메뉴 건너뛰기




Volumn , Issue , 2008, Pages 603-627

Theoretical Aspects of Shadowed Sets

Author keywords

Fuzzy and shadowed sets; impossibility operator as 'not possibility'; Intuitionistic fuzzy sets; Level fuzzy sets; Paradigm algebraic framework; Shadowed sets theoretical aspects; Shadowed sets and knowledge granulation tools

Indexed keywords


EID: 69049113076     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470724163.ch27     Document Type: Chapter
Times cited : (10)

References (45)
  • 1
    • 34248666540 scopus 로고
    • Fuzzy sets
    • L.A. Zadeh. Fuzzy sets. Inf. Control 8 (1965) 338-353.
    • (1965) Inf. Control , vol.8 , pp. 338-353
    • Zadeh, L.A.1
  • 2
    • 0031996836 scopus 로고    scopus 로고
    • Shadowed sets: Representing and processing fuzzy sets
    • W. Pedrycz. Shadowed sets: Representing and processing fuzzy sets. IEEE Trans. Syst. Man Cybern. 28(1) (1998) 103-109.
    • (1998) IEEE Trans. Syst. Man Cybern. , vol.28 , Issue.1 , pp. 103-109
    • Pedrycz, W.1
  • 3
    • 0008435541 scopus 로고    scopus 로고
    • Shadowed sets: Bridging fuzzy and rough sets
    • In: S. Pal and A. Skowron (eds), Springer-Verlag, Singapore
    • W. Pedrycz. Shadowed sets: Bridging fuzzy and rough sets. In: S. Pal and A. Skowron (eds) , Rough Fuzzy Hybridization. Springer-Verlag, Singapore, 1999, pp. 179-199.
    • (1999) Rough Fuzzy Hybridization , pp. 179-199
    • Pedrycz, W.1
  • 4
    • 0036471403 scopus 로고    scopus 로고
    • Granular computing with shadowed sets
    • W. Pedrycz and G. Vukovich. Granular computing with shadowed sets. Int. J. Intell. Syst. 17 (2002) 173-197.
    • (2002) Int. J. Intell. Syst. , vol.17 , pp. 173-197
    • Pedrycz, W.1    Vukovich, G.2
  • 5
    • 0004128728 scopus 로고    scopus 로고
    • Triangular Norms
    • Kluwer Academic, Dordrecht
    • E.P. Klement, R. Mesiar, and E. Pap. Triangular Norms. Kluwer Academic, Dordrecht, 2000.
    • (2000)
    • Klement, E.P.1    Mesiar, R.2    Pap, E.3
  • 6
    • 84914745872 scopus 로고
    • Level fuzzy sets
    • T. Radecki. Level fuzzy sets. J. Cybern. 7 (1977) 189-198.
    • (1977) J. Cybern. , vol.7 , pp. 189-198
    • Radecki, T.1
  • 7
    • 0003891870 scopus 로고
    • Fuzzy Sets and Systems. Theory and Applications
    • Academic Press, New York
    • D. Dubois and H. Prade. Fuzzy Sets and Systems. Theory and Applications. Academic Press, New York, 1980.
    • (1980)
    • Dubois, D.1    Prade, H.2
  • 8
    • 84889267124 scopus 로고    scopus 로고
    • Generalized rough approximations inίΠ-. Int. J. Approx
    • Reason., doi: 10.1016 lj.ijar. 2007.10.2006.
    • D. Ciucci and T. Flaminio. Generalized rough approximations inίΠ-. Int. J. Approx. Reason. 2007. doi: 10.1016 lj.ijar. 2007.10.2006.
    • (2007)
    • Ciucci, D.1    Flaminio, T.2
  • 9
    • 84975987883 scopus 로고
    • Abstract orthogonality and orthocomplementation
    • G. Cattaneo and A. Mania. Abstract orthogonality and orthocomplementation. Proc. Camb. Phil. Soc. 76 (1974) 115-132.
    • (1974) Proc. Camb. Phil. Soc. , vol.76 , pp. 115-132
    • Cattaneo, G.1    Mania, A.2
  • 11
    • 0002740725 scopus 로고
    • Intuitionistic fuzzy sets
    • K.T. Atanassov. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 (1986) 87-96.
    • (1986) Fuzzy Sets Syst , vol.20 , pp. 87-96
    • Atanassov, K.T.1
  • 12
    • 38249004171 scopus 로고
    • More on intuitionistic fuzzy sets
    • K.T. Atanassov. More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 33 (1989) 37-45.
    • (1989) Fuzzy Sets Syst , vol.33 , pp. 37-45
    • Atanassov, K.T.1
  • 13
    • 26944458219 scopus 로고    scopus 로고
