Fuzzy set

In mathematics, fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced by Lotfi A. Zadeh and Dieter Klaua in 1965 as an extension of the classical notion of set. At the same time, Salii (1965) defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are used now in different areas, such as linguistics (De Cock, Bodenhofer & Kerre 2000) decision-making (Kuzmin 1982) and clustering (Bezdek 1978), are special cases of L-relations when L is the unit interval [0, 1].

In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition — an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0, 1]. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. In fuzzy set theory, classical bivalent sets are usually called crisp sets. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics.

Collective Soul (2009 album)

Collective Soul, also known as Rabbit to differentiate it from the band's 1995 album of the same name, is the eighth studio album by American rock band Collective Soul. It was released on August 25, 2009.

Background

Rabbit is Collective Soul's first release with a parent label since the group started its own independent El Music Group label in 2004. It also effectively marks their return to Atlantic Records, as that label purchased Roadrunner in 2006.

Rabbit includes two songs ("You" and "Understanding") that were written by all members in the band, a first for Collective Soul. According to the singer, guitarist and keyboard player Ed Roland: "I think it's the confidence that the other guys have gotten in their music skills and the songwriting and also, for lack of a better term, me letting go of my ego a little bit..."

Track listing

All songs written by Ed Roland except where noted.

Fuzzy (album)

Released in 1993, Fuzzy is the debut album by Los Angeles rock group Grant Lee Buffalo. Called "The best album of the year hands down" by R.E.M's Michael Stipe, "Fuzzy would galvanize the sound of Grant Lee Buffalo, i.e., the acoustic feedback howl of overdriven 12-string guitars, melodic distorto-bass, tribal drum bombast, the old world churn of pump organs and parlor pianos."

Track listing

References

External links

Set (music)

A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.

A set by itself does not necessarily possess any additional structure, such as an ordering. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.

Two-element sets are called dyads, three-element sets trichords (occasionally "triads", though this is easily confused with the traditional meaning of the word triad). Sets of higher cardinalities are called tetrachords (or tetrads), pentachords (or pentads), hexachords (or hexads), heptachords (heptads or, sometimes, mixing Latin and Greek roots, "septachords"—e.g.,), octachords (octads), nonachords (nonads), decachords (decads), undecachords, and, finally, the dodecachord.

Set (darts)

A set in darts consists of a sequence of legs (games) played, ending when the count of legs won meets certain criteria. Throwing first is considered an advantage in a leg, so players alternate who throws first in each leg during the set.

Generally, a set will consist of the best of five legs (first player to win three) - although there are some exceptions. The most notable being the Winmau World Masters, where a set is the best of three legs (first to two).

Example

During the final of the 2007 PDC World Darts Championship, Raymond van Barneveld defeated Phil Taylor by seven sets to six in one of the most dramatic darts matches of all-time. The breakdown of how each set went is shown here.

Taylor won the first two sets by three legs to nil, then added the third set before van Barneveld took the next two. The match continued and went to six sets all. Neither player managed to gain a two-leg advantage in the final set "tiebreak" so the deciding leg was played when the score reached 5-5. Before the final leg, the players threw for the bullseye with the nearest given the advantage of throwing first.

Set construction

Set construction is the process by which a construction manager undertakes to build full scale scenery suitable for viewing by camera, as specified by a production designer or art director working in collaboration with the director of a production to create a set for a theatrical, film or television production. The set designer produces a scale model, scale drawings, paint elevations (a scale painting supplied to the scenic painter of each element that requires painting), and research about props, textures, and so on. Scale drawings typically include a groundplan, elevation, and section of the complete set, as well as more detailed drawings of individual scenic elements which, in theatrical productions, may be static, flown, or built onto scenery wagons. Models and paint elevations are frequently hand-produced, though in recent years, many Production Designers and most commercial theatres have begun producing scale drawings with the aid of computer drafting programs such as AutoCAD or Vectorworks.