Linguistic temporal discrete Z-numbers and its application

Abstract

The concepts of temporal intuitionistic fuzzy set and temporal fuzzy set were introduced by earlier researchers to model Spatio-temporal and dynamic motions of complex physical systems, respectively. However, the temporal intuitionistic fuzzy set has not been properly applied to solve systems with temporal information. Furthermore, both concepts do not address the problem of uncertainty with respect to the time of occurrence. In this thesis, the discrete and continuous Z-numbers are proven to be ordered by employing a linear ordering relation. This new concept of ordered discrete Z-number leads to the development of two families of temporal Z-number, namely, linguistic temporal discrete Z-number (LTDZ) and temporal discrete Z-number (TDZ). Some of the basic arithmetic operations for LTDZ are introduced and their properties are proven in this thesis. In relation to that, a method for measuring uncertainty for LTDZ with respect to its time of occurrence is proposed by modifying the method for measuring the uncertainty of discrete Z-number. The temporal discrete Z-number is developed for the purpose of analyzing the electroencephalographic (EEG) signal of an epileptic seizure. Numerical examples are included to show the feasibility of the proposed concepts.