fuzzy(sets)
fuzzy()所属R语言包：sets
Fuzzy logic
模糊逻辑
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Fuzzy Logic
模糊逻辑
用法----------Usage----------
fuzzy_logic(new, ...)
.N.(x)
.T.(x, y)
.S.(x, y)
.I.(x, y)
参数----------Arguments----------
参数：x, y
Numeric vectors.
数值向量。
参数：new
A character string specifying one of the available fuzzy logic “families” (see details).
一个字符串指定一个可用的模糊逻辑“家庭”（见详情）。
参数：...
optional parameters for the selected family.
可选参数为选定的家庭。
Details
详细信息----------Details----------
A call to fuzzy_logic() without arguments returns the currently set fuzzy logic, i.e., a named list with four components N, T, S, and I containing the corresponding functions for negation, conjunction (“t-norm”), disjunction (“t-conorm”), and residual implication (which may not be available).
fuzzy_logic()不带参数，返回当前设置的模糊逻辑，即四部分组成，命名列表N，T，S和I包含呼叫相应的否定，结合（“t-模”），分离（t-余范“），和残留的意义（这可能不可用）。
The package provides several fuzzy logic families. A concrete fuzzy logic is selected by calling fuzzy_logic with a character string specifying the family name, and optional parameters. Let us refer to N(x) = 1 - x as the standard negation, and, for a t-norm T, let S(x, y) = 1 - T(1 - x, 1 - y) be the dual (or complementary) t-conorm. Available specifications and corresponding families are as follows, with the standard negation used unless stated otherwise.
这个包提供了几个模糊逻辑家庭。一个具体的模糊逻辑是通过调用fuzzy_logic一个字符串指定的系列名称，参数和可选参数。让我们N(x) = 1 - x的标准否定的，为t-模T，让S(x, y) = 1 - T(1 - x, 1 - y)是双（或补充）t-余范。可用的规范及相应的家庭如下，除非另有说明，所使用的标准否定。
"Zadeh" Zadeh's logic with T = \min and S = \max. Note that the minimum t-norm, also known as the G枚del t-norm, is the pointwise largest t-norm, and that the
"Zadeh"T = \min和S = \maxZadeh的逻辑。需要注意的最低标准，也被称为哥德尔t-模，是逐点最大的t-模，而
"drastic" the drastic logic with t-norm T(x, y) = y if x = 1, x if y = 1, and 0 otherwise, and complementary t-conorm S(x, y) = y if x = 0, x if y = 0, and 1 otherwise. Note that the drastic t-norm and t-conorm are the smallest t-norm and
"drastic"大幅逻辑与t-模T(x, y) = y如果x = 1，x如果y = 1，否则为0，而互补的t-余范S(x, y) = y如果x = 0，x如果y = 0，否则为1。需要注意的是大幅t-模和t-余范是最小的t-模，
"product" the family with the product t-norm
"product"t-模的产品系列
"Lukasiewicz" the Lukasiewicz logic with t-norm T(x, y) = \max(0, x + y - 1) and dual t-conorm
"Lukasiewicz"Lukasiewicz逻辑与t-模T(x, y) = \max(0, x + y - 1)和双T-余模
"Fodor" the family with Fodor's nilpotent minimum t-norm given by T(x, y) = \min(x, y) if x + y > 1, and 0 otherwise, and the dual t-conorm given by
"Fodor"的家庭与Fodor的幂零的最低t-模由T(x, y) = \min(x, y)如果x + y > 1，否则为0，和双t-余范给出的
"Frank" the family of Frank t-norms T_p, p ≥ 0, which gives the Zadeh, product and Lukasiewicz t-norms for p = 0, 1, and Inf, respectively, and otherwise is given by
"Frank"的家庭弗兰克t-模T_p，p ≥ 0，这给扎德，产品和卢卡西维茨t-模p = 0，1，和Inf的 ，分别和否则给出的
"Hamacher" the three-parameter family of Hamacher, with negation N_γ(x) = (1 - x) / (1 + γ x), t-norm T_α(x, y) = xy / (α + (1 - α)(x + y - xy)), and t-conorm S_β(x, y) = (x + y + (β - 1) xy) / (1 + β xy), where α ≥ 0 and β, γ ≥ -1. This gives a deMorgan triple (for which N(S(x, y)) = T(N(x), N(y)) iff α = (1 + β) / (1 + γ). The parameters can be specified as alpha, beta and gamma, respectively. If α is not given, it is taken as α = (1 + β) / (1 + γ). The default values for β and γ are 0, so that
"Hamacher"三参数的三种，家庭的否定N_γ(x) = (1 - x) / (1 + γ x)，t-模T_α(x, y) = xy / (α + (1 - α)(x + y - xy))，和t-余范S_β(x, y) = (x + y + (β - 1) xy) / (1 + β xy)，其中α ≥ 0和<X >。这给了的德摩根三（β, γ ≥ -1，当且仅当N(S(x, y)) = T(N(x), N(y))。参数可以被指定为α = (1 + β) / (1 + γ)，alpha和beta，如果<X >没有给出，它是作为gammaα和α = (1 + β) / (1 + γ)0的默认值，因此，
The following parametric families are obtained by combining the corresponding families of t-norms with the standard negation.
