In this paper we investigate the propositional logic of standard algebras for Hájek’s Basic Fuzzy Logic BL in a language expanded with propositional constants for the idempotent elements delimiting the L-, G-, and Π-components of the algebra. We start from a fixed standard BL-algebra; introduce new propositional constants; present a suitable set of axioms; investigate completeness results; and ...

This paper presents a tableau calculus for finding a model for a set-satisfiable finite set of formulas of a fuzzy logic BL△∼, a fuzzy logic BL with additional Baaz connective △ and the involutive negation ∼, if such a model exists. The calculus is a generalisation of a tableau calculus for BL, which is based on the decomposition theorem for a continuous t-norm. The aforementioned tableau calcu...

This work focuses on adapting artificial intelligence techniques for urban growth modeling using multitemporal imagery. Fuzzy set theory and cellular automata are used for this purpose. Fuzzy set theory preserves the spatial continuity of the growth process through allowing a test pixel to be partially developed unlike the binary crisp system (developed/undeveloped). The development level ident...

We show that the 2-parameter Podles sphere is a q-fuzzy sphere precisely interpolating between the fuzzy sphere as quotient of the angular momentum algebra U(su2) and the standard q-sphere Cq [S] as subalgebra of the quantum group Cq [SU2]. Whereas the classical sphere as CP 1 can be defined as the algebra generated by the matrix entries of a projector e with trace(e) = 1, the fuzzy-sphere is d...

An interpretation of lattice-valued logic, defined by Titani, in basic fuzzy logic, defined by Hájek, is presented. Moreover, Titani’s axioms of lattice-valued set theory are interpreted in fuzzy set theory, under slight modifications of the fuzzy set theory axiomatics.

BL-algebras are algebraic structures corresponding to Hajek’s basic fuzzy logic. The aim of this paper is analyze the structure using commutative rings. Due computational considerations, we interested in finite case. We present new ways generate rings and provide summarizing statistics. Furthermore, investigated BL-rings, i.e., whose lattice ideals can be equipped with a BL-algebra. A character...