Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Form...

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.

Fuzzy logic is frequently used in computing with words (CWW). When input words to a CWW engine are modeled by interval type-2 fuzzy sets (IT2 FSs), the CWW engine’s output can also be an IT2 FS, e A, which needs to be mapped to a linguistic label so that it can be understood. Because each linguistic label is represented by an IT2 FS e Bi, there is a need to compare the similarity of e A and e B...

This paper, which is tutorial in nature, demonstrates how the Embedded Sets Representation Theorem (RT) for a general type-2 fuzzy set (T2 FS), when specialized to an interval (I)T2 FS, can be used as the starting point to solve many diverse problems that involve IT2 FSs. The problems considered are: set theoretic operations, centroid, uncertainty measures, similarity, inference engine computat...

The fuzzy logic control (FLC) has been successfully applied in diverse fields since Zadeh [8] first introduced the fuzzy set theory. Basically, one of the most widely adopted FLCs is the fuzzy-rule-based-system, the Mamdani FLC, which is based on human expertise and knowledge, so that precise and accurate descriptions of the mathematical model of the controlled plant are not required for design...

In this paper, the main concepts of interval type-2 (IT2), generalized (GT2), and type-3 (IT3) fuzzy logic systems (FLSs) are mathematically graphically studied. representation approaches sets (FSs), differences between IT2, GT2, IT3 were investigated. For first time, simple Matlab Simulink M-files by illustrative examples symmetrical FSs presented for practical use IT3-FLSs. The computations s...

In some applications of computing with words, it is necessary to map an interval type-2 fuzzy set (IT2 FS) into one of several classes, which are also represented by IT2 FSs. This classifier can be implemented by a subsethood measure. Five existing subsethood measures for IT2 FSs are considered in this paper. Comparative studies show that Vlachos and Sergiadis’s IT2 FS subsethood measure gives ...

This paper reports the strategy implementation, in simulation environment, for navigation of non-holonomic vehicles using an Interval Type-2 (IT2) Fuzzy Logic System (FLS). A Graphical User Interface (GUI) in MATLAB has been designed to aid the simulations of navigation starting from any position and orientation in a designated area to a designated parking place and fixed orientation. The FLS t...

In the previous paper, we have proposed linguistic weighted average (LWA) algorithms that can be used in distributed and hierarchical decision making. The original LWA algorithms were completely based on the representation theorem for interval type-2 fuzzy sets (IT2 FSs). In later usage, we found that when the lower membership functions (LMFs) of the inputs and weights are of different heights,...

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertai...