Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops and coops. As part of an investigation into the metatheory of propositional continuous logic...

A new fuzzy edge detector based on uninorms is proposed and deeply studied. The behaviour of different classes of uninorms is discussed. The obtained results suggest that the best uninorm in order to improve the edge detection process is the uninorm Umin, with underlying Lukasiewicz operators. This algorithm gets statistically substantial better results than the others obtained by well known ed...

In this paper we study extensions of the arithmetic operators +, −, ·, ÷ to the lattice L of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must fulfill, we investigate which properties they satisfy. We also investigate some classes of t-norms on L which can be generated using these operators; these classes provide natural extensions of the ...

Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truthvalues. In this paper we apply this idea to introduce multi-adjoint logic programs as an extension of monotonic logic programs. The continuity of the immediate consequences operators is proved a...

A dialogue game based approach to the problem of providing a deeper semantic foundation for t-norm based fuzzy logics is explored. In particular, various versions, extensions and alternatives to Robin Giles’s dialogue and betting game for Lukasiewicz logic are re-visited and put in the context of other foundational research in logic. It emerges that dialogue games cover a wide range of topics r...

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Lukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras ar...

trate, and Sulfate from Dried Urine Filter Paper Spots in a Pediatric Population, Nenad Blau, Ana Matasovic, Anna Lukasiewicz-Wedlechowicz, Claus W. Heizmann, and Ernst Leumann (Divisions of 1 Clinical Chemistry and Biochemistry and 2 Nephrology, University Children’s Hospital, Steinwiesstrasse 75, 8032 Zürich, Switzerland; * address for correspondence: University Children’s Hospital, Division ...

Continuing to pursue a research direction that we already explored in connection with Gödel-Dummett logic and Ruspini partitions, we show here that Lukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis. En route to our main result we obtain an elementary, logic-independent characterisation of triangu...

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, fuzzy MCDM method provide more acceptable and efficient outcomes to select best alternatives. This work consists of consensus-based technique for selecting evaluating suppliers in an incomplete preference relations (IFPRs) environment utilizing...