46,605 research outputs found
Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets
Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures
Aggregation, non-contradiction ans excluded-middle
This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators
The Topology of Wireless Communication
In this paper we study the topological properties of wireless communication
maps and their usability in algorithmic design. We consider the SINR model,
which compares the received power of a signal at a receiver against the sum of
strengths of other interfering signals plus background noise. To describe the
behavior of a multi-station network, we use the convenient representation of a
\emph{reception map}. In the SINR model, the resulting \emph{SINR diagram}
partitions the plane into reception zones, one per station, and the
complementary region of the plane where no station can be heard. We consider
the general case where transmission energies are arbitrary (or non-uniform).
Under that setting, the reception zones are not necessarily convex or even
connected. This poses the algorithmic challenge of designing efficient point
location techniques as well as the theoretical challenge of understanding the
geometry of SINR diagrams. We achieve several results in both directions. We
establish a form of weaker convexity in the case where stations are aligned on
a line. In addition, one of our key results concerns the behavior of a
-dimensional map. Specifically, although the -dimensional map might
be highly fractured, drawing the map in one dimension higher "heals" the zones,
which become connected. In addition, as a step toward establishing a weaker
form of convexity for the -dimensional map, we study the interference
function and show that it satisfies the maximum principle. Finally, we turn to
consider algorithmic applications, and propose a new variant of approximate
point location.Comment: 64 pages, appeared in STOC'1
Menorah Review (No. 28, Spring, 1993)
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