    • Generalized negations and intuitionistic fuzzy sets. A criticism to a widely used terminology
    • In:, University of Applied Sciences of Zittau-Goerlitz, Zittau
    • G. Cattaneo and D. Ciucci. Generalized negations and intuitionistic fuzzy sets. A criticism to a widely used terminology. In: Proceedings of International Conference in Fuzzy Logic and Technology (EUSFLAT03) , University of Applied Sciences of Zittau-Goerlitz, Zittau, 2003, pp. 147-152.
    • (2003) Proceedings of International Conference in Fuzzy Logic and Technology (EUSFLAT03) , pp. 147-152
    • Cattaneo, G.1    Ciucci, D.2
  • 15
    • 26944497184 scopus 로고    scopus 로고
    • Terminological difficulties in fuzzy set theory-the case of intuitionistic fuzzy sets
    • D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, and H. Prade. Terminological difficulties in fuzzy set theory-the case of intuitionistic fuzzy sets. Fuzzy Sets Syst. 156 (2005) 485-491.
    • (2005) Fuzzy Sets Syst , vol.156 , pp. 485-491
    • Dubois, D.1    Gottwald, S.2    Hajek, P.3    Kacprzyk, J.4    Prade, H.5
  • 16
    • 26944497185 scopus 로고    scopus 로고
    • Some notes on (Atanassov) Intuitionistic fuzzy sets
    • P. Grzegorzewski and E. Mrowka. Some notes on (Atanassov) Intuitionistic fuzzy sets. Fuzzy Sets Syst. 156 (2005) 492-195.
    • (2005) Fuzzy Sets Syst , vol.156 , pp. 492-195
    • Grzegorzewski, P.1    Mrowka, E.2
  • 17
    • 26944448930 scopus 로고    scopus 로고
    • paper 'terminological difficulties in fuzzy set theory-the case of intuitionistic fuzzy sets
    • Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper
    • K.T. Atanassov. Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper 'terminological difficulties in fuzzy set theory-the case of intuitionistic fuzzy sets.' Fuzzy Sets Syst. 156 (2005) 496-499.
    • (2005) Fuzzy Sets Syst , vol.156 , pp. 496-499
    • Atanassov, K.T.1
  • 18
    • 33750719988 scopus 로고    scopus 로고
    • Basic intuitionistic principles in fuzzy set theories and its extensions (a terminological debate on atanassov IFS)
    • G. Cattaneo and D. Ciucci. Basic intuitionistic principles in fuzzy set theories and its extensions (a terminological debate on atanassov IFS) . Fuzzy Sets Syst. 157 (2006) 3198-3219.
    • (2006) Fuzzy Sets Syst , vol.157 , pp. 3198-3219
    • Cattaneo, G.1    Ciucci, D.2
  • 20
    • 84889342205 scopus 로고
    • Les ensembles flous et la logique atrois valeurs (texte inédit)
    • In:, chapter 15
    • G.C. Moisil. Les ensembles flous et la logique atrois valeurs (texte inédit) . In: [21], 1972, chapter 15, pp. 99-103.
    • (1972) , Issue.21 , pp. 99-103
    • Moisil, G.C.1
  • 21
    • 0042456551 scopus 로고
    • Essais sur les logiques non Chrysippiennes
    • Edition de l'Académie de la République Socialiste de Roumanie, Bucharest
    • G.C. Moisil. Essais sur les logiques non Chrysippiennes. Edition de l'Académie de la République Socialiste de Roumanie, Bucharest, 1972.
    • (1972)
    • Moisil, G.C.1
  • 22
    • 0001016354 scopus 로고
    • Brouwer-Zadeh posets and three valued-Lukasiewicz posets
    • G. Cattaneo and G. Nisticö. Brouwer-Zadeh posets and three valued-Lukasiewicz posets. Fuzzy Sets Syst. 33 (1989) 165-190.
    • (1989) Fuzzy Sets Syst , vol.33 , pp. 165-190
    • Cattaneo, G.1    Nisticö, G.2
  • 23
    • 0039385212 scopus 로고    scopus 로고
    • A note on intuitionistic sets and intuitionistic points
    • D. Coker. A note on intuitionistic sets and intuitionistic points. Turk. J. Math. 20 (1996) 343-351.
    • (1996) Turk. J. Math. , vol.20 , pp. 343-351
    • Coker, D.1
  • 24
