This paper is devoted to the evaluation of conditions involving aggregates in the context of flexible querying of relational databases. An example of such a condition is “the maximum salary of young employees is high”, where the aggregate max applies to a fuzzy set of salaries. At first, we consider the evaluation of quantified statements where the aggregate count (the cardinality) is implicitl...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

Many financial decisions involve a need to satisfy multiple criteria (goals). This situation becomes particularly apparent in problems of investment allocation where we are faced with the problem of selecting from a collection of alternative investment packages one that meets our subjective goals such as growth, security and a reasonable return on investment. Another closely related problem, on...

nThis paper transmits a FORTRAN-IV coding of the fuzzy c-means (FCM) clustering program. The FCM program is applicable to a wide variety of geostatistical data analysis problems. This program generates fuzzy partitions and prototypes for any set of numerical data. These partitions are useful for corroborating known substructures or suggesting substructure in unexplored data. The clustering crit...

Aggregating measure scores is an important step in multiple criteria decision-making, determining the overall effectiveness from dissimilar measures. One of the most popular aggregating methods is Simple Additive Weighting (SAW), which assigns weights to measures based on subjective preference information, and sum weighted scores up. The quality of overall score is highly dependent on the quali...