Document (#21926)

Author

Turunen, E.

Title

Mathematics behind fuzzy logic

Imprint

Heidelberg : Springer

Year

1999

Pages

X,191 S

Isbn

3-7908-1221-8

Series

Advances in soft computing

Abstract

Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus nor previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities

Similar documents (content)

1. Marzano, G.: Introduzione alla teoria degli insiemi fuzzy (1992) 0.17

   0.16893718 = sum of:
     0.16893718 = product of:
       1.0558574 = sum of:
         0.08516535 = weight(abstract_txt:reasoning in 3186) [ClassicSimilarity], result of:
           0.08516535 = score(doc=3186,freq=1.0), product of:
             0.14170697 = queryWeight, product of:
               1.1792558 = boost
               6.410626 = idf(docFreq=196, maxDocs=44083)
               0.018744884 = queryNorm
             0.6009962 = fieldWeight in 3186, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.410626 = idf(docFreq=196, maxDocs=44083)
               0.09375 = fieldNorm(doc=3186)
         0.1967767 = weight(abstract_txt:algebra in 3186) [ClassicSimilarity], result of:
           0.1967767 = score(doc=3186,freq=1.0), product of:
             0.24766524 = queryWeight, product of:
               1.5589958 = boost
               8.474954 = idf(docFreq=24, maxDocs=44083)
               0.018744884 = queryNorm
             0.79452693 = fieldWeight in 3186, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.474954 = idf(docFreq=24, maxDocs=44083)
               0.09375 = fieldNorm(doc=3186)
         0.23594967 = weight(abstract_txt:logic in 3186) [ClassicSimilarity], result of:
           0.23594967 = score(doc=3186,freq=1.0), product of:
             0.4031524 = queryWeight, product of:
               3.4451466 = boost
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.018744884 = queryNorm
             0.5852617 = fieldWeight in 3186, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.09375 = fieldNorm(doc=3186)
         0.53796566 = weight(abstract_txt:fuzzy in 3186) [ClassicSimilarity], result of:
           0.53796566 = score(doc=3186,freq=3.0), product of:
             0.48423067 = queryWeight, product of:
               3.7757149 = boost
               6.8417993 = idf(docFreq=127, maxDocs=44083)
               0.018744884 = queryNorm
             1.1109698 = fieldWeight in 3186, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.8417993 = idf(docFreq=127, maxDocs=44083)
               0.09375 = fieldNorm(doc=3186)
       0.16 = coord(4/25)
   

2. Computing with words in information / intelligent systems 1 : Foundations (1999) 0.16

   0.15522859 = sum of:
     0.15522859 = product of:
       0.9701787 = sum of:
         0.1135538 = weight(abstract_txt:reasoning in 4927) [ClassicSimilarity], result of:
           0.1135538 = score(doc=4927,freq=1.0), product of:
             0.14170697 = queryWeight, product of:
               1.1792558 = boost
               6.410626 = idf(docFreq=196, maxDocs=44083)
               0.018744884 = queryNorm
             0.80132824 = fieldWeight in 4927, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.410626 = idf(docFreq=196, maxDocs=44083)
               0.125 = fieldNorm(doc=4927)
         0.12789923 = weight(abstract_txt:foundations in 4927) [ClassicSimilarity], result of:
           0.12789923 = score(doc=4927,freq=1.0), product of:
             0.15340355 = queryWeight, product of:
               1.2269592 = boost
               6.669949 = idf(docFreq=151, maxDocs=44083)
               0.018744884 = queryNorm
             0.83374363 = fieldWeight in 4927, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.669949 = idf(docFreq=151, maxDocs=44083)
               0.125 = fieldNorm(doc=4927)
         0.31459954 = weight(abstract_txt:logic in 4927) [ClassicSimilarity], result of:
           0.31459954 = score(doc=4927,freq=1.0), product of:
             0.4031524 = queryWeight, product of:
               3.4451466 = boost
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.018744884 = queryNorm
             0.7803489 = fieldWeight in 4927, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.125 = fieldNorm(doc=4927)
         0.41412613 = weight(abstract_txt:fuzzy in 4927) [ClassicSimilarity], result of:
           0.41412613 = score(doc=4927,freq=1.0), product of:
             0.48423067 = queryWeight, product of:
               3.7757149 = boost
               6.8417993 = idf(docFreq=127, maxDocs=44083)
               0.018744884 = queryNorm
             0.8552249 = fieldWeight in 4927, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.8417993 = idf(docFreq=127, maxDocs=44083)
               0.125 = fieldNorm(doc=4927)
       0.16 = coord(4/25)
   

