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

• Main Authors: Avishek Chakraborty, Sankar Prasad Mondal, Shariful Alam, Ali Ahmadian, Norazak Senu, Debashis De, Soheil Salahshour
• Format: Article
• Language: English
• Published: MDPI AG 2019-02-01
• Series: Symmetry
• Subjects: pentagonal fuzzy number (PFN); non-linear interval-valued fuzzy number; ranking; defuzzification
• Online Access: https://www.mdpi.com/2073-8994/11/2/248

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.