@@ -5,9 +5,9 @@ <h2>OPTIONS</h2>
55require null values.
66</ dd >
77< dt > < b > points</ b > </ dt >
8- < dd > A list containing 4 (A,B,C,D) or 2 A,B) points defining set boundaries.
9- Points must not to be in map range, but it may lead to only 0 o 1 membership for
10- the whole map. For "both" side parameters range between A and D defines base,
8+ < dd > A list containing 4 (A,B,C,D) or 2 ( A,B) points defining set boundaries.
9+ Points do not have to be in map range, but this may lead to only 0 o 1 membership for
10+ the whole map. For side parameter "both", range between A and D defines base,
1111but range between B and C core of the fuzzy set. Between A and B and C and D are
1212set's boundaries. If side is "both" it require 4 points, else 2 points.
1313< center >
@@ -16,7 +16,7 @@ <h3>Fuzzy set definition:</h3>
1616</ center >
1717</ dd >
1818< dt > < b > side</ b > </ dt >
19- < dd > Option indicate if set is fuzzified of both sides (both), left or right
19+ < dd > Option indicates if set is fuzzified of both sides (both), left or right
2020side. See description for details.
2121< center >
2222< h3 > Boundary definition:</ h3 >
@@ -42,7 +42,7 @@ <h2>FUZZY SET PARAMETERS</h2>
4242< dt > < b > shape</ b > </ dt >
4343< dd > Optional shape modifier. Range from -1 to 1. The default value is 0 and
4444should not be changed in most of the time. The negative values indicate more
45- dilatant set, the positive values more concentrate set. See description for
45+ dilatant set, the positive values more concentrate set. See NOTES for
4646details.
4747< center >
4848< h3 > Impact of shape parameter on shape boundary:</ h3 >
@@ -51,22 +51,22 @@ <h3>Impact of shape parameter on shape boundary:</h3>
5151</ dd >
5252< dt > < b > height</ b > </ dt >
5353< dd > Optional height modifier. Range from 0 to 1. The default value is 1 and
54- indicate full membership between points B and C . If height is lesser than one the
54+ indicates full membership. If height is less than one the
5555maximum membership is equal to height. See image: Fuzzy set definition.</ dd >
5656</ dl >
5757
5858< h2 > DESCRIPTION</ h2 >
5959
6060< h4 > Definition of fuzzy set</ h4 >
6161Fuzzy sets are sets whose elements have degrees of membership. Zadeh (1965)
62- introduced Fuzzy sets as an extension of the classical notion of set . Classical
62+ introduced Fuzzy sets as an extension of the classical notion of sets . Classical
6363membership of elements in a set are binary terms: an element either belongs or
6464does not belong to the set. Fuzzy set theory use the gradual assessment of the
6565membership of elements in a set. A membership function valued in the real unit
6666interval [0, 1]. Classical sets, are special cases of the membership functions
6767of fuzzy sets, if the latter only take values 0 or 1. Classical sets are in
68- fuzzy set theory usually called crisp sets. The fuzzy set theory can be used in
69- a wide range of domains in which information is imprecise, such as most of the
68+ fuzzy set theory usually called crisp sets. Fuzzy set theory can be used in
69+ a wide range of domains in which information is imprecise, including many
7070GIS operations.
