{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:26:02Z","timestamp":1760232362090,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T00:00:00Z","timestamp":1667174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61962001","YCX22196","2020KYQD 14"],"award-info":[{"award-number":["61962001","YCX22196","2020KYQD 14"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012481","name":"Graduate Innovation Project of North Minzu University","doi-asserted-by":"publisher","award":["61962001","YCX22196","2020KYQD 14"],"award-info":[{"award-number":["61962001","YCX22196","2020KYQD 14"]}],"id":[{"id":"10.13039\/501100012481","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Project of Introducing Personnel from North Minzu University","award":["61962001","YCX22196","2020KYQD 14"],"award-info":[{"award-number":["61962001","YCX22196","2020KYQD 14"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we focus on the symmetrical relationship between multi-properties objective reachability problems and multi-objective sets reachability problems over FKS based on Zadeh logic. First, we give the formal definitions of those two problems. Then, we study their relationships and find that a multi-properties objective reachability problem and a special case of multi-objective sets reachability problems have symmetry. Finally, we give a polynomial time algorithm based on this symmetry to convert a multi-properties objective reachability problem to a multi-objective sets reachability problem. In addition, an illustrative example is listed to express some possible application methods based on our work.<\/jats:p>","DOI":"10.3390\/sym14112278","type":"journal-article","created":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T06:49:02Z","timestamp":1667371742000},"page":"2278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Method Converting Multi-Properties Objective Reachability Problems to Multi-Objective Sets Reachability Problems over FKS"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5350-956X","authenticated-orcid":false,"given":"Zhaokai","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, North Minzu University, Yinchuan 750000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanyou","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, North Minzu University, Yinchuan 750000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xia","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, North Minzu University, Yinchuan 750000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingnan","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, North Minzu University, Yinchuan 750000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhou, J., Wu, S., and Gao, J. 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