The main concern of this paper is with the equations satisfied by the algebra of truth values of type-2 fuzzy sets. That algebra has elements all mappings from the unit interval into itself with operations given by certain convolutions of operations on the unit interval. There are a number of positive results. Among them is a decision procedure, similar to the method of truth tables, to determi...

A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [25]. An analogous approach to representing and manipulating uncertainty in choosing among alternatives (design imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. Examples using both approaches are ...

We study graded properties (α–properties) of fuzzy relations, which are parameterized versions of fuzzy relation properties defined by L.A. Zadeh. Namely, we take into account fuzzy relations which are: α–reflexive, α– irreflexive, α–symmetric, α–antisymmetric, α–asymmetric, α–connected, α–transitive, where α ∈ [0, 1]. We also pay our attention to the composed versions of these basic properties...

In this paper, the Fuzzy Vector Median is proposed, defined as an extension of Vector Median. It is based on a novel distance definition of multidimensional fuzzy numbers (fuzzy vectors), which satisfy the property of angle decomposition. The proposed distance of two fuzzy vectors depends on the classical distance of the fuzzy set centers and on the fuzziness that every fuzzy set holds. As a re...

Three definitions of fuzzy random variables (FRVs) have been cited in the current literature: the first is due to Kwakernaak (1978), who viewed a FRV as a vague perception of a crisp but unobservable RV; the second is due to Puri and Ralescu (1986), who regarded FRVs as random fuzzy sets; and the third is due to Liu and Liu (2003), whose notion of FRV was based on a concept they called a credib...

The division operator is well known in the context of fuzzy relational databases. Fuzzy approaches to this operator can be found in the literature to solve flexible queries: these approaches try to compute to which extent each element of a candidate set is connected with a given (fuzzy) set of elements. This kind of queries is also interesting in the framework of fuzzy object databases, where t...

Multisets alias bags are similar to fuzzy sets but essentially different in basic concepts and operations. We overview multisets together with basics of fuzzy sets in order to observe differences between the two. We then introduce fuzzy multisets and the combination of the both concepts. There is another concept of real-valued multisets as a generalization of multisets. Rough approximations of ...

Effective retrieval of structured documents should exploit the content and structural knowledge associated with the documents. This knowledge can be used to focus retrieval to the best entry points: document components that contain relevant information, and from which users can browse to retrieve further relevant components. To enable this, suitable representation methods must be developed. Thi...

Remarks on history, theory, and applications of intuitionistic fuzzy sets are given. Some open problems are introduced.

Let R be a commutative ring with non-zero identity and let M be a non-zero unitary R-module. The concept of fuzzy coprimary submodule as a dual notion of fuzzy primary one will be introduced and some of its properties will be studied. Among other things, the behavior of this concept with respect to fuzzy localization formation and fuzzy quotient will be examined.