## An Elliptic Intuitionistic Fuzzy Model for Franchisor Selection

### Velichka Traneva, Stoyan Tranev

DOI: http://dx.doi.org/10.15439/2023F9747

Citation: Communication Papers of the 18th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 37, pages 343–349 (2023)

Abstract. Choosing a successful franchise company in the ever-changing business environment is a challenge for any investor. The work suggests the creation of an optimal algorithm (E-IFFr) for selecting a franchise company using the concepts of index matrices and elliptic intuitionistic fuzzy sets for modeling this variability in the business environment to optimally solve this optimal problem with elliptic intuitionistic fuzzy parameters. The E-IFFr approach involves experts with dynamic ranks performing evaluations by the selection criteria while also taking into consideration the relative importance of the criteria for each investor. The efficacy of the suggested strategy is demonstrated by a numerical example of the best franchisor selection for the courier business. In an optimistic, average, and pessimistic scenario, the investor has three options to choose from.

### References

- K. Atanassov, “Generalized index matrices,” Comptes rendus de l’Academie Bulgare des Sciences, vol. 40(11), 1987, pp. 15-18.
- K. Atanassov, “Index Matrices: Towards an Augmented Matrix Calculus,” Studies in Computational Intelligence, Springer, vol. 573, 2014.
- K. Atanassov, “On Intuitionistic Fuzzy Sets Theory,” STUDFUZZ, vol. 283, Springer, Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29127-2.
- K. Atanassov, “Circular Intuitionistic Fuzzy Sets,” Journal of Intelligent & Fuzzy Systems, vol. 39 (5), 2020, pp. 5981-5986.
- K. Atanassov, “Elliptic Intuitionistic Fuzzy Sets,” Comptes rendus de l’Académie bulgare des Sciences, vol. 74 (65), 2021, pp. 812-819 (2021)
- K. Atanassov, G. Gargov, “Interval valued intuitionistic fuzzy sets,” Fuzzy sets and systems, vol. 31 (3), 1989, 343-349.
- K. Atanassov, D. Mavrov, V. Atanassova, “Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets,” Issues in IFSs and Generalized Nets, vol. 11, 2014, pp. 1-8.
- K. Atanassov, E. Marinov, “Four Distances for Circular Intuitionistic Fuzzy Sets,” Mathematics, vol. 9 (10), 2021, pp. 11-21.
- K. Atanassov, E. Szmidt, J. Kacprzyk, V. Atanassova, “An approach to a constructive simplification of multiagent multicriteria decision making problems via ICrA,” Comptes rendus de lAcademie bulgare des Sciences, vol. 70 (8), 2017, pp. 1147-1156.
- K. Atanassov, P. Vassilev, O. Roeva, “Level Operators over Intuitionistic Fuzzy Index Matrices,” Mathematics, vol. 9, 2021, pp. 366.
- V. Atanassova, O. Roeva, “Computational complexity and influence of numerical precision on the results of ICrA in the decision-making process,” Notes on IFSs, vol. 24 (3), 2018, pp. 53-63.
- E. Boltürk, C. Kahraman, “Interval-valued and circular intuitionistic fuzzy present worth analyses,” Informatica, vol. 33 (4), 2022, pp. 693-711.
- E. Çakır, M. A. Taş, Z. Ulukan, “Circular Intuitionistic Fuzzy Sets in Multi-Criteria Decision Making, in Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds) 11th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence. ICSCCW 2021. Lecture Notes in Networks and Systems, Springer, Cham, vol. 362, 2022, pp. 34-42.
- C. B. Cuong, V. Kreinovich, “Picture fuzzy sets-a new concept for computational intelligence problems,” In: Proceedings of the Third World Congress on Information and Communication Technologies WICT’2013, Hanoi, Vietnam, 2013, pp. 1-6.
- P. Hsu, B. Chen, “Developing and Implementing a Selection Model for Bedding Chain Retail Store Franchisee Using Delphi and Fuzzy AHP,” Quality & Quantity, vol. 41, 2007, pp. 275-290.
