Ranking Z-numbers using the optimal clustering method
saeed jafari
1
(
Department of Electrical Engineering, Islamic Azad University, Bushehr, Branch
)
مجتبی Najafi
2
(
Department of Electrical Engineering, Islamic Azad University, Bushehr, Branch
)
Naghi Moaddabi Pirkolahchahi
3
(
Department of Electrical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran.
)
najmeh cheraghi shirazi
4
(
Department of Electrical Engineering, Islamic Azad University, Bushehr, Branch
)
Keywords: Z-number, KZ-number, K-means, probability-possibility, fuzzy-,
Abstract :
The use of new concepts in performing calculations by natural language words in order to model uncertainties has been considered in recent years. In this regard, the concept of Z-number was proposed by Dr. Zadeh in 2011. In this concept, data uncertainty is introduced as a pair of fuzzy numbers (A, B). The purpose of Z number is to model imprecise natural language sentences, so that the first factor of Z-number indicates the possibility of occurrence and the second factor indicates the probability of occurrence of the first factor. However, Z-numbers have complex problems and high computational cost. In the Z-number in order to form the first and second components of the pair of fuzzy numbers (A, B), experts may provide inappropriate solutions in high number of data, which causes the final results to not be calculated correctly, this weakness in Group decisions are more visible when using the Z-number. In order to solve this challenge, the authors suggest the purposeful grouping of all data. In this solution, data grouping is done based on clustering (k-means) and then the first and second components of the Z-number are formed purposefully. In order to show the effectiveness of the proposed method, we calculate the uncertainty of the current price of electricity in the PJM market. At the end, the results obtained by the proposed method have been compared with the results obtained by the fuzzy method, Z-number and real data.
