Type-2 fuzzy sets have come to play an increasingly important role in both applications and in the general theory of fuzzy sets. The basis of type-2 fuzzy sets is a certain algebra of truth values, as set forth by Zadeh. This paper is a survey of results about this algebra, along with some new material.

Grey systems and interval valued fuzzy sets appear to be similar concepts. This abstract provides a brief introduction to grey systems and compares them to interval valued fuzzy sets. We argue that grey system is similar to an interval fuzzy set, but has different properties. Grey systems focus on the interval range of the system property itself, but interval fuzzy sets consider the fuzzy membe...

The purpose of this paper is to introduce a general framework for comparing fuzzy sets with respect to fuzzy orderings in a gradual way. This approach is applicable to fuzzy subsets of any kind of universe for which a fuzzy ordering, no matter whether linear or not, is known.

In this work we introduce the concept of a fusion operator for type-2 fuzzy sets as a mapping that takes m functions from [0, 1] to [0, 1] and brings back a new function of the same type. We study in depth the properties of pointwise fusion operators and representable fusion operators. Finally, we study the union and intersection of type2 fuzzy sets and we analyze when these functions are point...

Fuzziness is discussed in the context of multivalued lo&, and a corresponding view of fuzzy sets is given. Fuzzy random variables are introduced as random variables whose values are not real but fuzzy numbers, and subsequently redefined as a particular kind of fuzzy set. Expectations of fuzzy random variables, characteristic f~cti~ of fuzzy events, probabilities connected to fuzzy random variab...

In this paper we highlight the specific meaning of images of fuzzy sets under fuzzy relations in the context of fuzzy topology. More precisely we show that fuzzy modifiers taking direct and superdirect images of fuzzy sets under fuzzy pre-orderings are respectively closure and interior operators, inducing fuzzy topologies. Furthermore we investigate under which conditions the same applies to th...

Two definitions of fuzzy sets with Boolean-valued membership functions, introduced by Drossos and Markakis and called by them external and internal Boolean fuzzy sets, are compared with a third, classical definition descending more directly from the original Zadeh's and Goguen's ideas. Under some rather general conditions, internal and classical Boolean fuzzy sets are proved to be equivalent in...

the main purpose of this paper is to find t-best approximations in fuzzy normed spaces. we introduce the notions of t-proximinal sets and f-approximations and prove some interesting theorems. in particular, we investigate the set of all t-best approximations to an element from a set.

background: advances in information technology and data collection methods have enabled high-speed collection and storage of huge amounts of data. data mining can be used to derive laws from large data volumes and their characteristics. similarly, fuzzy logic by facilitating the understanding of events is considered a suitable complement to scientific data mining. materials and methods: the pre...

the present research aims to apply several approaches for suitability evaluation of lands under cultivation ofalfalfa and barley in chaharmil mechanized farming center, ardestan town, isfahan province, iran. climatic andsoil maps of the climate and soil data were provided in raster format. land evaluation carried out using maximumlimitation, parametric and multi-criteria (analytical hierarchy p...