Employing zSlices based general type-2 fuzzy sets to model multi level agreement

In this paper, we introduce the concept of Multi Level Agreement (MLA) based on (zSlices based) general type-2 fuzzy sets. We define the notion of MLA and describe how it can be computed based on a series of interval type-2 fuzzy sets. We provide examples, visualizing the nature of MLA sets and discuss their properties and interpretation. Moreover, we specifically address the reason for introducing MLA in order to allow the modeling of agreement in real world applications using fuzzy sets while still maintaining an uncertainty model and show that the use of general type-2 fuzzy sets is essential for MLA as classical sets, type-1 and interval type-2 fuzzy sets do not provide a degree of freedom which could be employed to model agreement. © 2011 IEEE

On transitioning from type-1 to interval type-2 fuzzy logic systems

Capturing the uncertainty arising from system noise has been a core feature of fuzzy logic systems (FLSs) for many years. This paper builds on previous work and explores the methodological transition of type-l (Tl) to interval type-2 fuzzy sets (IT2 FSs) for given "levels" of uncertainty. Specifically, we propose to transition from Tl to IT2 FLSs through varying the size of the Footprint Of Uncertainty (FOU) of their respective FSs while maintaining the original FS shape (e.g., triangular) and keeping the size of the FOU over the FS as constant as possible. The latter is important as it enables the systematic relating of FOU size to levels of uncertainty and vice versa, while the former enables an intuitive comparison between the Tl and T2 FSs. The effectiveness of the proposed method is demonstrated through a series of experiments using the well-known Mackey-Glass (MG) time series prediction problem. The results are compared with the results of the IT2 FS creation method introduced in [1] which follows a similar methodology as the proposed approach but does not maintain the membership function (MF) shape

Enhancement of Set-Based Design Practices Via Introduction of Uncertainty Through Use of Interval Type-2 Modeling and General Type-2 Fuzzy Logic Agent Based Methods.

The goal of this research was to discern the effects of introducing uncertainty representation into a set-based design process with applications in ship design. The hypothesis was that introduction of design uncertainty would enhance the facilitation of set-based design practices. A presentation of three fuzzy logic agent based methods for facilitation of set-based ship design practices is offered. The first method utilized a type-1 fuzzy logic system to facilitate set-based design practices and possessed no uncertainty modeling. The next two methods included representation of design uncertainty in the set-based design space. Of these two methods, one utilized a novel approach that harnessed techniques of randomization to model an interval type-2 fuzzy logic system, the other method made use of general type-2 fuzzy logic methods that were well-known, but still relatively under-utilized in academics and industry when compared to type-1 fuzzy logic systems. Comparisons of the newly developed fuzzy logic systems with each other, and the type-1 agent based fuzzy logic system provided the basis for conclusions as to the effects of introducing uncertainty modeling into a set-based design process. The results of this experimental research have shown that the inclusion of uncertainty modeling in the set-based design process for the negotiation of design variables enhances the overall set-based design progression, especially when working with highly constrained designs. In the case of a highly constrained design, the type-1 fuzzy logic system was unable to promote set-convergence within the allotted experimental time without repeated design failures, while the use of uncertainty modeling allowed the interval type-2 modeling and general type-2 fuzzy logic systems to achieve feasible set-based design convergence. When performing a simplistic, loosely constrained design, all three fuzzy logic systems were capable of facilitating the principle practices of set-based design within the feasible solution space; specifically, the set-based practices of delaying design decisions and gradual reduction of the feasible solution space. This research has led to the enhancement of the set-based design process by providing capabilities to now represent uncertainty in the set-based design space though the use of either the newly developed interval type-2 or general type-2 fuzzy logic systems.Ph.D.Naval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86265/1/grayale_1.pd