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Fuzzy logic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this...
In this paper, our aim is to compare and contrast various ways of modeling uncertainty by using different type-2 fuzzy membership functions available in literature. In particular we focus on a novel type-2 fuzzy membership function, — “Elliptic membership function”. After briefly explaining the motivation behind the suggestion of the elliptic membership function, we analyse the uncertainty distribution...
This paper investigates the use of grey theory to enhance the concept of an R-fuzzy set, with regards to the precision of the encapsulating set of returned significance values. The use of lower and upper approximations from rough set theory, allow for an R-fuzzy approach to encapsulate uncertain fuzzy membership values; both collectively generic and individually specific. The authors have previously...
This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parameters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional...
Fuzzy logic controllers (FLCs) have extensively been used for the autonomous control and guidance of unmanned aerial vehicles (UAVs) due to their capability of handling uncertainties and delivering adequate control without the need for a precise, mathematical system model which is often either unavailable or highly costly to develop. Despite the fact that non-singleton FLCs (NSFLCs) have shown more...
In non-singleton fuzzy logic systems (NSFLSs) input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty such as sensor noise. The performance of NSFLSs in handling such uncertainties depends both on the actual input fuzzy sets (and their inherent model of uncertainty) and on the way that they affect the inference process. This paper proposes a novel type of NSFLS...
Interval type-2 defuzzification maps an interval type-2 fuzzy set to a crisp number. We show that the semantic meaning of the interval type-2 fuzzy set (the associated opportunity or risk) has to be considered in the choice of an appropriate interval type-2 defuzzification method. Motivated by a list of “axioms” for type-1 defuzzification we introduce twelve mathematical properties for interval type-2...
This paper presents a newly created significance measure based on a variation of Bayes' theorem, one which quantifies the significance of any value contained within an R-fuzzy set. An R-fuzzy set is a relatively new concept and an extension to fuzzy sets. By utilising the lower and upper approximations from rough set theory, an R-fuzzy approach allows for uncertain fuzzy membership values to be encapsulated...
Selection of an appropriate supplier is a crucial and challenging task in the effective management of a supply chain. Also, appropriate inventory management is critical to the success of a supply chain operation. In recent years, there has been a growing interest in the area of selection of an appropriate vendor and creating good inventory planning using supplier selection information. In this paper,...
This paper reports on a new approach for automatic learning of general type-2 fuzzy logic systems (GT2FLSs) using simulated annealing (SA). The learning process in this work starts without an initial interval type-2 fuzzy system and has an objective to optimize all membership function parameters involved in the general type-2 fuzzy set in two stages. This is a novel methodology for learning GT2FLSs...
This paper presents a new defuzzification algorithm for interval type-2 fuzzy sets. The algorithm exploits the fact that we can treat an interval type-2 fuzzy set as two type-2 fuzzy sets. We suggest in this paper that monotonicity is an important property for defuzzifiers and so we provide a definition of monotonicity for type-2 defuzzifiers based on previous work by Runkler. The research reported...
In this paper, a new fuzzy regression model that is supported by support vector regression is presented. Type-2 fuzzy systems are able to tackle applications that have significant uncertainty. However general type-2 fuzzy systems are more complex than type-1 fuzzy systems. Support vector machines are similar to fuzzy systems in that they can also model systems that are non-linear in nature. In the...
Following the concepts of Mpdf and J̃-plane, in this paper, the authors propose a new Type-2 Fuzzy Probabilistic System - Type-2 Fuzzy SARIMA System for real-valued uncertain non-stationary data-intensive seasonal time series forecasting. The system is implemented in Wireless Soft-Switch (WSS) communication network CAPS forecasting and is compared with the statistical model SARIMA to show that Type-2...
In this paper, simulated annealing algorithm is used to design general type-2 fuzzy logic systems (GT2FLS) with the aid of interval type-2 fuzzy logic systems (IT2FLS). The proposed practical design methodology aims to reduce computations needed to get the best footprint of uncertainty (FOU) using IT2FLS. Simulated annealing is used to learn IT2FLS followed by learning the secondary membership functions...
In previous work the Authors defined the alpha-cut representation for type-2 fuzzy sets. The strength of this representation is that it allows type-2 fuzzy sets to be fully defined by a collection of crisp sets. Each of these crisp sets may be independently processed within a fuzzy logic system prior to defuzzification. This independence means this representation is ideal for parallel implementation...
Alpha-cuts and the extension principle form a methodology for extending mathematical concepts from crisp sets to fuzzy sets. They have been applied to many operations, and have also been extended to interval valued fuzzy sets. Recently, some researchers defined new representations of type-2 fuzzy sets, namely, the alpha-plane representation and the zSlice representation. In this paper we investigate...
The planning of resources within a supply chain can prove to be a deciding factor in the success or failure of an operation. This research continues the authors' previous work using an extended Interval Type-2 Fuzzy Logic supply chain model, with an Evolutionary Algorithm to search for good resource plans. A set of enhanced experiments is conducted to validate our novel approach with optimal configurations,...
In this paper, a combination of a Takagi-Sugeno fuzzy system (TSK) and simulated annealing is used to predict well known time series by searching for the best configuration of the fuzzy system. Simulated annealing is used to optimise the parameters of the antecedent and the consequent parts of the fuzzy system rules. The results of the proposed method are encouraging indicating that simulated annealing...
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