Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a type quantum computational logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness theorem.

In this paper, we made an attempt to study the algebraic nature of an anti (T, S)-fuzzy normal ideals and translations of anti S-fuzzy subhemiring of a hemiring. 2000 AMS Subject classification: 03F55, 06D72, 08A72.

We focus on some important fuzzy logic algebras on residuated lattices. These interesting algebraic structures and their main properties are reviewed, and their relationships are clarified. Corresponding formal deductive systems for fuzzy logic are

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

We have defined fuzzy bipolar soft sets and basic operations of union, intersection and complementation for fuzzy bipolar soft sets. The algebraic properties of fuzzy bipolar soft sets are discussed. The concept of bipolar fuzzy soft set is also given and the equivalence of both structures is established. An application of fuzzy bipolar soft sets in decision making problems is presented with th...

In 2004, G. Ganesan and C. Raghavendra Rao introduced the concept of Rough Fuzzy Groups. In this paper, we have adapted this approach in defining the algebraic closure of a given fuzzy graph using each vertex.

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is a powerful scheme for solving polynomial optimization problems with compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the case of non-compact semi-algebraic feasible sets. We d...

Physical Unclonable Functions (PUFs) provide cryptographic keys for embedded systems without secure non-volatile key storage. Several error correction schemes for key generation with PUFs were introduced, analyzed and implemented over the last years. This work abstracts from the typical algorithmic level and provides an algebraic view to reveal fundamental similarities and differences in the se...

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Fuzzy implication is proposed with the help of algebraic operations and a lattice stru...