G. Degli Antoni

Approximated Type-2 Fuzzy Set Operations

Type-2 fuzzy sets, an elaboration over type-1 fuzzy sets, are an interesting method for handling uncertainty in rules and parameters in fuzzy systems. However, their adoption has not been as wide as one could have expected. In this paper we provide a simple introduction to type-2 fuzzy sets; then we propose a novel method for calculating operations on type-2 fuzzy sets with normal type-1 membership values, for which we redefine set ordering. Finally, based on the max ordering of fuzzy set and highest degree of separation, we propose an approximation for performing the operations, which ensures that the calculation is accurate for the most important parts of the membership values.

A Simple Method for Performing Type-2 Fuzzy Set Operations Based on Highest Degree of Intersection Hyperplane

Regarding the three dimensional nature of type-2 fuzzy sets their related operations are costly, in terms of time and computation, which is one of the main burdens among the popularity of type-2 fuzzy sets. In this paper we will provide a novel method for performing type-2 fuzzy set operations. We will prove that the operations would be simply performed based on the hyperplane of the highest degree of intersection of two type-1 fuzzy sets.

Augmented Interval Type-2 Fuzzy Set Methodologies for Email Granulation

Email, as one the most popular Internet service is confronted with the plague of spam, which results in bandwidth, time and money waste. Moreover spam has evolved into a true security issue that enforces organizations to fight back in order to address security measures confidentiality, integrity and availability. To this end, we have proposed a dynamic model to classify incoming messages into five granules namely, spam, suspicious-spam, suspicious, suspicious-non-spam and non-spam, using interval type-2 fuzzy set methodologies augmented with the concept of general intervals. Despite the intrinsic complexities of higher order fuzzy sets, the error ratio of misclassification of the proposed method is noticeable. However it should be stressed that no single method can achieve one hundred percent precision, the proposed model should be used in conjunction with other complementing technologies.

email granulation based on distributed-interval type-2 fuzzy set methodologies

This paper proposes a dynamic model to classify incoming emails into five granules namely, spam, suspicious-spam, suspicious, suspicious-non-spam and non-spam, using distributed-interval type-2 fuzzy set methodologies. Toward this end we have used the concept of general intervals and applied the distributed intervals in interval type-2 fuzzy sets. The method confirmed that, the process of spam filtering is rather intellectual than statistical and moreover some different methods should be used complementarity to get to the higher precision.

Spam filtering model based on interval type-2 fuzzy set paradigm

This paper discusses a model for detecting spam based on interval type-2 fuzzy sets. The method confirmed that although dynamic models for spam filtering are preferred, by the way they cannot be used solely and must be integrated with other methods. The method is based on surveying the experts in the field and building the relevant interval type-2 fuzzy map of the given text and then comparing the map with the frames of reference. The method enables personalization and specialization of the filter.

Use of bipartite graphs as a notation for data bases

Abstract Studies on computing systems making use of data bases have produced various notations to represent “schemata” of relations between data. These notations use graphs both as a tool to describe features relevant to applications and as an effective method of teaching. However, a critical limit may be the fact that they handle in different ways the concepts relevant to data and those relevant to programs. As a matter of fact, the ways of handling concepts relevant to programs are often unsuitable. For example, note that an answer to easy requests may require fairly complex programs. This paper introduces a uniform notation both for data-base schemata and for a class of application programs. This is accomplished by associating a suitable interpretation with bipartite graphs.