3. Frické, M.: Boolean logic (2021) 0.15

   0.14641406 = sum of:
     0.14641406 = product of:
       0.9150879 = sum of:
         0.06025886 = weight(abstract_txt:introduced in 451) [ClassicSimilarity], result of:
           0.06025886 = score(doc=451,freq=1.0), product of:
             0.11252005 = queryWeight, product of:
               1.0508177 = boost
               5.712415 = idf(docFreq=395, maxDocs=44083)
               0.018744884 = queryNorm
             0.5355389 = fieldWeight in 451, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.712415 = idf(docFreq=395, maxDocs=44083)
               0.09375 = fieldNorm(doc=451)
         0.1304528 = weight(abstract_txt:truth in 451) [ClassicSimilarity], result of:
           0.1304528 = score(doc=451,freq=1.0), product of:
             0.18830054 = queryWeight, product of:
               1.3593717 = boost
               7.3897643 = idf(docFreq=73, maxDocs=44083)
               0.018744884 = queryNorm
             0.6927904 = fieldWeight in 451, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.3897643 = idf(docFreq=73, maxDocs=44083)
               0.09375 = fieldNorm(doc=451)
         0.1967767 = weight(abstract_txt:algebra in 451) [ClassicSimilarity], result of:
           0.1967767 = score(doc=451,freq=1.0), product of:
             0.24766524 = queryWeight, product of:
               1.5589958 = boost
               8.474954 = idf(docFreq=24, maxDocs=44083)
               0.018744884 = queryNorm
             0.79452693 = fieldWeight in 451, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.474954 = idf(docFreq=24, maxDocs=44083)
               0.09375 = fieldNorm(doc=451)
         0.5275995 = weight(abstract_txt:logic in 451) [ClassicSimilarity], result of:
           0.5275995 = score(doc=451,freq=5.0), product of:
             0.4031524 = queryWeight, product of:
               3.4451466 = boost
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.018744884 = queryNorm
             1.308685 = fieldWeight in 451, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.09375 = fieldNorm(doc=451)
       0.16 = coord(4/25)
   