- R. J. Kuo, S. C. Chi, S. S. Kao, “A decision support system for selecting convenience store location through the integration of FAHP and artificial neural network,” Computers in Industry, vol. 47 (2), 2002, pp. 199-214.
- T. Mahmood, S. Abdullah, S. -ur-Rashid, M. Bilal, “Multicriteria decision making based on a cubic set,” Journal of New Theory, vol. 16, 2017, pp. 1-9.
- A. Mieszkowicz-Rolka, L. Rolka, “Multi-Criteria Decision-Making with Linguistic Labels,” in: M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds), Proceedings of the 17th Conference FedCSIS, ACSIS, vol. 30, (2022), pp. 263–267.
- A. R. Mishra, P. Rani, K. Pandey, A. Mardani, J. Streimikis, D. Streimikiene, M. Alrasheedi, “Novel Multi-Criteria Intuitionistic Fuzzy SWARA–COPRAS Approach for Sustainability Evaluation of the Bioenergy Production Process,” Sustainability, vol. 12, 2020, pp. 4155. http://dx.doi.org/10.3390/su12104155
- X. T. Nguyen, V. D. Nguyen, “Support-Intuitionistic Fuzzy Set: A New Concept for Soft Computing,” I.J. Intelligent Systems and Applications, 2015, 04, 2015, pp. 11-16.
- İ. Otay, C. Kahraman, “A novel circular intuitionistic fuzzy AHP & VIKOR methodology: An application to a multi-expert supplier evaluation problem,” Pamukkale Univ. J. Eng. Sci., vol. 28 (1), 2021, pp. 194–207.
- F. Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, Amer. Res. Press, Rehoboth, USA; 1998.
- E. Szmidt, J. Kacprzyk, “Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives,” in: Rakus-Andersson, E., Yager, R., Ichalkaranje, N., etc. (eds.), Recent Advances in Decision Making, SCI, Springer, Heidelberg, vol. 222, 2009, pp. 7–19.
- V. Torra, “Hesitant fuzzy sets,” International Journal of Intelligent Systems, vol. 25 (6), 2010, pp. 529-539.
- V. Traneva, D. Mavrov, S. Tranev, “Software Implementation of the Optimal Temporal Intuitionistic Fuzzy Algorithm for Franchisee Selection,” In: Proceedings of the 17th Conference on Computer Science and Intelligence Systems (FedCSIS), 2022, pp. 387-390.
- V. Traneva, S. Tranev, “Intuitionistic Fuzzy Model for Franchisee Selection,” in: Kahraman, C., Tolga, A.C., Cevik Onar, S., Cebi, S., etc. (eds) Intelligent and Fuzzy Systems, INFUS 2022, Lecture Notes in Networks and Systems, Springer, Cham, vol. 504, 2022, pp. 632-640.
- V. Traneva, P. Petrov, S. Tranev, “Circular IF Knapsack problem,” Lecture Notes in Networks and Systems, (2023) (in press)
- V. Traneva, S. Tranev, D. Mavrov, “Interval-Valued Intuitionistic Fuzzy Decision-Making Method using Index Matrices and Application in Outsourcing,” in: Proceedings of the 16th Conference on Computer Science and Information Systems (FedCSIS), Sofia, Bulgaria, vol. 25, 2021, pp. 251–255.
- V. Traneva, P. Petrov, S. Tranev, “Petrol Station Franchisor Selection through Circular Intuitionistic Fuzzy Multicriteria Analysis,” Lecture Notes in Networks and Systems, (2023) (in press)
- V. Traneva, S. Tranev, M. Stoenchev, K. Atanassov, “ Scaled aggregation operations over two- and three-dimensional index matrices,” Soft computing, vol. 22, 2019, pp. 5115-5120.
- V. Traneva, S. Tranev, Index Matrices as a Tool for Managerial Decision Making, Publ. House of the USB; 2017 (in Bulgarian).
- P. Vassilev, K. Atanassov, Modifications and extensions of Intuitionistic Fuzzy Sets, “Prof. Marin Drinov” Academic Publishing House, Sofia, 2019.
- X. Xu, Y. Lei, W. Dai, “Intuitionistic Fuzzy Integer Programming Based on Improved Particle Swarm Optimization,” J. Comput. Appl.,, vol. 9, 2008, pp. 062.
- L. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8 (3), 1965, pp. 338-353.