Document (#21926)

Author

Atanassow, K.T.

Title

Intuitionistic Fuzzy Sets

Imprint

Heidelberg : Springer

Year

1999

Pages

XVIII,323 S

Isbn

3-7908-1228-5

Series

Studies in fuzziness and soft computing; vol.35

Abstract

The basic definitions and properties of the Intuitionistic Fuzzy Sets (IFSs) are introduced in the book. The IFSs are substantial extensions of the ordinary fuzzy sets. IFSs are objects having degrees of membership and of non-membership, such that their sum is exactly 1. The most important property of IFS not shared by the fuzzy sets is that modal-like operatores can be defined over IFSs

Similar documents (content)

1. Zadeh, L.A.: Fuzzy sets (1965) 0.48

   0.48395073 = sum of:
     0.48395073 = product of:
       1.7283955 = sum of:
         0.01752566 = weight(abstract_txt:such in 5459) [ClassicSimilarity], result of:
           0.01752566 = score(doc=5459,freq=2.0), product of:
             0.038639706 = queryWeight, product of:
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.011294824 = queryNorm
             0.4535661 = fieldWeight in 5459, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
         0.008188118 = weight(abstract_txt:that in 5459) [ClassicSimilarity], result of:
           0.008188118 = score(doc=5459,freq=1.0), product of:
             0.036931213 = queryWeight, product of:
               1.3825947 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.011294824 = queryNorm
             0.22171268 = fieldWeight in 5459, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
         0.05041487 = weight(abstract_txt:objects in 5459) [ClassicSimilarity], result of:
           0.05041487 = score(doc=5459,freq=1.0), product of:
             0.0984691 = queryWeight, product of:
               1.5963682 = boost
               5.4611917 = idf(docFreq=512, maxDocs=44421)
               0.011294824 = queryNorm
             0.51198673 = fieldWeight in 5459, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.4611917 = idf(docFreq=512, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
         0.06287509 = weight(abstract_txt:properties in 5459) [ClassicSimilarity], result of:
           0.06287509 = score(doc=5459,freq=1.0), product of:
             0.11408975 = queryWeight, product of:
               1.7183293 = boost
               5.878422 = idf(docFreq=337, maxDocs=44421)
               0.011294824 = queryNorm
             0.55110204 = fieldWeight in 5459, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.878422 = idf(docFreq=337, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
         0.45176288 = weight(abstract_txt:membership in 5459) [ClassicSimilarity], result of:
           0.45176288 = score(doc=5459,freq=3.0), product of:
             0.37111127 = queryWeight, product of:
               4.382785 = boost
               7.496775 = idf(docFreq=66, maxDocs=44421)
               0.011294824 = queryNorm
             1.2173246 = fieldWeight in 5459, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               7.496775 = idf(docFreq=66, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
         0.34463477 = weight(abstract_txt:sets in 5459) [ClassicSimilarity], result of:
           0.34463477 = score(doc=5459,freq=4.0), product of:
             0.35467744 = queryWeight, product of:
               6.0594034 = boost
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.011294824 = queryNorm
             0.97168505 = fieldWeight in 5459, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
         0.792994 = weight(abstract_txt:fuzzy in 5459) [ClassicSimilarity], result of:
           0.792994 = score(doc=5459,freq=4.0), product of:
             0.61816937 = queryWeight, product of:
               7.9995737 = boost
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.011294824 = queryNorm
             1.2828103 = fieldWeight in 5459, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.09375 = fieldNorm(doc=5459)
       0.28 = coord(7/25)
   

