The Fuzzification of Classical Structures: A General View

The aim of this survey article, dedicated to the 50th anniversary of Zadeh’s pioneering paper "Fuzzy Sets" (1965), is to offer a unitary view to some important spaces in fuzzy mathematics: fuzzy real line, fuzzy topological spaces, fuzzy metric spaces, fuzzy topological vector spaces, fuzzy normed linear spaces. We believe that this paper will be a support for future research in this field.

[1]  Dan Tufis,et al.  From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence , 2008 .

[2]  Jianzhong Xiao,et al.  On linearly topological structure and property of fuzzy normed linear space , 2002, Fuzzy Sets Syst..

[3]  A. Sostak On a fuzzy topological structure , 1985 .

[4]  Marian Matloka Convex fuzzy processes , 2000, Fuzzy Sets Syst..

[5]  Ismat Beg VECTOR-VALUED FUZZY MULTIFUNCTIONS , 2001 .

[6]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[7]  A. George,et al.  On some results in fuzzy metric spaces , 1994 .

[8]  Bernard De Baets,et al.  Continuity of fuzzy multivalued mappings , 1998, Fuzzy Sets Syst..

[9]  Valentín Gregory,et al.  Some properites of fuzzy metric spaces , 2000 .

[10]  Sorin Nădăban,et al.  Fuzzy Euclidean Normed Spaces for Data Mining Applications , 2014, Int. J. Comput. Commun. Control.

[11]  R. Osuna-Gómez,et al.  s-Convex fuzzy processes☆ , 2004 .

[12]  S. K. Samanta,et al.  FINITE DIMENSIONAL FUZZY NORMED LINEAR SPACES , 2003 .

[13]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[14]  Ivan Kramosil,et al.  Fuzzy metrics and statistical metric spaces , 1975, Kybernetika.

[15]  R. Lowen Fuzzy topological spaces and fuzzy compactness , 1976 .

[16]  R. Lowen Initial and Final Fuzzy Topologies and the Fuzzy Tychonoff Theorem , 1977 .

[17]  Salvador Romaguera,et al.  Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms , 2010, Fuzzy Sets Syst..

[18]  Sorin Hoară,et al.  Katsaras's Type Fuzzy Norm under Triangular Norms , 2015 .

[19]  Ramesh C. Jain Tolerance analysis using fuzzy sets , 1976 .

[20]  B. Schweizer,et al.  Statistical metric spaces. , 1960 .

[21]  Osmo Kaleva,et al.  On fuzzy metric spaces , 1984 .

[22]  R. H. Warren Neighborhoods, bases and continuity in fuzzy topological spaces , 1978 .

[23]  Etienne Kerre,et al.  A tribute to Zadeh's extension principle , 2011, Sci. Iran..

[24]  Ioan Golet,et al.  On generalized fuzzy normed spaces and coincidence point theorems , 2010, Fuzzy Sets Syst..

[25]  I. Sadeqi,et al.  Fuzzy normed linear space and its topological structure , 2009 .

[26]  Chinyao Low,et al.  A note on convex fuzzy processes , 2002, Appl. Math. Lett..

[27]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[28]  Ismat Beg CONTINUITY OF FUZZY MULTIFUNCTIONS , 1999 .

[29]  Sorin Nadaban,et al.  Special Types of Fuzzy Relations , 2014, ITQM.

[30]  Sorin Nadaban,et al.  Fuzzy Continuous Mappings in Fuzzy Normed Linear Spaces , 2015, Int. J. Comput. Commun. Control.

[31]  Joseph A. Goguen,et al.  The fuzzy tychonoff theorem , 1973 .

[32]  Sorin Nadaban,et al.  Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications , 2014, Informatica.

[33]  Bernard De Baets,et al.  A fuzzy inclusion based approach to upper inverse images under fuzzy multivalued mappings , 1997, Fuzzy Sets Syst..

[34]  Nikolaos S. Papageorgiou Fuzzy topology and fuzzy multifunctions , 1985 .

[35]  S. V. Krishna,et al.  Fuzzy topological vector spaces-topological generation and normability , 1991 .

[36]  Reza Saadati,et al.  Some results on fuzzy Banach spaces , 2005 .

[37]  R. Saadati On the intuitionistic fuzzy topological spaces , 2005, math/0501149.

[38]  Werner Gähler,et al.  Basic notions for fuzzy topology, 1 , 1988 .

[39]  A. K. Katsaras,et al.  Fuzzy topological vector spaces II , 1981 .

[40]  S. K. Samanta,et al.  Fuzzy bounded linear operators , 2005, Fuzzy Sets Syst..

[41]  C. L. Chang,et al.  Fuzzy topological spaces , 1968 .

[42]  Reza Saadati,et al.  Intuitionistic Fuzzy Euclidean Normed Spaces , 2006 .

[43]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[44]  A. Katsaras,et al.  Fuzzy vector spaces and fuzzy topological vector spaces , 1977 .

[45]  Dong Qiu,et al.  On Convex Fuzzy Processes and Their Generalizations , 2010 .

[46]  H. Baghani,et al.  ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND FUZZY BOUNDED OPERATORS , 2011 .

[47]  Samuel Morillas,et al.  Some questions in fuzzy metric spaces , 2012, Fuzzy Sets Syst..

[48]  Muneo Chō,et al.  Fuzzy bounded operators , 1998 .

[49]  S. K. Samanta,et al.  A comparative study of fuzzy norms on a linear space , 2008, Fuzzy Sets Syst..

[50]  T. Bag,et al.  Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces , 2008, Fuzzy Sets Syst..

[51]  A. P. Shostak Two decades of fuzzy topology: basic ideas, notions, and results , 1989 .