The Pentagonal Fuzzy Number:Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems

Symmetry - Tập 11 Số 2 - Trang 248
Avishek Chakraborty1,2, Sankar Prasad Mondal3, Shariful Alam2, Ali Ahmadian4, Norazak Senu4, Debashis De5, Soheil Salahshour6
1Department of Basic Science, Narula Institute of Technology, Agarpara, Kolkata-700109, India
2Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India
3Department of Natural Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia, West Bengal 741249, India
4Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor 43400 UPM, Malaysia
5Department of Computer Science and Engineering, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia, West Bengal 741249, India
6Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran

Tóm tắt

In this paper, different measures of interval-valued pentagonal fuzzy numbers (IVPFN) associated with assorted membership functions (MF) were explored, considering significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies. Also, the idea of MF is generalized somewhat to nonlinear membership functions for viewing the symmetries and asymmetries of the pentagonal fuzzy structures. Accordingly, the construction of level sets, for each case of linear and nonlinear MF was also carried out. Besides, defuzzification was undertaken using three methods and a ranking method, which were also the main features of this framework. The developed intellects were implemented in a game problem by taking the parameters as PFNs, ultimately resulting in a new direction for modeling real world problems and to comprehend the uncertainty of the parameters more precisely in the evaluation process.

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Tài liệu tham khảo

Zadeh, 1965, Fuzzy sets, Inf. Control, 8, 338, 10.1016/S0019-9958(65)90241-X

Chang, 1972, On fuzzy mappings and control, IEEE Trans. Syst. Man Cybern., 2, 30, 10.1109/TSMC.1972.5408553

Dubois, 1978, Operations on fuzzy numbers, Int. J. Syst. Sci., 9, 613, 10.1080/00207727808941724

Atanassov, K.T. (1983). Intuitionistic Fuzzy Sets, VII ITKR’s Session.

Smarandache, F. (1998). A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, American Research Press.

Dubois, D., and Prade, H. (2000). Fundamental of Fuzzy Sets. The Handbooks of Fuzzy Sets, Springer.

Guijun, 1998, The applications of interval-valued fuzzy numbers and interval distribution numbers, Fuzzy Sets Syst., 98, 331, 10.1016/S0165-0114(96)00368-5

Wang, 2001, Correlation and information energy of interval-valued fuzzy number, Fuzzy Sets Syst., 103, 169, 10.1016/S0165-0114(97)00303-5

Lin, 2002, Fuzzy job-shop scheduling based on ranking level (α,β) interval-valued fuzzy numbers, IEEE Trans. Fuzzy Syst., 10, 510, 10.1109/TFUZZ.2002.800659

Wei, 2009, A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, Expert Syst. Appl., 36, 589, 10.1016/j.eswa.2007.09.033

Kalaichelvi, 2012, Application of interval fuzzy matrices and interval valued fuzzy soft sets in the analysis of/the factors influencing high scores in higher secondary examinations, Int. J. Math. Sci. Appl., 2, 777

Kumar, 2015, Fuzzy fault tree analysis using level (?,?) interval-valued fuzzy numbers, Ind. Eng. Lett., 5, 36

Abirami, 2015, On L-R type interval valued fuzzy numbers in critical path analysis, Int. J. Fuzzy Math. Arch., 6, 77

Su, 2007, Fuzzy programming based on interval-valued fuzzy numbers and ranking, Int. J. Contemp. Math. Sci., 2, 393, 10.12988/ijcms.2007.07033

Bhatia, 2012, Sensitivity analysis for interval valued fully fuzzy linear programming problems, J. Appl. Res. Technol., 10, 871, 10.22201/icat.16656423.2012.10.6.347

Mondal, 2016, Differential equation with interval valued fuzzy number and its applications, Int. J. Syst. Assur. Eng. Manag., 7, 370, 10.1007/s13198-016-0474-7

Ebrahimnejad, 2018, A method for solvig linear programming with interval-valued fuzzy variables, RAIRO-Oper. Res., 52, 955, 10.1051/ro/2018007

Dahooie, J.H., Zavadskas, E.K., Abolhasani, M., Vanaki, A., and Turskis, Z. (2018). A Novel Approach for Evaluation of Projects Using an Interval–Valued Fuzzy Additive Ratio Assessment (ARAS) Method: A Case Study of Oil and Gas Well Drilling Projects. Symmetry, 10.

Panda, 2015, A study on pentagonal fuzzy number and its corresponding matrices, Pac. Sci. Rev. B Hum. Soc. Sci., 1, 131

Anitha, P., and Parvathi, P. (2016, January 16–21). An Inventory Model with Stock Dependent Demand, two parameter Weibull Distribution Deterioration in a juzzy environment. Proceedings of the 2016 Online International Conference on Green Engineering and Technologies (IC-GET), Hokkaido, Japan.