    • 0027543613 scopus 로고
    • Variable precision rough sets model
    • W. Ziarko. Variable precision rough sets model. J. Comput. Syst. Sei. 43(1) (1993) 39-59.
    • (1993) J. Comput. Syst. Sei. , vol.43 , Issue.1 , pp. 39-59
    • Ziarko, W.1
  • 25
    • 33646000606 scopus 로고    scopus 로고
    • Granular computing with shadowed sets
    • In: RSFDGrC2005,, Springer-Verlag, Berlin
    • W. Pedrycz. Granular computing with shadowed sets. In: RSFDGrC2005, Vol. 3641 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, 2005, pp. 23-32.
    • (2005) of Lecture Notes in Artificial Intelligence , vol.3641 , pp. 23-32
    • Pedrycz, W.1
  • 26
    • 0002105067 scopus 로고    scopus 로고
    • Some algebraic structures for many-valued logics
    • Special Issue: Quantum Structures II, Dedicated to Gudrun Kalmbach.
    • G. Cattaneo, M.L. Dalla Chiara, and R. Giuntini. Some algebraic structures for many-valued logics. Tatra Mt. Math. Publ. 15 (1998) 173-196. Special Issue: Quantum Structures II, Dedicated to Gudrun Kalmbach.
    • (1998) Tatra Mt. Math. Publ. , vol.15 , pp. 173-196
    • Cattaneo, G.1    Dalla Chiara, M.L.2    Giuntini, R.3
  • 27
    • 0002137628 scopus 로고    scopus 로고
    • BZMV®- and Stonian MV algebras (applications to fuzzy sets and rough approximations)
    • G. Cattaneo, R. Giuntini, and R. Pilla. BZMV®- and Stonian MV algebras (applications to fuzzy sets and rough approximations) . Fuzzy Sets Syst. 108 (1999) 201-222.
    • (1999) Fuzzy Sets Syst , vol.108 , pp. 201-222
    • Cattaneo, G.1    Giuntini, R.2    Pilla, R.3
  • 28
    • 84968495744 scopus 로고
    • Algebraic analysis of many valued logics
    • C.C. Chang. Algebraic analysis of many valued logics. Trans. Am. Math. Soc. 88 (1958) 467-190.
    • (1958) Trans. Am. Math. Soc. , vol.88 , pp. 467-190
    • Chang, C.C.1
  • 29
    • 0003406363 scopus 로고    scopus 로고
    • Mathematics behind Fuzzy Logic
    • Physica-Verlag, Heidelberg
    • E. Turanen. Mathematics behind Fuzzy Logic. Physica-Verlag, Heidelberg, 1999.
    • (1999)
    • Turanen, E.1
  • 31
    • 0002901936 scopus 로고    scopus 로고
    • Algebraic analysis of-Lukasiewicz Tarski's «-valued logical systems
    • In: R. Woijcicki and G. Malinowski (eds), Polish Academy of Sciences, Ossolineum, Wroclaw
    • R. Grigolia. Algebraic analysis of-Lukasiewicz Tarski's «-valued logical systems. In: R. Woijcicki and G. Malinowski (eds) , Selected Papers on-Lukasiewicz Sentential Calculi. Polish Academy of Sciences, Ossolineum, Wroclaw, 1997, pp. 81-92.
    • (1997) Selected Papers on-Lukasiewicz Sentential Calculi , pp. 81-92
    • Grigolia, R.1
  • 32
    • 24044474394 scopus 로고    scopus 로고
    • Algebraic structures related to many valued logical systems. Part II: Equivalence among some widespread structures
    • G. Cattaneo, D. Ciucci, R. Giuntini, and M. König. Algebraic structures related to many valued logical systems. Part II: Equivalence among some widespread structures. Fundam. Inf. 63(4) (2004) 357-373.
    • (2004) Fundam. Inf. , vol.63 , Issue.4 , pp. 357-373
    • Cattaneo, G.1    Ciucci, D.2    Giuntini, R.3    König, M.4
  • 33
    • 24044482292 scopus 로고    scopus 로고
    • Algebraic structures related to many valued logical systems. Part I: Heyting Wajsberg algebras
    • G. Cattaneo, D. Ciucci, R. Giuntini, and M. König. Algebraic structures related to many valued logical systems. Part I: Heyting Wajsberg algebras. Fundam. Inf. 63(4) (2004) 331-355.
    • (2004) Fundam. Inf. , vol.63 , Issue.4 , pp. 331-355
    • Cattaneo, G.1    Ciucci, D.2    Giuntini, R.3    König, M.4
  • 34
