Abstract
This paper presents an approach to prediction based on a new interval type-2 Atanassov-intuitionistic fuzzy logic system (IT2AIFLS) of the Takagi–Sugeno–Kang fuzzy inference with neural network learning capability. The gradient descent algorithm is used to adapt the parameters of the IT2AIFLS. The empirical comparison is made on the designed system using some benchmark regression problems—both artificial and real-world datasets. Analyses of our results reveal that IT2AIFLS outperforms its type-1 variant, other type-1 fuzzy logic approaches, and some type-2 fuzzy systems in the regression tasks. The reason for the improved performance of the proposed framework of IT2AIFLS is the introduction of nonmembership functions and intuitionistic fuzzy indices into the classical IT2FLS model. This increases the level of fuzziness in the proposed IT2AIFLS framework, thus providing more accurate approximations than AIFLS, classical type-1, and interval type-2 fuzzy logic systems.
Highlights
Fuzzy set (FS) theory was introduced by Zadeh [1] as a generalisation of the classical notion of a set and has served as an indispensable mathematical tool for handling uncertainty and computing with words [2]
We demonstrate the effectiveness of IT2AIFLS on some regression problems
We conclude that the proposed model of IT2AIFLS is a more viable method for regression problems
Summary
Fuzzy set (FS) theory was introduced by Zadeh [1] as a generalisation of the classical notion of a set and has served as an indispensable mathematical tool for handling uncertainty and computing with words [2]. Zadeh [5] introduced type-2 fuzzy set (T2FS) which has the capacity to handle uncertainties that T1 struggles with because membership grades of T2FS are themselves fuzzy which give them the flexibility to adapt to uncertain environments. This flexibility provides a soft decision boundary and has a close resemblance to human decision making [6] such that classes of objects can have a gradual rather than abrupt transition from membership to Atanassov [7] extended the concept of Zadeh’s fuzzy sets to intuitionistic fuzzy sets, hereafter referred to as AIFSs, which handle uncertainty by taking into account both the membership and non-membership degrees of an element x to a fuzzy set A together with extra degree of indeterminacy (hesitation). It is argued that AIFS is a tool for a more human consistent reasoning under imperfectly defined facts and imprecise knowledge [15]
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