the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

Type-2 defuzzification is a two-stage process. Type-reduction, the first stage, gives rise to a type-1 fuzzy set known as the type-reduced set (TRS), which for the second stage is defuzzified to give a crisp number. This paper focusses on the TRS itself, which reveals a fascinating internal structure. We provide a description of and explanation for this structure, then go on to suggest how it m...

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.

This paper introduces a new type of fuzzy inference systems, denoted as dynamic evolving neural-fuzzy inference system (DENFIS), for adaptive online and offline learning, and their application for dynamic time series prediction. DENFIS evolve through incremental, hybrid (supervised/unsupervised), learning, and accommodate new input data, including new features, new classes, etc., through local ...

The Greenfield-Chiclana Collapsing Defuzzifier comes in many variants, depending on the order of slice collapse. The accuracy of the fundamental variants of forward, backward, inward and outward, and the composite variants of forward-backward and outward right-left is compared experimentally for the discretised interval type-2 fuzzy set. Keywords— Centroid, Collapsing, Defuzzification, Interval...

In many practical situation, some of the attribute values for an object may be interval and set-valued. This paper introduces the interval and set-valued information systems and decision systems. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories: disjunctive (Type 1) and conjunctive (Type 2) systems. In this...

The paper deals with an extension of aggregation operators from the set of real numbers (or interval [0, 1]) to the set of fuzzy truth values (fuzzy sets in [0, 1]). We define so-called type-2 aggregation operator and show that an extension of ordinary aggregation operator by convolution is a type-2 aggregation operator. Finally we show that ordinary aggregation operator, as well as aggregation...

in this paper we determine the sequences of join spaces and atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.