Helen, 2015, A new operation and ranking on pentagon fuzzy numbers, Int. J. Math. Sci. Appl., 5, 341

Siji, 2016, An Approach for Solving Network Problem with Pentagonal Intuitionistic Fuzzy Numbers Using Ranking Technique, Middle-East J. Sci. Res., 24, 2977

Raj, 2016, Application of Pentagonal Fuzzy Number in Neural Network, Int. J. Math. Appl., 4, 149

Dhanamandand, 2016, Cost analysis on a probabilistic multi objective-multi item inventory model using pentagonal fuzzy number, Glob. J. Appl. Math. Math. Sci., 9, 151

Pathinathan, 2015, Reverse order Triangular, Trapezoidal and Pentagonal Fuzzy Numbers, Ann. Pure Appl. Math., 9, 107

Ponnivalavan, 2015, Intuitionistic pentagonal fuzzy number, ARPN J. Eng. Appl. Sci., 10, 5446

Christi, 2016, Transportation Problem with Pentagonal Intuitionistic Fuzzy Numbers Solved Using Ranking Technique and Russell’s Method, Int. J. Eng. Res. Appl., 6, 82

Mondal, 2017, Pentagonal fuzzy number, its properties and application in fuzzy equation, Future Comput. Inform. J., 2, 110, 10.1016/j.fcij.2017.09.001

Mondal, 2018, Non-linear interval-valued fuzzy numbers and their application in difference equations, Granul. Comput., 3, 177, 10.1007/s41066-017-0063-4

Chu, 2004, COA defuzzification method for evaluating Cpk under fuzzy environments, J. Discret. Math. Sci.Cryptogr., 7, 271, 10.1080/09720529.2004.10698008

Perumal, 2008, Largest of maximum (LOM) method for switching fuzzy control system, Aust. J. Electr. Electron. Eng., 4, 167, 10.1080/1448837X.2008.11464183

Tóth-Laufer, E., and Takács, M. (2012, January 26–28). The Effect of Aggregation and DefuzzificationMethod Selection on the Risk Level Calculation. Proceedings of the 10th IEEE Jubilee International Symposium on Applied Machine Intelligence and Informatics, Herl’any, Slovakia.

Mondal, 2018, Adaptive strategies for system of fuzzy differential equation: Application of arms race model, J. Math. Comput. Sci., 18, 192, 10.22436/jmcs.018.02.07

Abbasbandy, 2006, Ranking of fuzzy numbers by sign distance, Inform. Sci., 176, 2405, 10.1016/j.ins.2005.03.013

Abbasbandy, 2009, A new approach for ranking of trapezoidal fuzzy numbers, Comput. Math. Appl., 57, 413, 10.1016/j.camwa.2008.10.090

Abbasbandy, 2011, An improvement on centroid point method for ranking of fuzzy numbers, J. Sci. IAU, 78, 109

Asady, 2010, The revised method of ranking LR fuzzy number based on deviation degree, Expert Syst. Appl., 37, 5056, 10.1016/j.eswa.2009.12.005

Chen, 2003, A new method for handling multicriteria fuzzy decision making problems using FN-IOWA operators, Cybern. Syst., 34, 109, 10.1080/01969720302866

Chen, 2007, Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Appl. Intell., 26, 1, 10.1007/s10489-006-0003-5

Chen, 2009, Fuzzy risk analysis based on the ranking of generalized fuzzy numbers with different heights and different spreads, Expert Syst. Appl., 36, 6833, 10.1016/j.eswa.2008.08.015

Deng, 2005, A TOPSIS-based centroid index ranking method of fuzzy numbers and its application in decision-making, Cybern. Syst., 36, 581, 10.1080/01969720590961727

Deng, 2006, Ranking fuzzy numbers with an area method usingofgyration, Comput. Math. Appl., 51, 1127, 10.1016/j.camwa.2004.11.022

Hajjari, 2011, Ranking of fuzzy numbers based on ambiguity degree, Aust. J. Basic Appl. Sci., 5, 62

Hajjari, 2011, On deviation degree methods for ranking fuzzy numbers, Aust. J. Basic Appl. Sci., 5, 750

Wang, 2009, Ranking L-R fuzzy numbers based on deviation degree, Inform. Sci., 176, 2070, 10.1016/j.ins.2008.08.017

Chen, 2001, An approximate approach for ranking fuzzy numbers based on left and right dominance, Comput. Math. Appl., 41, 1589, 10.1016/S0898-1221(01)00124-9

Chen, 2002, The preference order of fuzzy numbers, Comput. Math. Appl., 44, 1455, 10.1016/S0898-1221(02)00270-5

Liu, 2005, Ranking fuzzy numbers with preference weighting function expectation, Comput. Math. Appl., 49, 1455, 10.1016/j.camwa.2004.11.014

Cheng, 1998, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets Syst., 95, 307, 10.1016/S0165-0114(96)00272-2

Chu, 2002, Ranking fuzzy numbers with an area between the centroid point and orginalpoint, Comput. Math. Appl., 43, 111, 10.1016/S0898-1221(01)00277-2

Wang, 2008, The revised method of ranking fuzzy numbers with an area between the centroid and original points, Comput. Math. Appl., 55, 2033, 10.1016/j.camwa.2007.07.015

Halgamuge, S., Runkler, T., and Glesner, M. (, January 8–11). On the neural defuzzification methods. Proceedings of the 5th IEEE International Conference on Fuzzy Systems, New Orleans, LA, USA.

Song, 1996, Adaptive learning defuzzificatin techniques and applications, Comput. Math. Appl., 81, 321

Yager, 1996, Knowledge-based defuzzification, Fuzzy Sets Syst., 80, 177, 10.1016/0165-0114(95)00191-3

Filev, 1991, A generalized defuzzification method via BADD distributions, Int. J. Intell. Syst., 6, 687, 10.1002/int.4550060702

Jiang, 1996, Generalized defuzzification strategies and their parameter learning procedure, IEEE Trans. Fuzzy Syst., 4, 64, 10.1109/91.481845

Ramon, E. (1979). Moore, Methods and Applications of Interval Analysis, SIAM. Studies in Applied and Numerical Mathematics.

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Symmetry

Tập 11 Số 2

248

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