the operations in the set of fuzzy numbers are usually obtained bythe zadeh extension principle. but these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. in fact the zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

The Generalized Constraint Language (GCL) , introduced by Zadeh, serves as a basis for computing with words (CW). It provides an agenda to express the imprecise and fuzzy information embedded in natural language and allows reasoning with perceptions. Despite its fundamental role, the definition of GCL has remained informal since its introduction by Zadeh (Zadeh 2004, 2005), and to our knowledge...

In many scientific and engineering applications, the fuzzy set concept plays an important role. The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables. The fuzzy set theory was introduced initially by Zadeh [1] in 1965. In the theory and applications of fuzzy sets, convexity is a most useful concept. In fact, in the basic and classical paper [1], Zad...

Reverse epidemiology, or risk factor paradox, has been used to describe the observed effect that traditional risk factors for cardiovascular disease may not necessarily signify the same risk for hemodialysis patients (HP) as for healthy populations. In fact, recent published findings have suggested counter-intuitive outcomes (Chavalitdhamrong, Danovitch, & Bunnapradist, 2007; Tsirpanlis et al.,...

Deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding, insightful analysis, and more e1ective design of fuzzy control systems. We previously developed a technique for deriving the analytical structure of the fuzzy controllers that use Zadeh fuzzy AND operator and the symmetric, identical trapezoidal or triangular input...

This paper describes the mathematical basis for a computer language which can be used for representing natural human reasoning with imprecise linguistic information. The approach to doing this employs a collection of abstraction mechanisms which are based on the concept of a linguistic variable first introduced by Zadeh [1975]. The present semantics differs from that of Zadeh, however, in that ...

Conventional system modeling techniques suggest constructing a model described by a set of differential or difference equations. This approach is effective only when the underlying system is mathematically well-defined and precisely expressible. They often fail to handle uncertain, vague or ill-defined physical systems, and yet most real-world problems do not obey such precise, idealized, and s...