2. Miyamoto, S.: Application of rough sets to information retrieval (1998) 0.30

   0.3014937 = sum of:
     0.3014937 = product of:
       1.5074685 = sum of:
         0.04421785 = weight(abstract_txt:defined in 1559) [ClassicSimilarity], result of:
           0.04421785 = score(doc=1559,freq=1.0), product of:
             0.0902248 = queryWeight, product of:
               1.5280799 = boost
               5.2275767 = idf(docFreq=647, maxDocs=44421)
               0.011294824 = queryNorm
             0.4900853 = fieldWeight in 1559, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.2275767 = idf(docFreq=647, maxDocs=44421)
               0.09375 = fieldNorm(doc=1559)
         0.057700094 = weight(abstract_txt:introduced in 1559) [ClassicSimilarity], result of:
           0.057700094 = score(doc=1559,freq=1.0), product of:
             0.10774039 = queryWeight, product of:
               1.6698303 = boost
               5.7125063 = idf(docFreq=398, maxDocs=44421)
               0.011294824 = queryNorm
             0.5355475 = fieldWeight in 1559, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.7125063 = idf(docFreq=398, maxDocs=44421)
               0.09375 = fieldNorm(doc=1559)
         0.36886284 = weight(abstract_txt:membership in 1559) [ClassicSimilarity], result of:
           0.36886284 = score(doc=1559,freq=2.0), product of:
             0.37111127 = queryWeight, product of:
               4.382785 = boost
               7.496775 = idf(docFreq=66, maxDocs=44421)
               0.011294824 = queryNorm
             0.99394137 = fieldWeight in 1559, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.496775 = idf(docFreq=66, maxDocs=44421)
               0.09375 = fieldNorm(doc=1559)
         0.24369358 = weight(abstract_txt:sets in 1559) [ClassicSimilarity], result of:
           0.24369358 = score(doc=1559,freq=2.0), product of:
             0.35467744 = queryWeight, product of:
               6.0594034 = boost
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.011294824 = queryNorm
             0.6870851 = fieldWeight in 1559, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.09375 = fieldNorm(doc=1559)
         0.792994 = weight(abstract_txt:fuzzy in 1559) [ClassicSimilarity], result of:
           0.792994 = score(doc=1559,freq=4.0), product of:
             0.61816937 = queryWeight, product of:
               7.9995737 = boost
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.011294824 = queryNorm
             1.2828103 = fieldWeight in 1559, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.09375 = fieldNorm(doc=1559)
       0.2 = coord(5/25)
   

3. Fuzziness in database management systems (1995) 0.28

   0.27920148 = sum of:
     0.27920148 = product of:
       1.3960073 = sum of:
         0.02363877 = weight(abstract_txt:over in 2191) [ClassicSimilarity], result of:
           0.02363877 = score(doc=2191,freq=1.0), product of:
             0.05943069 = queryWeight, product of:
               1.2401907 = boost
               4.242705 = idf(docFreq=1734, maxDocs=44421)
               0.011294824 = queryNorm
             0.3977536 = fieldWeight in 2191, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.242705 = idf(docFreq=1734, maxDocs=44421)
               0.09375 = fieldNorm(doc=2191)
         0.035457447 = weight(abstract_txt:book in 2191) [ClassicSimilarity], result of:
           0.035457447 = score(doc=2191,freq=1.0), product of:
             0.0778752 = queryWeight, product of:
               1.4196545 = boost
               4.8566523 = idf(docFreq=938, maxDocs=44421)
               0.011294824 = queryNorm
             0.45531115 = fieldWeight in 2191, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.8566523 = idf(docFreq=938, maxDocs=44421)
               0.09375 = fieldNorm(doc=2191)
         0.1220021 = weight(abstract_txt:extensions in 2191) [ClassicSimilarity], result of:
           0.1220021 = score(doc=2191,freq=1.0), product of:
             0.1774894 = queryWeight, product of:
               2.1432326 = boost
               7.33202 = idf(docFreq=78, maxDocs=44421)
               0.011294824 = queryNorm
             0.68737686 = fieldWeight in 2191, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.33202 = idf(docFreq=78, maxDocs=44421)
               0.09375 = fieldNorm(doc=2191)
         0.24369358 = weight(abstract_txt:sets in 2191) [ClassicSimilarity], result of:
           0.24369358 = score(doc=2191,freq=2.0), product of:
             0.35467744 = queryWeight, product of:
               6.0594034 = boost
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.011294824 = queryNorm
             0.6870851 = fieldWeight in 2191, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.09375 = fieldNorm(doc=2191)
         0.9712155 = weight(abstract_txt:fuzzy in 2191) [ClassicSimilarity], result of:
           0.9712155 = score(doc=2191,freq=6.0), product of:
             0.61816937 = queryWeight, product of:
               7.9995737 = boost
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.011294824 = queryNorm
             1.5711155 = fieldWeight in 2191, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.09375 = fieldNorm(doc=2191)
       0.2 = coord(5/25)
   

4. Chen, R.-S.; Hu, Y.-C.: ¬A novel method for discovering Fuzzy sequential patterns using the simple Fuzzy partition method (2003) 0.28

