision making for integrated energy system using sta and fuzzy topsis. Expert Syst. Appl. 2024, 240, 122539. [Google Scholar] [CrossRef]
- Shekhovtsov, A.; Kizielewicz, B.; Salabun, W. Advancing individual decision-making: An extension of the characteristic objects method using expected solution point. Inf. Sci. 2023, 647, 119456. [Google Scholar] [CrossRef]
- Wieckowski, J.; Salabun, W. A new sensitivity analysis method for decision-making with multiple parameters modification. Inf. Sci. 2024, 678, 120902. [Google Scholar] [CrossRef]
- Antczak, T. On optimality for fuzzy optimization problems with granular differentiable fuzzy objective functions. Expert Syst. Appl. 2024, 240, 121891. [Google Scholar] [CrossRef]
- Song, H.-H.; Dutta, B.; García-Zamora, D.; Wang, Y.-M.; Martínez, L. Managing non-cooperative behaviors in consensus reaching process: A novel multi-stage linguistic lsgdm framework. Expert Syst. Appl. 2024, 240, 122555. [Google Scholar] [CrossRef]
- Wu, M.; Song, J.; Fan, J. A q-rung orthopair fuzzy multi-attribute group decision making model based on attribute reduction and evidential reasoning methodology. Expert Syst. Appl. 2024, 240, 122558. [Google Scholar] [CrossRef]
(a) | ||
(b) | ||
(a) | ||
(b) | ||
(a) | ||
(b) | ||
(a) | ||
(b) | ||
(a) | ||
(b) | ||
(a) | ||
(b) | ||
Proposed Operators | Alternative Score Value | Ranking | |||
---|---|---|---|---|---|
IHFRDWA | 0.5034 | 0.5194 | 0.5016 | 0.5081 | |
IHFRDOWA | 0.4996 | 0.5119 | 0.4945 | 0.4977 | |
IHFRDHWA | 0.3493 | 0.3546 | 0.3494 | 0.3541 | > > > |
Score Values | Ranking | Best Alternative | ||||
---|---|---|---|---|---|---|
1 | 0.5034 | 0.5194 | 0.5016 | 0.5081 | ||
2 | 0.5071 | 0.5265 | 0.5054 | 0.5114 | ||
3 | 0.5106 | 0.5330 | 0.5088 | 0.5144 | ||
4 | 0.5139 | 0.5385 | 0.5118 | 0.5170 | ||
5 | 0.5169 | 0.5430 | 0.5145 | 0.5194 | ||
10 | 0.5276 | 0.5554 | 0.5231 | 0.5277 | ||
20 | 0.5361 | 0.5645 | 0.5301 | 0.5353 | ||
50 | 0.6242 | 0.6418 | 0.5896 | 0.5976 | ||
100 | 0.5439 | 0.5739 | 0.5377 | 0.5432 |
MADM Methods | CT | Simplicity | MC | Stability | IT |
---|---|---|---|---|---|
TOPSIS ([60]) | Moderate | Moderately critical | Moderate | Medium | Quantitative |
MOORA ([61]) | Very low | Very simple | Minimum | Good | Quantitative |
AHP ([62]) | Very high | Very critical | Maximum | Poor | Mixed |
VIKOR ([63]) | Less | Simple | Moderate | Medium | Quantitative |
ELECTRE ([64]) | High | Moderately critical | Moderate | Medium | Mixed |
PROMETHEE ([65])) | High | Moderately critical | Moderate | Medium | Mixed |
Score Values of Alternatives | Ranking | Best Alternative | |||
---|---|---|---|---|---|
0.5403 | 0.4064 | 0.7182 | 0.4436 |
Methods | Membership | Grading | Hesitancy | Multi-Parameter | 2-D |
---|---|---|---|---|---|
[1] | ✓ | × | × | × | × |
[44] | ✓ | × | ✓ | × | × |
[67] | ✓ | ✓ | ✓ | ✓ | × |
[66] | × | ✓ | ✓ | ✓ | × |
[69] | ✓ | × | ✓ | × | ✓ |
[70] | ✓ | × | ✓ | × | × |
[71] | ✓ | ✓ | × | ✓ | ✓ |
[68] | ✓ | ✓ | ✓ | ✓ | ✓ |
Proposed approach | ✓ | ✓ | ✓ | ✓ | ✓ |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Attaullah; Alyobi, S.; Alharthi, M.; Alrashedi, Y. Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information. Axioms 2024, 13, 610. https://doi.org/10.3390/axioms13090610
Attaullah, Alyobi S, Alharthi M, Alrashedi Y. Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information. Axioms. 2024; 13(9):610. https://doi.org/10.3390/axioms13090610
Chicago/Turabian StyleAttaullah, Sultan Alyobi, Mohammed Alharthi, and Yasser Alrashedi. 2024. "Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information" Axioms 13, no. 9: 610. https://doi.org/10.3390/axioms13090610
APA StyleAttaullah, Alyobi, S., Alharthi, M., & Alrashedi, Y. (2024). Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information. Axioms, 13(9), 610. https://doi.org/10.3390/axioms13090610