Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions
الموضوعات : Transactions on Fuzzy Sets and Systems
1 - Department of Applied Science and Humanities (Mathematics), Guru Nanak Institute of Technology, Sodepur, Kolkata 700114, West Bengal, India.
2 - Department of Mathematics, JIS University, 81, Nilgunj Road, Agarpara, Kolkata 700109, West Bengal, India.
الکلمات المفتاحية: Multi objective structural problem, Hesitant fuzzy set, Intuitionistic fuzzy optimization, Intuitionistic-hesitant fuzzy optimization, Pareto optimal solution,
ملخص المقالة :
In real life, structural problems can be described in linear and nonlinear forms. This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature. Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membership and non-membership value to judge an option. Hesitant fuzzy sets were used to manage scenarios in which experts pause between many possible membership values while evaluating an alternative. A new growing area of a generalized fuzzy set theory called intuitionistic hesitant fuzzy set (IHFS) provides useful tools for dealing with uncertainty in structural design problem that is observed in the actual world. In this article, we have developed a procedure to solve non-linear structural problem in an intuitionistic hesitant fuzzy (IHF) environment. The concept of an intuitionistic hesitant fuzzy set is introduced to provide a computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values. This important feature is not available in the intuitionistic fuzzy optimization technique. Here we have discussed the solution procedure of intuitionistic hesitant fuzzy optimization technique dedicatedly for linear, exponential, and hyperbolic types of membership and non-membership functions. Some theoretical development based on these functions has been discussed. A numerical illustration is given to justify the effectiveness and efficiency of the proposed method in comparison with fuzzy multi-objective nonlinear programming method and intuitionistic fuzzy multi-objective nonlinear programming method. Finally, based on the proposed work, conclusions and future research directions are addressed.
[1] A. A. H. Ahmadini, F. Ahmad, A novel intuitionistic fuzzy preference relations for multiobjective goal programming problems, Journal of Intelligent & Fuzzy Systems, 40(3) (2021), 4761-4777.
[2] M. Akram, S. M. U. Shah, M. M. A. Al-Shamiri, S. A. Edalatpanah, Fractional transportation problem under interval-valued Fermatean fuzzy sets, AIMS Mathematics, 7(9) (2022), 17327-17348.
[3] P. P. Angelov, Optimization in an intuitionistic fuzzy environment, Fuzzy sets and Systems, 86(3) (1997), 299-306.
[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[5] K.T. Atanassov, Interval valued intuitionistic fuzzy sets, Intuitionistic Fuzzy Sets: Theory and Applications, (1999),139-177.
[6] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Management science, 17(4) (1970), 141-164.
[7] S. K. Bharati, Solving optimization problems under hesitant fuzzy environment, Life Cycle Reliability and Safety Engineering, 7(3) (2018), 127-136.
[8] S. K. Bharati, An interval-valued intuitionistic hesitant fuzzy methodology and application, New Generation Computing, 39(2) (2021), 377-407.
[9] S. K. Bharati, A new interval-valued hesitant fuzzy-based optimization method, New Mathematics and Natural Computation, 18(02) (2022), 469-494.
[10] S. K. Bharati, Hesitant intuitionistic fuzzy algorithm for multiobjective optimization problem, Operational Research, 22(4) (2022), 3521-3547.
[11] X. Changwen, Fuzzy optimization of structures by the two-phase method, Computers and Structures, 31(4) (1989), 575-580.
[12] Y. Yi-Cherng, H. Deh-Shiu, Structural optimization with fuzzy parameters, Computers and structures, 37(6) (1990), 917-924.
[13] S. Dey, T. K. Roy, Intuitionistic fuzzy goal programming technique for solving non-linear multi-objective structural problem, Journal of Fuzzy Set Valued Analysis, 3 (2015), 179-193.
[14] S. Dey, T. K. Roy, Multi-objective Structural Optimization Using Fuzzy and Intuitionistic Fuzzy Optimization, International Journal of Intelligent Systems Technologies and Applications, 7(5) (2015), 57-65.
[15] S. Dey, T. K. Roy, Multi-objective structural design problem optimization using parameterized t-norm based fuzzy optimization programming Technique, Journal of Intelligent & Fuzzy Systems, 30(2) (2016), 971-982.
[16] L. Dymova, K. Kaczmarek, P. Sevastjanov, J. Kulawik, A fuzzy multiple criteria decision making approach with a complete user friendly computer implementation, Entropy, 23(2) (2021), 203.
[17] J. A. Goguen, L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338-353.
[18] B. Jana, T. K. Roy, Multi-objective intuitionistic fuzzy linear programming and its application in transportation model, Notes on Intuitionistic Fuzzy Sets, 13(1) (2007), 34-51.
[19] Y. Luo, C. Yu, A fuzzy optimization method for multi-criteria decision making problem based on the inclusion degrees of intuitionistic fuzzy sets, Journal of Information & Computing Science, 3(2) (2008), 146-152.
[20] M. Ranjbar, S. M. Miri, S. Effati, Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle, Iranian Journal of Fuzzy Systems, 19(1) (2022), 97-114.
[21] M. Sarkar, T. K. Roy, Multi-objective welded beam design optimization using T-norm and T-co-norm based intuitionistic fuzzy optimization technique, Advances in Fuzzy Mathematics, 12(3) (2017), 549-575.
[22] M. K. Sharma, A. Dhaka, A. Nandal, H. G. Rosales, F. E. L. Monteagudo, A. G. Hernndez, V. T. Hoang, Fermatean Fuzzy Programming with New Score Function: A New Methodology to Multi-Objective Transportation Problems, Electronics, 12(2) (2023), 277.
[23] C. J. Shih, C. C. Chi, J. H. Hsiao, Alternative α-level-cuts methods for optimum structural design with fuzzy resources, Computers & structures, 81(28-29) (2003), 2579-2587.
[24] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, IEEE international conference on fuzzy systems, Jeju, Korea (South), (2009), 1378-1382.
[25] V. Torra, Hesitant fuzzy sets, International journal of intelligent systems, 25(6) (2010), 529-539.
[26] S. P. Wan,Y. L. Qin, J. Y. Dong, A hesitant fuzzy mathematical programming method for hybrid multicriteria group decision making with hesitant fuzzy truth degrees, Knowledge-Based Systems, 138 (2017), 232-248.
[27] G. Y. Wang, W. Q. Wang, Fuzzy optimum design of structures,In Engineering Mechanics in Civil Engineering, 8(4) (1985), 50-53.
[28] M. Xia, Z. Xu, Hesitant fuzzy information aggregation in decision making, International journal of approximate reasoning, 52(3) (2011), 395-407.
[29] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on systems, Man, and Cybernetics, 3(1) (1973), 28-44.
[30] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy sets & systems, 1(1) (1978), 45-55.
