The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program. This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming.

in today’s competitive market, for a business firm to win higher profit among its rivals, it is of necessity to evaluate, and rank its potential customer segments to improve its customer relationship management (crm). this brings the importance of having more efficient decision making methods considering the current fast growing information era. these decisions usually involve several criteria,...

The main goal of this publication is to show that the basic constructions in theories fuzzy sets, soft hesitant sets or intuitionistic have a common background, based on theory monads categories. It proven ad hoc defined concepts individual theories, such as power set structures these relations approximation operators by are only special examples applications monad This makes it possible, one h...

In this paper, a different approach to extract the threshold value β of Variable Precision Rough Set (VPRS) applied to continuous information systems is presented. This study combines the Fuzzy Set and Rough Fuzzy Set (RFS) theories to determine the β value of VPRS. The β value was determined by the Fuzzy C-means and relevant Fuzzy theories, for the reason that errors of system classification c...