7171
7272
@@ -78,10 +78,10 @@ <h4>Calculation of boundary shape</h4>
7878< b > Linear:</ b > the membership is calculated according following equation:< br >
7979< pre > < code >
8080value < = A -> x = 0
81- A< value > B -> x = (value-A)/(B-A)
81+ A < value > B -> x = (value-A)/(B-A)
8282B < = value > = C -> x = 1
83- C< value > D -> x = (D-value)/(D-C)
84- value > = D -> x = 0
83+ C < value > D -> x = (D-value)/(D-C)
84+ value > = D -> x = 0
8585
8686where x: membership
8787</ code > </ pre >
@@ -117,31 +117,37 @@ <h4>Calculation of boundary shape</h4>
117117< h2 > SEE ALSO</ h2 >
118118
119119< em >
120- < a href ="r.fuzzy.logic.html "> r.fuzzy.logic</ a > ,
120+ < a href ="r.fuzzy.logic.html "> r.fuzzy.logic</ a > addon,
121+ < a href ="r.fuzzy.system.html "> r.fuzzy.system</ a > addon,
121122< a href ="r.mapcalc.html "> r.mapcalc</ a > ,
122123</ em >
123124
124125
125126< h2 > REFERENCES</ h2 >
126127
127- < p > Zadeh, L.A. (1965). "Fuzzy sets". Information and Control 8 (3): 338–353.
128- doi:10.1016/S0019-9958(65)90241-X. ISSN 0019-9958.</ P >
128+ < ul >
129+ < li > Jasiewicz, J. (2011). A new GRASS GIS fuzzy inference system for massive data analysis.
130+ Computers & Geosciences (37) 1525-1531. DOI < a href =https://doi.org/10.1016/j.cageo.2010.09.008 "> https://doi.org/10.1016/j.cageo.2010.09.008</ a >
129131
130- < p > Novák, Vilém (1989 ). Fuzzy Sets and Their Applications. Bristol: Adam Hilger .
131- ISBN 0-85274-583-4. </ P >
132+ < li > Zadeh, L.A. (1965 ). " Fuzzy sets". Information and Control 8 (3): 338–353 .
133+ < a href =" https://doi.org/10.1016/S0019-9958(65)90241-X " > < a href =" https://doi.org/10.1016/S0019-9958(65)90241-X " </ a > .
132134
133- < p > Klir, George J.; Yuan, Bo (1995 ). Fuzzy sets and fuzzy logic: theory and
134- applications. Upper Saddle River, NJ: Prentice Hall PTR. ISBN 0-13-101171-5. </ P >
135+ < li > Novák, Vilém (1989 ). Fuzzy Sets and Their Applications. Bristol: Adam Hilger.
136+ ISBN 0-85274-583-4.
135137
136- < p > Klir, George J.; St Clair, Ute H.; Yuan, Bo (1997). Fuzzy set theory:
138+ < li > Klir, George J.; Yuan, Bo (1995). Fuzzy sets and fuzzy logic: theory and
139+ applications. Upper Saddle River, NJ: Prentice Hall PTR. ISBN 0-13-101171-5.
140+
141+ < li > Klir, George J.; St Clair, Ute H.; Yuan, Bo (1997). Fuzzy set theory:
137142foundations and applications. Englewood Cliffs, NJ: Prentice Hall. ISBN
138- 0133410587.</ P >
143+ 0133410587.
139144
140- < p > Meyer D, Hornik K (2009a). \ Generalized and Customizable Sets in R." Journal
141- of Statistical Software, 31(2), 1{ 27. URL http ://www.jstatsoft. org/v31/ i02/. </ P >
145+ < li > Meyer D, Hornik K (2009a). Generalized and Customizable Sets in R. Journal of
146+ Statistical Software, 31(2), 1- 27. DOI < a href =" https ://doi. org/10.18637/jss.v031. i02" > https://doi.org/10.18637/jss.v031.i02 </ a >
142147
143- Meyer D, Hornik K (2009b). sets: Sets, Generalized Sets, and Customizable Sets.
144- R~package version~1.0, URL http://CRAN.R-project.org/package=sets.< p >
148+ < li > Meyer D, Hornik K (2009b). sets: Sets, Generalized Sets, and Customizable Sets.
149+ R~package version~1.0, URL < a href ="http://CRAN.R-project.org/package=sets "> http://CRAN.R-project.org/package=sets</ a > .
150+ </ ul >
145151
146152< h2 > AUTHOR</ h2 >
147153Jarek Jasiewicz
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