    • 0001944480 scopus 로고    scopus 로고
    • Infinite-valued Gödel logics with 0-1 projections and relativizations
    • In: P. Hájek (ed.), of Lecture Notes in Logic. Springer-Verlag, Berlin
    • M. Baaz. Infinite-valued Gödel logics with 0-1 projections and relativizations. In: P. Hájek (ed.) , GÖDEL96-Logical Foundations of Mathematics, Computer Science and Physics, Vol. 6 of Lecture Notes in Logic. Springer-Verlag, Berlin, 1996, pp. 23-33.
    • (1996) GÖDEL96-Logical Foundations of Mathematics, Computer Science and Physics , vol.6 , pp. 23-33
    • Baaz, M.1
  • 35
    • 0004130617 scopus 로고    scopus 로고
    • Metamathematics of Fuzzy Logic
    • Kluwer, Dordrecht
    • P. Hájek. Metamathematics of Fuzzy Logic. Kluwer, Dordrecht, 1998.
    • (1998)
    • Hájek, P.1
  • 36
    • 0031567814 scopus 로고    scopus 로고
    • Generalized fuzzy connectives on MV-algebras
    • L.P. Belluce. Generalized fuzzy connectives on MV-algebras. J. Math. Anal. Appl. 206(1) (1997) 485-499.
    • (1997) J. Math. Anal. Appl. , vol.206 , Issue.1 , pp. 485-499
    • Belluce, L.P.1
  • 39
    • 0004161482 scopus 로고
    • The Mathematics of Metamathematics
    • of, 3rded. Polish Scientific Publishers, Warszawa
    • H. Rasiowaand R. Sikorski. The Mathematics of Metamathematics, Vol. 41 of Monografie Matematyczne, 3rded. Polish Scientific Publishers, Warszawa, 1970.
    • (1970) Monografie Matematyczne , vol.41
    • Rasiowaand, H.1    Sikorski, R.2
  • 40
    • 33746747048 scopus 로고    scopus 로고
    • Some methodological remarks about categorical equivalence in the abstract approach to roughness. Part I
    • In: RSKT2006, of, Springer-Verlag, Berlin
    • G. Cattaneo and D. Ciucci. Some methodological remarks about categorical equivalence in the abstract approach to roughness. Part I. In: RSKT2006, Vol. 4062 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, 2006, pp. 277-283.
    • (2006) Lecture Notes in Artificial Intelligence , vol.4062 , pp. 277-283
    • Cattaneo, G.1    Ciucci, D.2
  • 41
    • 0003097477 scopus 로고    scopus 로고
    • Abstract approximation spaces for rough theories
    • In: L. Polkowski and A. Skowron (eds), Physica-Verlag, Heidelberg New York
    • G. Cattaneo. Abstract approximation spaces for rough theories. In: L. Polkowski and A. Skowron (eds) Rough Sets in Knowledge Discovery 1. Physica-Verlag, Heidelberg New York, 1998, pp. 59-98.
    • (1998) Rough Sets in Knowledge Discovery 1 , pp. 59-98
    • Cattaneo, G.1
  • 42
    • 0141717657 scopus 로고    scopus 로고
    • Shadowed sets and related algebraic structures
    • G. Cattaneo and D. Ciucci. Shadowed sets and related algebraic structures. Fundam. Inf. 55 (2003) 255-284.
    • (2003) Fundam. Inf. , vol.55 , pp. 255-284
    • Cattaneo, G.1    Ciucci, D.2
  • 43
    • 0002141730 scopus 로고
    • A theorem about infinite-valued sentential logic
    • R. McNaughton. A theorem about infinite-valued sentential logic. J. Symbol. Log. 16 (1951) 1-13.
    • (1951) J. Symbol. Log. , vol.16 , pp. 1-13
    • McNaughton, R.1
  • 44
    • 0037660964 scopus 로고    scopus 로고
    • Advances in theU7 and-L/7\ logics
    • P. Cintula. Advances in theU7 and-L/7\ logics. Arch. Math. Log. 42 (2003) 449-468.
    • (2003) Arch. Math. Log. , vol.42 , pp. 449-468
    • Cintula, P.1
  • 45
    • 0041402569 scopus 로고    scopus 로고
    • Adding structure to mv-algebras
    • F. Montagna and G. Panti. Adding structure to mv-algebras. J. Pure Appl. Algebr. 164 (2001) 356-387.
    • (2001) J. Pure Appl. Algebr. , vol.164 , pp. 356-387
    • Montagna, F.1    Panti, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.