{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:14:49Z","timestamp":1777706089235,"version":"3.51.4"},"reference-count":50,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2022,6,1]]},"abstract":"<jats:p>The numbers of Helly, Carath\u00e9odory and Radon are a central theme in classic convex spaces and each of them is invariant under isomorphism. The theory of M-fuzzifying convex spaces is an active research field since it is presented. This paper focus on convex invariants of M-fuzzifying convex spaces. The degrees of Helly independent, Carath\u00e9odory independent and Radon independent of non-empty set are defined in the framework of M-fuzzifying convex spaces. By those definitions, we introduce the Helly number, Carath\u00e9odory number and Radon number of M-fuzzifying convex spaces. Finally, we inspect M-fuzzifying topology and M-fuzzifying JHC which are characterized by convex invariants of M-fuzzifying convex spaces.<\/jats:p>","DOI":"10.3233\/jifs-213081","type":"journal-article","created":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T12:07:00Z","timestamp":1643371620000},"page":"1077-1090","source":"Crossref","is-referenced-by-count":0,"title":["Convex invariants of M-fuzzifying convex spaces"],"prefix":"10.1177","volume":"43","author":[{"given":"Shaojun","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Fujian Normal University, Fuzhou, China"},{"name":"Center for Applied Mathematics of Fujian Province, Fujian Normal University, Fuzhou, China"},{"name":"State Key Laboratory of Cryptology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyi","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China"},{"name":"Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"1","key":"10.3233\/JIFS-213081_ref1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0012-365X(83)90173-5","article-title":"Median algebras","volume":"45","author":"Bandelt","year":"1983","journal-title":"Discrete Mathematics"},{"issue":"1","key":"10.3233\/JIFS-213081_ref2","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/0022-247X(68)90057-7","article-title":"Fuzzy topological spaces","volume":"24","author":"Chang","year":"1968","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"1","key":"10.3233\/JIFS-213081_ref3","doi-asserted-by":"crossref","first-page":"221","DOI":"10.3233\/JIFS-171142","article-title":"A new approach to the fuzzification of arity, JHC and CUP of L-convexities","volume":"34","author":"Chen","year":"2018","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"3","key":"10.3233\/JIFS-213081_ref4","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0165-0114(88)90055-3","article-title":"Fuzzy matroids","volume":"27","author":"Goetschel","year":"1988","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-213081_ref5","first-page":"521","article-title":"Introduction to the theory of convexitytopological spaces","author":"Guay","year":"1978","journal-title":"Topology, Vol. II (Proc. 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