Eyoh, Imo
(2018)
Interval type2 Atanassovintuitionistic fuzzy logic for uncertainty modelling.
PhD thesis, University of Nottingham.
Abstract
This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type2 fuzzy logic system that utilises fuzzy sets with membership and nonmembership functions that are intervals. Fuzzy logic systems, employing type1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type2, a generalisation of type1 fuzzy logic systems that utilise type2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type2 fuzzy logic systems, with particular reference to interval type2 fuzzy logic systems, is that the membership functions of interval type2 fuzzy sets are themselves fuzzy. These give interval type2 fuzzy logic systems an advantage over their type1 counterparts which have precise membership functions. Whilst the interval type2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type2 fuzzy sets are only specified by membership functions with an implicit assertion that the nonmembership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the nonmembership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and nonmembership functions such that the sum of both membership and nonmembership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type2 fuzzy set namely, interval type2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type2 fuzzy logic system that utilises fuzzy sets with membership and nonmembership functions that are intervals. Fuzzy logic systems, employing type1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type2, a generalisation of type1 fuzzy logic systems that utilise type2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type2 fuzzy logic systems, with particular reference to interval type2 fuzzy logic systems, is that the membership functions of interval type2 fuzzy sets are themselves fuzzy. These give interval type2 fuzzy logic systems an advantage over their type1 counterparts which have precise membership functions. Whilst the interval type2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type2 fuzzy sets are only specified by membership functions with an implicit assertion that the nonmembership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the nonmembership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and nonmembership functions such that the sum of both membership and nonmembership functions is less than or equal to 1.
In this thesis, the advantages of both worlds (interval type2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type2 fuzz set namely, interval type2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined.
First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (firstorder derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria.
Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (secondorder derivative) algorithm in order to address the shortcomings of the firstorder gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and nonmembership functions is significantly better than the classical interval type2 fuzzy logic systems which have only the fuzzy membership functions, and its type1 counterpart which are specified by single membership and nonmembership functions.
The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information.
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