{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:24:43Z","timestamp":1758273883136,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T00:00:00Z","timestamp":1650153600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T00:00:00Z","timestamp":1650153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61877014"],"award-info":[{"award-number":["61877014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s00500-022-07076-x","type":"journal-article","created":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T11:02:40Z","timestamp":1650193360000},"page":"5131-5142","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fuzzy relation inequality-based consistency of the wireless communication basic-station system considering the non-working state stations"],"prefix":"10.1007","volume":"26","author":[{"given":"Xiaopeng","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianzhong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,17]]},"reference":[{"key":"7076_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.08.012","author":"S Aliannezhadi","year":"2019","unstructured":"Aliannezhadi S, Molai AA (2019) Geometric programming with a single-term exponent subject to bipolar max-product fuzzy relation equation constraints. Fuzzy Sets Syst. https:\/\/doi.org\/10.1016\/j.fss.2019.08.012","journal-title":"Fuzzy Sets Syst"},{"key":"7076_CR2","doi-asserted-by":"crossref","unstructured":"Bourke MM, Fisher DG (1998) Solution algorithms for fuzzy relational equations with max-product composition. Fuzzy Sets Syst 94:61\u201369","DOI":"10.1016\/S0165-0114(96)00246-1"},{"key":"7076_CR3","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1007\/s00500-001-0157-3","volume":"6","author":"L Chen","year":"2002","unstructured":"Chen L, Wang PP (2002) Fuzzy relation equations (I): the general and specialized solving algorithms. Soft Comput 6:428\u2013435","journal-title":"Soft Comput"},{"key":"7076_CR4","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.compeleceng.2006.01.015","volume":"32","author":"K-C Chu","year":"2006","unstructured":"Chu K-C, Lin FY-S (2006) Survivability and performance optimization of mobile wireless communication networks in the event of base station failure. Comput Elect Eng 32:50\u201364","journal-title":"Comput Elect Eng"},{"key":"7076_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.09.051","author":"M Cornejo","year":"2019","unstructured":"Cornejo M, Lobo D, Medina J (2019) On the solvability of bipolar max-product fuzzy relation equations with the product negation. J Comput Appl Math. https:\/\/doi.org\/10.1016\/j.cam.2018.09.051","journal-title":"J Comput Appl Math"},{"key":"7076_CR6","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5646","author":"M Cornejo","year":"2019","unstructured":"Cornejo M, Lobo D, Medina J (2019) Bipolar fuzzy relation equations systems based on the product t-norm. Math Methods Appl Sci. https:\/\/doi.org\/10.1002\/mma.5646","journal-title":"Math Methods Appl Sci"},{"key":"7076_CR7","doi-asserted-by":"crossref","unstructured":"Cornejo M, Lobo D, Medina J (2017) Bipolar fuzzy relation equations based on product t-norm, Proceedings of 2017 IEEE international conference on fuzzy systems","DOI":"10.1109\/FUZZ-IEEE.2017.8015691"},{"key":"7076_CR8","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/0165-0114(82)90043-4","volume":"7","author":"E Czogala","year":"1982","unstructured":"Czogala E, Drewniak J, Pedrycz W (1982) Fuzzy relation equations on a finite set. Fuzzy Sets Syst 7:89\u2013101","journal-title":"Fuzzy Sets Syst"},{"key":"7076_CR9","doi-asserted-by":"crossref","unstructured":"De Baets B (2000) Analytical solution methods for fuzzy relational equations, In: D. Dubois, H. Prade (Eds.), Fundamentals of fuzzy sets, in: Handb. Fuzzy Sets Ser., vol.1, Kluwer Academic Publishers, 291-340","DOI":"10.1007\/978-1-4615-4429-6_7"},{"key":"7076_CR10","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.ins.2011.06.009","volume":"234","author":"S Freson","year":"2013","unstructured":"Freson S, De Baets B, De Meyer H (2013) Linear optimization with bipolar max-min constraints. Inf Sci 234:3\u201315","journal-title":"Inf Sci"},{"key":"7076_CR11","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s00500-019-04289-5","volume":"24","author":"A Garai","year":"2020","unstructured":"Garai A, Roy TK (2020) Multi-objective optimization of cost-effective and customer-centric closed-loop supply chain management model in T-environment. Soft Comput 24:155\u2013178","journal-title":"Soft Comput"},{"key":"7076_CR12","doi-asserted-by":"publisher","first-page":"950","DOI":"10.1007\/s12597-016-0260-y","volume":"53","author":"A Garai","year":"2016","unstructured":"Garai A, Mandal P, Roy TK (2016) Intuitionistic fuzzy T-sets based optimization technique for production-distribution planning in supply chain management. OPSEARCH 53:950\u2013975","journal-title":"OPSEARCH"},{"key":"7076_CR13","doi-asserted-by":"publisher","first-page":"106949","DOI":"10.1016\/j.asoc.2020.106949","volume":"100","author":"A Garai","year":"2021","unstructured":"Garai A, Chowdhury S, Sarkar B, Roy TK (2021) Cost-effective subsidy