{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:52:52Z","timestamp":1777704772545,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,1,4]]},"abstract":"<jats:p>In this paper, notions of L-interval spaces and L-2-arity convex spaces are introduced. It is showed that there is a Galois\u2019s connection between the category of L-convex spaces and the category of L-interval spaces. In particular, the category of L-2-arity convex spaces can be embedded in the category of L-interval spaces as a coreflective subcategory. Further, some properties of L-interval spaces are introduced including L-geometric (resp. L-Peano, L-Pasch and L-sand-glass) property. It is proved that an L-2-arity convex space is an L-JHC convex space iff its segment operator has L-Peano property. It is also proved that an L-JHC convex space with an L-idempotent segment operator has L-sand-glass property. Further, it is also proved that an L-idempotent interval space having L-Peano+L-Pasch property has L-geometric property and L-sand-glass property.<\/jats:p>","DOI":"10.3233\/jifs-182525","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T12:59:55Z","timestamp":1591707595000},"page":"13-25","source":"Crossref","is-referenced-by-count":0,"title":["L-interval spaces and some of their properties"],"prefix":"10.1177","volume":"40","author":[{"given":"Xiu-Yun","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Anhui Normal University, Wuhui, China"},{"name":"School of Science, HunanUniversity of Science and Engineering, Yongzhou, China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-182525_ref1","volume-title":"Wiley","author":"Ad\u00e1mek","year":"1990"},{"issue":"1","key":"10.3233\/JIFS-182525_ref2","doi-asserted-by":"crossref","first-page":"221","DOI":"10.3233\/JIFS-171142","article-title":"A new approach to fuzzification of arity, JHC and CUP of L-convexities","volume":"34","author":"Chen","year":"2018","journal-title":"J Intell Fuzzy Syst"},{"issue":"2","key":"10.3233\/JIFS-182525_ref3","doi-asserted-by":"crossref","first-page":"135","DOI":"10.2989\/16073606.2018.1441920","article-title":"Connectedness for lattice-valued subsets in lattice-valued convergence spaces","volume":"42","author":"Jin","year":"2019","journal-title":"Quaest Math"},{"key":"10.3233\/JIFS-182525_ref4","doi-asserted-by":"crossref","first-page":"228","DOI":"10.3390\/math7030228","article-title":"P-toplolgocalness\u2013a relative topologicalness in T-convergence spaces","volume":"7","author":"Li","year":"2019","journal-title":"Mathematics"},{"issue":"5","key":"10.3233\/JIFS-182525_ref5","first-page":"2256","article-title":"Degrees of special mappings in the theory of L-convex spaces","volume":"37","author":"Li","year":"2019","journal-title":"J Intell Fuzzy Syst"},{"key":"10.3233\/JIFS-182525_ref6","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1515\/math-2019-0133","article-title":"L-topological-convex spaces generated by L-convex bases","volume":"17","author":"Liao","year":"2019","journal-title":"Open Math"},{"key":"10.3233\/JIFS-182525_ref7","first-page":"22","article-title":"Lattice-valued fuzzy convex geometry","volume":"1641","author":"Maruyama","year":"2009","journal-title":"Optimization"},{"issue":"11","key":"10.3233\/JIFS-182525_ref8","doi-asserted-by":"crossref","first-page":"4021","DOI":"10.2298\/FIL1811021P","article-title":"Categorical properties of L-fuzzifying convergence spaces","volume":"32","author":"Pang","year":"2018","journal-title":"Filomat"},{"issue":"11","key":"10.3233\/JIFS-182525_ref9","doi-asserted-by":"crossref","first-page":"4811","DOI":"10.2298\/FIL1915811P","article-title":"Convenient properties of stratified L-convergence tower spaces","volume":"33","author":"Pang","year":"2019","journal-title":"Filomat"},{"issue":"15","key":"10.3233\/JIFS-182525_ref10","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.fss.2018.05.012","article-title":"Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces","volume":"369","author":"Pang","year":"2019","journal-title":"Fuzzy Sets Syst"},{"issue":"15","key":"10.3233\/JIFS-182525_ref11","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.fss.2018.08.002","article-title":"An axiomatic approach to bases and subbases in L-convex spaces and their applications","volume":"369","author":"Pang","year":"2019","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/JIFS-182525_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.11.010"},{"key":"10.3233\/JIFS-182525_ref13","doi-asserted-by":"publisher","DOI":"10.2989\/16073606.2019.1637379"},{"key":"10.3233\/JIFS-182525_ref14","doi-asserted-by":"crossref","unstructured":"Prenowitz W. , Jantosciak J. , Join Geometries, Springer Verlag. 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