以下参数家庭得到的相结合的相应的t-模与家庭的标准否定。
"Schweizer-Sklar" the Schweizer-Sklar family T_p, -Inf <= p <= Inf, which gives the Zadeh (minimum), product and drastic t-norms for p = -Inf, 0, and Inf, respectively, and otherwise is given by
"Schweizer-Sklar"了Schweizer-斯克拉家庭T_p，-Inf <= p <= Inf，这给的扎德（最小），产品和激烈的t-模p = -Inf，0， Inf，分别和其他被给予
"Yager" the Yager family T_p, p ≥ 0, which gives the drastic and minimum t-norms for p = 0 and Inf, respectively, and otherwise is given by
"Yager"彰显出家庭T_p，p ≥ 0，它给人的激烈和最小的t-模p = 0和Inf，分别和其他
"Dombi" the Dombi family T_p, p ≥ 0, which gives the drastic and minimum t-norms for p = 0 and Inf, respectively, and otherwise is given by T_p(x, y) = 0 if x = 0 or y = 0, and T_p(x, y) = 1 / (1 + ((1/x - 1)^p + (1/y - 1)^p)^{1/p}) if
"Dombi"Dombi家庭T_p，p ≥ 0，它给人的激烈和最小的t-模p = 0和Inf，分别和其他的 T_p(x, y) = 0，如果x = 0或y = 0和T_p(x, y) = 1 / (1 + ((1/x - 1)^p + (1/y - 1)^p)^{1/p})，如果
"Aczel-Alsina" the family of t-norms T_p, p ≥ 0, introduced by Acz茅l and Alsina, which gives the drastic and minimum t-norms for p = 0 and Inf, respectively, and otherwise is given by
"Aczel-Alsina"t-模的家人T_p，p ≥ 0，引入，给出了激烈的和最小的T-p = 0和Inf规范Aczél和阿尔西纳，分别和否则给出的
"Sugeno-Weber" the family of t-norms T_p, -1 <= p <= Inf, introduced by Weber with dual t-conorms introduced by Sugeno, which gives the drastic and product t-norms for p = -1 and Inf, respectively, and otherwise is given by
"Sugeno-Weber"t-模的家人T_p，-1 <= p <= Inf，韦伯双T-Sugeno型，给人的激烈，产品T-p = -1规范引入conorms和Inf，分别，并以其他方式由下式给出
"Dubois-Prade" the family of t-norms T_p, 0 ≤ p ≤ 1, introduced by Dubois and Prade, which gives the minimum and product t-norms for p = 0 and 1, respectively, and otherwise is given by
"Dubois-Prade"t-模的家人T_p，0 ≤ p ≤ 1，引入杜波依斯和普拉德，给出了最小的产品t-模p = 0和1 ，分别和否则给出的
"Yu" the family of t-norms T_p, p ≥ -1, introduced by Yu, which gives the product and drastic t-norms for p = -1 and Inf, respectively, and otherwise is
"Yu"t-模的家人T_p，p ≥ -1，分别于引入，使得产品和激烈的p = -1和Inft-模， ，否则为
By default, the Zadeh logic is used.
默认情况下，扎德逻辑。
.N., .T., .S., and .I. are dynamic functions, i.e., wrappers that call the corresponding function of the current fuzzy logic. Thus, the behavior of code using these functions will change according to the chosen logic.
.N.，.T.，.S.和.I.是动态的功能，即包装的模糊逻辑，调用相应的函数。因此，使用这些函数的代码的行为将改变，根据所选择的逻辑。
参考文献----------References----------
Associative Functions: Triangular Norms and Copulas. World Scientific. ISBN 981-256-671-6.
A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets and Systems 8, 149–163.
Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht.
Generalized and customizable sets in R, Journal of Statistical Software 31(2), 1–27. http://www.jstatsoft.org/v31/i02/
Probabilistic Metric Spaces. North-Holland, New York. ISBN 0-444-00666-4.
实例----------Examples----------
x <- c(0.7, 0.8)
y <- c(0.2, 0.3)
## Use default family ("Zadeh")[＃使用默认的家庭（“扎德”）]
.N.(x)
.T.(x, y)
.S.(x, y)
.I.(x, y)
## Switch family and try again[＃开关产品系列，然后再试一次]
fuzzy_logic("Fodor")
.N.(x)
.T.(x, y)
.S.(x, y)
.I.(x, y)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 01:33:21
