Dear Colleagues

Dear Colleagues This and the next special issues of Reliable Computing contain a rich set of articles that attest to the synergism between interval analysis and fuzzy set theory. The relationships between interval analysis and fuzzy set theory are many. The most obvious relationship is arithmetic since fuzzy arithmetic is interval arithmetic on alpha-cuts (see [3], [4]). The second more basic relationship, since it is how interval and fuzzy arithmetic can be derived as well as how functions in the interval and fuzzy analysis setting (and many mathematical relationships) are defined, is the extension principle (see [8], [12], [14]). The extension principle in interval analysis is called the united extension (see [5]–[7]). The third relationship is perhaps more explicit; this is fuzzy interval analysis (see [1], [2]). Here, the use of interval analysis in fuzzy set theory is direct. Of course, from the beginning ([9], [11], [13]) an interval [a, b] was considered as a number and this lead to interval analysis. Moveover, an interval is also a set. As a set, an interval is also a fuzzy set with rectangular membership function 1, x ∈ [a, b], µ (x)= [a, b] 0, otherwise. Therefore, from the point of view of Reliable Computing Springer Journals

Dear Colleagues

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Kluwer Academic Publishers
Copyright © 2004 by Kluwer Academic Publishers
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
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