4. Langville, A.N.; Meyer, C.D.: Google's PageRank and beyond : the science of search engine rankings (2006) 0.14

   0.14473112 = sum of:
     0.14473112 = product of:
       0.45228475 = sum of:
         0.037137635 = weight(abstract_txt:self in 1007) [ClassicSimilarity], result of:
           0.037137635 = score(doc=1007,freq=1.0), product of:
             0.106779106 = queryWeight, product of:
               1.0236596 = boost
               5.5647793 = idf(docFreq=458, maxDocs=44083)
               0.018744884 = queryNorm
             0.3477987 = fieldWeight in 1007, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.5647793 = idf(docFreq=458, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.04414318 = weight(abstract_txt:complete in 1007) [ClassicSimilarity], result of:
           0.04414318 = score(doc=1007,freq=1.0), product of:
             0.119817205 = queryWeight, product of:
               1.0843563 = boost
               5.894737 = idf(docFreq=329, maxDocs=44083)
               0.018744884 = queryNorm
             0.36842105 = fieldWeight in 1007, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.894737 = idf(docFreq=329, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.06422693 = weight(abstract_txt:contains in 1007) [ClassicSimilarity], result of:
           0.06422693 = score(doc=1007,freq=2.0), product of:
             0.12210822 = queryWeight, product of:
               1.0946742 = boost
               5.950826 = idf(docFreq=311, maxDocs=44083)
               0.018744884 = queryNorm
             0.5259837 = fieldWeight in 1007, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.950826 = idf(docFreq=311, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.053093348 = weight(abstract_txt:answers in 1007) [ClassicSimilarity], result of:
           0.053093348 = score(doc=1007,freq=1.0), product of:
             0.13550964 = queryWeight, product of:
               1.1531811 = boost
               6.2688794 = idf(docFreq=226, maxDocs=44083)
               0.018744884 = queryNorm
             0.39180496 = fieldWeight in 1007, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.2688794 = idf(docFreq=226, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.07791728 = weight(abstract_txt:mathematical in 1007) [ClassicSimilarity], result of:
           0.07791728 = score(doc=1007,freq=2.0), product of:
             0.13889585 = queryWeight, product of:
               1.1675005 = boost
               6.346722 = idf(docFreq=209, maxDocs=44083)
               0.018744884 = queryNorm
             0.56097627 = fieldWeight in 1007, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.346722 = idf(docFreq=209, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.055471417 = weight(abstract_txt:contained in 1007) [ClassicSimilarity], result of:
           0.055471417 = score(doc=1007,freq=1.0), product of:
             0.13952637 = queryWeight, product of:
               1.1701474 = boost
               6.3611107 = idf(docFreq=206, maxDocs=44083)
               0.018744884 = queryNorm
             0.39756942 = fieldWeight in 1007, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.3611107 = idf(docFreq=206, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.09097826 = weight(abstract_txt:mathematics in 1007) [ClassicSimilarity], result of:
           0.09097826 = score(doc=1007,freq=2.0), product of:
             0.15401341 = queryWeight, product of:
               1.2293957 = boost
               6.683194 = idf(docFreq=149, maxDocs=44083)
               0.018744884 = queryNorm
             0.5907165 = fieldWeight in 1007, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.683194 = idf(docFreq=149, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
         0.029316707 = weight(abstract_txt:many in 1007) [ClassicSimilarity], result of:
           0.029316707 = score(doc=1007,freq=1.0), product of:
             0.11491152 = queryWeight, product of:
               1.50179 = boost
               4.081987 = idf(docFreq=2021, maxDocs=44083)
               0.018744884 = queryNorm
             0.25512418 = fieldWeight in 1007, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.081987 = idf(docFreq=2021, maxDocs=44083)
               0.0625 = fieldNorm(doc=1007)
       0.32 = coord(8/25)
   

5. Hisdal, E.: Logical structures for representation of knowledge and uncertainty (1998) 0.14

   0.13777031 = sum of:
     0.13777031 = product of:
       0.8610645 = sum of:
         0.1135538 = weight(abstract_txt:reasoning in 972) [ClassicSimilarity], result of:
           0.1135538 = score(doc=972,freq=1.0), product of:
             0.14170697 = queryWeight, product of:
               1.1792558 = boost
               6.410626 = idf(docFreq=196, maxDocs=44083)
               0.018744884 = queryNorm
             0.80132824 = fieldWeight in 972, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.410626 = idf(docFreq=196, maxDocs=44083)
               0.125 = fieldNorm(doc=972)
         0.12866269 = weight(abstract_txt:mathematics in 972) [ClassicSimilarity], result of:
           0.12866269 = score(doc=972,freq=1.0), product of:
             0.15401341 = queryWeight, product of:
               1.2293957 = boost
               6.683194 = idf(docFreq=149, maxDocs=44083)
               0.018744884 = queryNorm
             0.83539927 = fieldWeight in 972, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.683194 = idf(docFreq=149, maxDocs=44083)
               0.125 = fieldNorm(doc=972)
         0.17393707 = weight(abstract_txt:truth in 972) [ClassicSimilarity], result of:
           0.17393707 = score(doc=972,freq=1.0), product of:
             0.18830054 = queryWeight, product of:
               1.3593717 = boost
               7.3897643 = idf(docFreq=73, maxDocs=44083)
               0.018744884 = queryNorm
             0.92372054 = fieldWeight in 972, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.3897643 = idf(docFreq=73, maxDocs=44083)
               0.125 = fieldNorm(doc=972)
         0.44491094 = weight(abstract_txt:logic in 972) [ClassicSimilarity], result of:
           0.44491094 = score(doc=972,freq=2.0), product of:
             0.4031524 = queryWeight, product of:
               3.4451466 = boost
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.018744884 = queryNorm
             1.10358 = fieldWeight in 972, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.242791 = idf(docFreq=232, maxDocs=44083)
               0.125 = fieldNorm(doc=972)
       0.16 = coord(4/25)