Interval type-2 intuitionistic fuzzy logic systems - a comparative evaluation

Several fuzzy modeling techniques have been employed for handling uncertainties in data. This study presents a comparative evaluation of a new class of interval type-2 fuzzy logic system (IT2FLS) namely: interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi Sugeno-Kang (TSK)-type with classical IT2FLS and its type-1 variant (IFLS). Simulations are conducted using a real-world gas compression system (GCS) dataset. Study shows that the performance of the proposed framework with membership functions (MFs) and non-membership functions (NMFs) that are each intervals is superior to classical IT2FLS with only MFs (upper and lower) and IFLS with MFs and NMFs that are not intervals in this problem domain

Comments on: Interval Type-2 Fuzzy Sets are generalization of Interval-Valued Fuzzy Sets: Towards a Wider view on their relationship

This Letter makes some observations about [2] that further support the distinction between an interval type-2 fuzzy set (IT2 FS) and an interval-valued fuzzy set (IV FS), points out that all operations, methods and systems that have been developed and published about IT2 FSs are, so far, only valid in the special case when IT2 FS = IVFS, and suggests some research opportunities

Type-2 fuzzy linear systems

Fuzzy Linear Systems (FLSs) are used in practical situations where some of the systems parameters or variables are uncertain. To date, investigations conducted on FLSs are restricted to those in which the uncertainty is assumed to be modeled by Type-1 Fuzzy Sets (T1FSs). However, there are many situations where considering the uncertainty as T1FSs may not be possible due to different interpretations of experts about the uncertainty. Moreover, solutions of FLSs are T1FSs which do not provide any information about a measure of the dispersion of uncertainty around the T1FSs. Therefore, in this research a model of uncertain linear equations system called a type-2 fuzzy linear system is presented to overcome the shortcomings. The uncertainty is represented by a special class of type-2 fuzzy sets – triangular perfect quasi type-2 fuzzy numbers. Additionally, conditions for the existence of a unique type–2 fuzzy solution to the linear system are derived. A definition of a type-2 fuzzy solution is also given. The applicability of the proposed model is illustrated using examples in the pulp and paper industry, and electrical engineering

Slicing Strategies for the Generalised Type-2 Mamdani Fuzzy Inferencing System

The final publication is available at Springer via http://dx.doi.org/[insert DOI]".As a three-dimensional object, there are a number of ways of slicing a generalised type-2 fuzzy set. In the context of the Mamdani Fuzzy Inferencing System, this paper concerns three accepted slicing strategies, the vertical slice, the wavy slice, and the horizontal slice or alpha -plane. Two ways of de ning the generalised type-2 fuzzy set, vertical slices and wavy slices, are presented. Fuzzi cation and inferencing is presented in terms of vertical slices. After that, the application of all three slicing strategies to defuzzi cation is described, and their strengths and weaknesses assessed

Interval type-2 fuzzy modelling and stochastic search for real-world inventory management

Real-world systems present a variety of challenges to the modeller, not least of which is the problem of uncertainty inherent in their operation. In this research, an interval type-2 fuzzy model is applied to a real-world problem, the goal being to discover a suitable optimisation configuration to enable a search for an inventory plan using the model. To this end, a series of simulated annealing configurations and the interval type-2 fuzzy model were used to search for appropriate inventory plans for a large-scale real-world problem. A further set of tests were conducted in which the performance of the interval type-2 fuzzy model was compared with a corresponding type-1 fuzzy model. In these tests the results were inconclusive, though, as will be discussed there are many ways in which type-2 fuzzy logic can be exploited to demonstrate its advantages over a type-1 approach. To conclude, in this research we have shown that a combination of interval type-2 fuzzy logic and simulated annealing is a logical choice for inventory management modelling and inventory plan search, and propose that the benefits that a type-2 model offers, can make it preferable to a corresponding type-1 system

Uncertainty Measurement for the Interval Type-2 Fuzzy Set

In this paper, two measures of uncertainty for interval type-2 fuzzy sets are presented, evaluated, compared and contrasted. Wu and Mendel regard the length of the type-reduced set as a measure of the uncertainty in an interval set. Green eld and John argue that the volume under the surface of the type-2 fuzzy set is a measure of the uncertainty relating to the set. For an interval type-2 fuzzy set, the volume measure is equivalent to the area of the footprint of uncertainty of the set. Experiments show that though the two measures give di erent results, there is considerable commonality between them. The concept of invariance under vertical translation is introduced; the uncertainty measure of a fuzzy set has the property of invariance under vertical translation if the value it generates remains constant under any vertical translation of the fuzzy set. It is left unresolved whether invariance under vertical translation is an essential property of a type-2 uncertainty measure

Service workload patterns for QoS-driven cloud resource management

Cloud service providers negotiate SLAs for customer services they offer based on the reliability of performance and availability of their lower-level platform infrastructure. While availability management is more mature, performance management is less reliable. In order to support a continuous approach that supports the initial static infrastructure configuration as well as dynamic reconfiguration and auto-scaling, an accurate and efficient solution is required. We propose a prediction technique that combines a workload pattern mining approach with a traditional collaborative filtering solution to meet the accuracy and efficiency requirements. Service workload patterns abstract common infrastructure workloads from monitoring logs and act as a part of a first-stage high-performant configuration mechanism before more complex traditional methods are considered. This enhances current reactive rule-based scalability approaches and basic prediction techniques by a hybrid prediction solution. Uncertainty and noise are additional challenges that emerge in multi-layered, often federated cloud architectures. We specifically add log smoothing combined with a fuzzy logic approach to make the prediction solution more robust in the context of these challenges

Interval type-2 defuzzification using uncertainty weights

One of the most popular interval type-2 defuzzification methods is the Karnik-Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type-2 membership functions to a single type-1 membership function by averaging the upper and lower memberships, and then applies a type-1 centroid defuzzification. In this paper we propose a modification of the NT algorithm which takes into account the uncertainty of the (interval type-2) memberships. We call this method the uncertainty weight (UW) method. Extensive numerical experiments motivated by typical fuzzy controller scenarios compare the KM, NT, and UW methods. The experiments show that (i) in many cases NT can be considered a good approximation of KM with much lower computational complexity, but not for highly unbalanced uncertainties, and (ii) UW yields more reasonable results than KM and NT if more certain decision alternatives should obtain a larger weight than more uncertain alternatives