Triangle algebras: a formal logic approach to interval-valued residuated lattices, fuzzy sets and systems.

Content Provider	CiteSeerX
Author	Gasse, B. Van Cornelis, C. Deschrijver, G. Kerre, E. E.
Abstract	In this paper, we introduce triangle algebras: a variety of residuated lattices equipped with approximation operators, and with a third angular point u, different from 0 and 1. We show that these algebras serve as an equational representation of intervalvalued residuated lattices (IVRLs). Furthermore, we present Triangle Logic (TL), a system of many-valued logic capturing the tautologies of IVRLs. Triangle algebras are used to cast the essence of using closed intervals of L as truth values into a set of appropriate logical axioms. Our results constitute a crucial first step towards solving an important research challenge: the axiomatic formalization of residuated t-norm based logics on L I, the lattice of closed intervals of [0,1], in a similar way as was done for formal fuzzy logics on the unit interval. Key words: formal logic, interval-valued fuzzy set theory, residuated lattices
File Format	PDF
Access Restriction	Open
Subject Keyword	Triangle Algebra Interval-valued Residuated Lattice Fuzzy Set Formal Logic Approach Residuated Lattice Closed Interval Third Angular Point Approximation Operator Formal Fuzzy Logic Interval-valued Fuzzy Set Theory Many-valued Logic Unit Interval Truth Value Important Research Challenge Triangle Logic Axiomatic Formalization Equational Representation Crucial First Step Towards Appropriate Logical Axiom Key Word Formal Logic Similar Way
Content Type	Text