Logical Foundations of Fuzzy Mathematics Logické základy fuzzy matematiky

General Logical Formalism for Fuzzy Mathematics: Methodology and Apparatus∗

There is a programme in the formal foundations of fuzzy mathematics proposed by the authors, the goal of which is to encompass a large part of existing fuzzy mathematics within a general logical formalism. This paper presents the methodology behind this programme and reviews the technical aspects of a particular apparatus for this enterprise.

Mathematics behind Fuzzy Logic

Fuzzy set theoretical approach to numerous problems of applied mathematics and, especially, fuzzy logical analysis of those problems become frequent in the modern mathematical modelling of the real world. It is desirable to offer the mathematically oriented reader a summary of the background of the principles of fuzzy logic in a lucid and compact form. The referred book aims to offer such summa...

POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES

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...

A duality between LM-fuzzy possibility computations and their logical semantics

Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. T...

Possible New Directions in Mathematical Foundations of Fuzzy Technology: a Contribution to the Mathematics of Fuzzy Theory