… of crisp sets can be embedded into an algebra of fuzzy sets, and by Theorem 2.1 we have
seen that an algebra of fuzzy sets can always be identified with a non-Boolean algebra of …

… We assume basic familiarity with fuzzy logic and fuzzy sets [16, 13, 6]. An element may belong
to a fuzzy set in an intermediate … In general, there may be several crisp Bc’s with A = B↓ …

… , we refer to the latter as crisp sets. This name is now generally accepted in the literature.
In our presentation, we assume that the reader is familiar with fundamentals of the theory of …

… ; set theoretic operations for crisp and type-1 fuzzy sets; crisp … The same question could be
asked about crisp sets, and one … expected that analogous things can be done with fuzzy sets. …

… crisp results into fuzzy results, when such transference is possible. The focus of this work is
the area of fuzzy algebraic … As a final illustration we provide the analogous fuzzy ring theoretic …

… crisp reachability relation by a binary fuzzy relation whereas the set to be approximated remains
crisp… Finally, we state that there are surprising analogies between Fuzzy Diamond as we …

… in the study of fuzzy sets. We will see that fuzzy sets are natural generalizations of crisp sets.
… In fact, we will see that they satisfy ten properties which are analogues of those given in …

… This course would be analogous to a pre-calculus course where a student studies algebra,
… In order to see the connection between regular sets (now called crisp sets) and fuzzy sets …

… crisp and fuzzy sets is their membership function; a crisp set has a unique membership
function, whereas a fuzzy set … This is analogous to a two-input and single-output fuzzy system. …

… fuzzy set-theoretic-based methods can provide a perspective for describing illness and health
that is not available from conventional, crisp set-… of aging; analogous results were noted in …