112 research outputs found
Visual characterization of associative quasitrivial nondecreasing operations on finite chains
In this paper we provide visual characterization of associative quasitrivial
nondecreasing operations on finite chains. We also provide a characterization
of bisymmetric quasitrivial nondecreasing binary operations on finite chains.
Finally, we estimate the number of functions belonging to the previous classes.Comment: 25 pages, 18 Figure
Distributivity between extended nullnorms and uninorms on fuzzy truth values
This paper mainly investigates the distributive laws between extended
nullnorms and uninorms on fuzzy truth values under the condition that the
nullnorm is conditionally distributive over the uninorm. It presents the
distributive laws between the extended nullnorm and t-conorm, and the left and
right distributive laws between the extended generalization nullnorm and
uninorm, where a generalization nullnorm is an operator from the class of
aggregation operators with absorbing element that generalizes a nullnorm.Comment: 2
Implication functions in interval-valued fuzzy set theory
Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory
Relating Kleene algebras with pseudo uninorms
This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect is potentially useful as a source of formalism to capture and model programs acting with fuzzy behaviours and domains.publishe
Distributivity of strong implications over conjunctive and disjunctive uninorms
summary:This paper deals with implications defined from disjunctive uninorms by the expression where is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a -norm or a -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications are derived from -conorms
On the distributivity equation for uni-nullnorms
summary:A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet been fully characterized
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