A fuzzification of the category of M-valued L-topological spaces
Submitted: 2013-11-26
|Accepted: 2013-11-26
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Keywords:
M-valued L-topology, (L, M)-fuzzy topology, L-fuzzy category, GL-monoid, Power-set operators, M)-interior operator, M)-neighborhood system
Supporting agencies:
Abstract:
A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.
References:
U.Höhle, Uppersemicontinuous fuzzy sets and applications, J. Math. Anal. Appl. 78 (1980), 659-673. http://dx.doi.org/10.1016/0022-247X(80)90173-0
U.Höhle, Commutative, residuated l-monoids, In: Non-classical Logics and Their Applications to Fuzzy Subsets: A Handbook of the Mathematical Foundations of Fuzzy Subsets, E.P. Klement and U. Höhle eds., Kluwer Acad. Publ., 1994, 53-106.
U. Höhle, M-valued sets and sheaves over integral commutative cl-monoids, In: Applications of Category Theory to Fuzzy Sets., S.E. Rodabaugh, E.P. Klement and U. Höhle eds., Kluwer Acad. Publ., 1992, pp. 33-72. http://dx.doi.org/10.1007/978-94-011-2616-8_3
U. Höhle and A. Sostak, Axiomatic foundations of fixed-basis fuzzy topology, In: Mathematics of Fuzzy Sets: Logics, Topology and Measure Theory,pp. 123-273. U. Höhle and S.E. Rodabaugh eds., Kluwer Academic Publ., 1999. Boston, Dodrecht, London.
T. Kubiak, On Fuzzy Topologies, Ph.D. Thesis, Adam Mickiewicz University, Poznan, Poland, 1985.
T. Kubiak and A. Sostak, Foundations of the theory of (L,M)-fuzzy topologies, Part I, to appear.
T. Kubiak and A. Sostak, Foundations of the theory of (L,M)-fuzzy topologies, Part II, to appear.
S. E. Rodabaugh, Powerset operator based foundations for point-set lattice theoretic (poslat) fuzzy set theories and topologies, Quaest. Math. 20 (1997), 463-530. http://dx.doi.org/10.1080/16073606.1997.9632018
A. Sostak, On a fuzzy topological structure, Rend. Matem. Palermo, Ser II, 11 (1985), 89-103.
A. Sostak, Two decades of fuzzy topology, Russian Mathematical Surveys, 44:6 (1989), 125-186. http://dx.doi.org/10.1070/RM1989v044n06ABEH002295
A. Sostak, On a concept of a fuzzy category, In: 14th Linz Seminar on Fuzzy Set Theory: Non-classical Logics and Applications. Linz, Austria, 1992, pp. 62-66.
A. Sostak, Fuzzy categories versus categories of fuzzily structured sets: Elements of the theory of fuzzy categories, In: Mathematik-Arbeitspapiere, Universit¨at Bremen, vol 48 (1997), pp. 407-437.
A. Sostak, Fuzzy categories related to algebra and topology, Tatra Mount. Math. Publ. 16:1, (1999), 159-186.