   0.27690664 = sum of:
     0.27690664 = product of:
       1.3845332 = sum of:
         0.005458745 = weight(abstract_txt:that in 2614) [ClassicSimilarity], result of:
           0.005458745 = score(doc=2614,freq=1.0), product of:
             0.036931213 = queryWeight, product of:
               1.3825947 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.011294824 = queryNorm
             0.14780845 = fieldWeight in 2614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.0625 = fieldNorm(doc=2614)
         0.089668185 = weight(abstract_txt:exactly in 2614) [ClassicSimilarity], result of:
           0.089668185 = score(doc=2614,freq=1.0), product of:
             0.18941481 = queryWeight, product of:
               2.2140634 = boost
               7.574333 = idf(docFreq=61, maxDocs=44421)
               0.011294824 = queryNorm
             0.47339582 = fieldWeight in 2614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.574333 = idf(docFreq=61, maxDocs=44421)
               0.0625 = fieldNorm(doc=2614)
         0.17388362 = weight(abstract_txt:membership in 2614) [ClassicSimilarity], result of:
           0.17388362 = score(doc=2614,freq=1.0), product of:
             0.37111127 = queryWeight, product of:
               4.382785 = boost
               7.496775 = idf(docFreq=66, maxDocs=44421)
               0.011294824 = queryNorm
             0.46854845 = fieldWeight in 2614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.496775 = idf(docFreq=66, maxDocs=44421)
               0.0625 = fieldNorm(doc=2614)
         0.16246238 = weight(abstract_txt:sets in 2614) [ClassicSimilarity], result of:
           0.16246238 = score(doc=2614,freq=2.0), product of:
             0.35467744 = queryWeight, product of:
               6.0594034 = boost
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.011294824 = queryNorm
             0.45805672 = fieldWeight in 2614, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.0625 = fieldNorm(doc=2614)
         0.9530602 = weight(abstract_txt:fuzzy in 2614) [ClassicSimilarity], result of:
           0.9530602 = score(doc=2614,freq=13.0), product of:
             0.61816937 = queryWeight, product of:
               7.9995737 = boost
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.011294824 = queryNorm
             1.5417461 = fieldWeight in 2614, product of:
               3.6055512 = tf(freq=13.0), with freq of:
                 13.0 = termFreq=13.0
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.0625 = fieldNorm(doc=2614)
       0.2 = coord(5/25)
   

5. Bookstein, A.: Fuzzy requests : an approach to weighted Boolean searches (1979) 0.19

   0.1947406 = sum of:
     0.1947406 = product of:
       0.97370297 = sum of:
         0.01752566 = weight(abstract_txt:such in 5503) [ClassicSimilarity], result of:
           0.01752566 = score(doc=5503,freq=2.0), product of:
             0.038639706 = queryWeight, product of:
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.011294824 = queryNorm
             0.4535661 = fieldWeight in 5503, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.09375 = fieldNorm(doc=5503)
         0.008188118 = weight(abstract_txt:that in 5503) [ClassicSimilarity], result of:
           0.008188118 = score(doc=5503,freq=1.0), product of:
             0.036931213 = queryWeight, product of:
               1.3825947 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.011294824 = queryNorm
             0.22171268 = fieldWeight in 5503, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.09375 = fieldNorm(doc=5503)
         0.08891881 = weight(abstract_txt:properties in 5503) [ClassicSimilarity], result of:
           0.08891881 = score(doc=5503,freq=2.0), product of:
             0.11408975 = queryWeight, product of:
               1.7183293 = boost
               5.878422 = idf(docFreq=337, maxDocs=44421)
               0.011294824 = queryNorm
             0.77937603 = fieldWeight in 5503, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.878422 = idf(docFreq=337, maxDocs=44421)
               0.09375 = fieldNorm(doc=5503)
         0.17231739 = weight(abstract_txt:sets in 5503) [ClassicSimilarity], result of:
           0.17231739 = score(doc=5503,freq=1.0), product of:
             0.35467744 = queryWeight, product of:
               6.0594034 = boost
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.011294824 = queryNorm
             0.48584253 = fieldWeight in 5503, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.18232 = idf(docFreq=677, maxDocs=44421)
               0.09375 = fieldNorm(doc=5503)
         0.686753 = weight(abstract_txt:fuzzy in 5503) [ClassicSimilarity], result of:
           0.686753 = score(doc=5503,freq=3.0), product of:
             0.61816937 = queryWeight, product of:
               7.9995737 = boost
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.011294824 = queryNorm
             1.1109463 = fieldWeight in 5503, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.8416553 = idf(docFreq=128, maxDocs=44421)
               0.09375 = fieldNorm(doc=5503)
       0.2 = coord(5/25)