Hull operators and interval operators in (L,M)-fuzzy convex spaces

Fuzzy Sets and Systems - Tập 405 - Trang 106-127 - 2021
Bin Pang1
1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Tài liệu tham khảo

Chang, 1968, Fuzzy topological spaces, J. Math. Anal. Appl., 24, 182, 10.1016/0022-247X(68)90057-7 Fang, 2010, Stratified L-ordered convergence structures, Fuzzy Sets Syst., 161, 2130, 10.1016/j.fss.2010.07.010 Gierz, 2003 Jäger, 2001, A category of L-fuzzy convergence spaces, Quaest. Math., 24, 501, 10.1080/16073606.2001.9639237 Jäger, 2016, Stratified LMN-convergence tower spaces, Fuzzy Sets Syst., 282, 62, 10.1016/j.fss.2015.03.016 Jin, 2016, On the embedding of L-convex spaces in stratified L-convex spaces, SpringerPlus, 5, 1610, 10.1186/s40064-016-3255-5 Kubiak, 1985 Li, 2017, On the category of enriched (L,M)-convex spaces, J. Intell. Fuzzy Syst., 33, 3209, 10.3233/JIFS-161491 Li, 2019, p-Topologicalness–a relative topologicalness in ⊤-convergence spaces, Mathematics, 7, 228, 10.3390/math7030228 Li, 2019, Lattice-valued convergence associated with CNS spaces, Fuzzy Sets Syst., 370, 91, 10.1016/j.fss.2018.05.023 Li, 2016, The lower and upper p-topological (p-regular) modifications for lattice-valued convergencespaces, Fuzzy Sets Syst., 282, 47, 10.1016/j.fss.2015.03.002 Li, 2019, Degrees of special mappings in the theory of L-convex spaces, J. Intell. Fuzzy Syst., 37, 2265, 10.3233/JIFS-182569 Maruyama, 2009, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku, 164, 22 Mayer-Kalkschmidt, 1964, Some theorems in set theory and applications in the ideal theory of partially ordered sets, Duke Math. J., 31, 287, 10.1215/S0012-7094-64-03127-8 Pang, 2014, On (L,M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238, 46, 10.1016/j.fss.2013.07.007 Pang, 2017, Stratified L-ordered filter spaces, Quaest. Math., 40, 661, 10.2989/16073606.2017.1308976 Pang, 2017, Degrees of separation properties in stratified L-generalized convergence spaces using residual implication, Filomat, 31, 6293, 10.2298/FIL1720293P Pang, 2018, Categorical properties of L-fuzzifying convergence spaces, Filomat, 32, 4021, 10.2298/FIL1811021P Pang, 2019, Convergence structures in M-fuzzifying convex spaces, Quaest. Math. Pang, 2017, Subcategories of the category of L-convex spaces, Fuzzy Sets Syst., 313, 61, 10.1016/j.fss.2016.02.014 Pang, 2018, Strong inclusion orders between L-subsets and its applications in L-convex spaces, Quaest. Math., 41, 1021, 10.2989/16073606.2018.1436613 Pang, 2019, Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces, Fuzzy Sets Syst., 369, 20, 10.1016/j.fss.2018.05.012 Pang, 2018, Stratified L-prefilter convergence structures in stratified L-topological spaces, Soft Comput., 22, 7539, 10.1007/s00500-018-3040-1 Pang, 2019, An axiomatic approach to bases and subbases in L-convex spaces and their applications, Fuzzy Sets Syst., 369, 40, 10.1016/j.fss.2018.08.002 Pang, 2016, Characterizations of L-convex spaces, Iran. J. Fuzzy Syst., 13, 51 Pang, 2018, A new definition of order relation for the introduction of algebraic fuzzy closure operators, Int. J. Approx. Reason., 92, 87, 10.1016/j.ijar.2017.07.003 Rosa, 1994, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets Syst., 62, 97, 10.1016/0165-0114(94)90076-0 Shen, 2018, L-convex systems and the categorical isomorphism to Scott-hull operators, Iran. J. Fuzzy Syst., 15, 23 Shi, 2001, Pointwise metrics in fuzzy set theory, Fuzzy Sets Syst., 121, 209, 10.1016/S0165-0114(00)00013-0 Shi, 2013, Categories isomorphic to the category of L-fuzzy closure system spaces, Iran. J. Fuzzy Syst., 10, 129 Shi, 2014, A new approach to the fuzzification of convex structures, J. Appl. Math., 2014, 1 Shi, 2015, The restricted hull operator of M-fuzzifying convex structures, J. Intell. Fuzzy Syst., 30, 409, 10.3233/IFS-151765 Shi, 2017, (L,M)-fuzzy convex structures, J. Nonlinear Sci. Appl., 10, 3655, 10.22436/jnsa.010.07.25 Šostak, 1985, On a fuzzy topological structure, Suppl. Rend. Circ. Mat. Palermo Ser. II, 11, 89 Van de Vel, 1993 Wang, 2019, A categorical approach to abstract convex spaces and interval spaces, Open Math., 17, 374, 10.1515/math-2019-0029 Wang, 2019, A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies, Open Math., 17, 913, 10.1515/math-2019-0072 Wu, 2016, On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces, J. Intell. Fuzzy Syst., 30, 2447, 10.3233/IFS-152015 Wu, 2017, Geometric properties of M-fuzzifying convex structures, J. Intell. Fuzzy Syst., 32, 4273, 10.3233/JIFS-16667 Wu, 2019, Category and subcategories of (L,M)-fuzzy convex spaces, Iran. J. Fuzzy Syst., 16, 173 Xiu, 2017, M-fuzzifying interval spaces, Iran. J. Fuzzy Syst., 14, 145 Xiu, 2017, M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces, J. Intell. Fuzzy Syst., 33, 613, 10.3233/JIFS-16661 Xiu, 2018, Base axioms and subbase axioms in M-fuzzifying convex spaces, Iran. J. Fuzzy Syst., 15, 75 Yao, 2010, Quantitative domains via fuzzy sets: part I: continuity of fuzzy directed complete posets, Fuzzy Sets Syst., 161, 973, 10.1016/j.fss.2009.06.018 Yao, 2011, An approach to fuzzy frames via fuzzy posets, Fuzzy Sets Syst., 166, 75, 10.1016/j.fss.2010.11.010 Yao, 2008, A note on specialization L-preorder of L-topological spaces, and L-fuzzy topological spaces, Fuzzy Sets Syst., 159, 2586, 10.1016/j.fss.2008.03.023 Ying, 1991, A new approach for fuzzy topology (I), Fuzzy Sets Syst., 39, 303, 10.1016/0165-0114(91)90100-5 Yue, 2010, On fuzzy pseudo-metric spaces, Fuzzy Sets Syst., 161, 1105, 10.1016/j.fss.2009.10.001 Yue, 2014, Fuzzy partial (pseudo-)metric spaces, J. Intell. Fuzzy Syst., 27, 1153, 10.3233/IFS-131078 Zhang, 2005, Continuity in quantitative domains, Fuzzy Sets Syst., 154, 118, 10.1016/j.fss.2005.01.007 Zhang, 2009, Fuzzy complete lattices, Fuzzy Sets Syst., 160, 2275, 10.1016/j.fss.2008.12.001