policy for growers and biofuels-plants in closed-loop supply chain of herbs and herbal medicines: an interactive bi-objective optimization in T-environment. Appl Soft Comput 100:106949","journal-title":"Appl Soft Comput"},{"key":"7076_CR14","doi-asserted-by":"crossref","unstructured":"Guo H, Zheng Cai-Fen, Zhu Tian-Xiang, Lin Hai-Tai, Yang Xiao-Peng (2018) Min-product fuzzy relation inequalities with application in supply chain, 2018 14th international conference on natural computation, Fuzzy systems and knowledge discovery (ICNC-FSKD), pp554-560","DOI":"10.1109\/FSKD.2018.8686941"},{"issue":"1","key":"7076_CR15","first-page":"1","volume":"16","author":"B Hedayatfar","year":"2019","unstructured":"Hedayatfar B, Molai AA, Aliannezhadi S (2019) Separable programming problems with the max-product fuzzy relation equation constraints. Iran J Fuzzy Syst 16(1):1\u201315","journal-title":"Iran J Fuzzy Syst"},{"key":"7076_CR16","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.apacoust.2019.04.020","volume":"154","author":"H Khelladi","year":"2019","unstructured":"Khelladi H, Mograne MA (2019) Optimization of some acoustic parameters intended for the wireless communication in seawater. Appl Acoust 154:59\u201367","journal-title":"Appl Acoust"},{"key":"7076_CR17","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s10700-008-9029-y","volume":"7","author":"P Li","year":"2008","unstructured":"Li P, Fang S-C (2008) On the resolution and optimization of a system of fuzzy relational equations with sup-$$T$$ composition. Fuzzy Opti Decis Mak 7:169\u2013214","journal-title":"Fuzzy Opti Decis Mak"},{"key":"7076_CR18","doi-asserted-by":"publisher","first-page":"1399","DOI":"10.1007\/s00500-013-1152-1","volume":"18","author":"P Li","year":"2014","unstructured":"Li P, Liu Y (2014) Linear optimization with bipolar fuzzy relational equation constraints using \u0141ukasiewicz triangular norm. Soft Comput 18:1399\u20131404","journal-title":"Soft Comput"},{"key":"7076_CR19","doi-asserted-by":"publisher","first-page":"177571","DOI":"10.1109\/ACCESS.2019.2958205","volume":"7","author":"G Li","year":"2019","unstructured":"Li G, Qiu J, Xiao G, Qu H, Yang X (2019) Optimal strong solution of the minimax problem with two-sided fuzzy relation inequality constraints. IEEE Access 7:177571\u2013177584","journal-title":"IEEE Access"},{"key":"7076_CR20","doi-asserted-by":"publisher","first-page":"593","DOI":"10.3233\/JIFS-191565","volume":"39","author":"G Li","year":"2020","unstructured":"Li G, Qiu J, Yang X (2020) Weighted minimax programming subject to the two-sides fuzzy relation inequalities with max-product composition. J Intel Fuzzy Syst 39:593\u2013605","journal-title":"J Intel Fuzzy Syst"},{"key":"7076_CR21","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.comcom.2019.08.023","volume":"147","author":"Z Lin","year":"2019","unstructured":"Lin Z, Wang P (2019) A review of data sets of short-range wireless networks. Comput Commun 147:138\u2013158","journal-title":"Comput Commun"},{"key":"7076_CR22","first-page":"4960638","volume":"2019","author":"H Lin","year":"2019","unstructured":"Lin H, Yang X, Guo H, Zheng C, Yang X (2019) Maximin optimization problem subject to min-product fuzzy relation inequalities with application in supply and demand scheme 2019:4960638","journal-title":"Maximin optimization problem subject to min-product fuzzy relation inequalities with application in supply and demand scheme"},{"key":"7076_CR23","doi-asserted-by":"publisher","first-page":"746","DOI":"10.1016\/j.proeng.2012.01.1096","volume":"31","author":"C Liu","year":"2012","unstructured":"Liu C, Zhou Q, Hu J, Xu H, Zhang H (2012) Modelling and simulation of centralized electric vehicle charging station wireless communication networks. Procedia Eng 31:746\u2013750","journal-title":"Procedia Eng"},{"key":"7076_CR24","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.ins.2016.04.041","volume":"360","author":"CC Liu","year":"2016","unstructured":"Liu CC, Lur YY, Wu YK (2016) Linear optimization of bipolar fuzzy relational equations with max-\u0141ukasiewicz composition. Inf Sci 360:149\u2013162","journal-title":"Inf Sci"},{"key":"7076_CR25","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1109\/91.784204","volume":"7","author":"J Loetamonphong","year":"1999","unstructured":"Loetamonphong J, Fang S-C (1999) An efficient solution procedure for fuzzy relation equations with max-product composition. IEEE Trans Fuzzy Syst 7:441\u2013445","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"7076_CR26","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.mcm.2010.02.046","volume":"52","author":"L Luoh","year":"2010","unstructured":"Luoh L, Liaw Y-K (2010) Novel approximate solving algorithm for fuzzy relational equations. Math Comput Model 52:303\u2013308","journal-title":"Math Comput Model"},{"issue":"1","key":"7076_CR27","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1109\/TFUZZ.2002.806322","volume":"11","author":"L Luoh","year":"2003","unstructured":"Luoh L, Wang W-J, Liaw Y-K (2003) Matrix-pattern-based computer algorithm for solving fuzzy relation equations. IEEE Trans Fuzzy Syst 11(1):100\u2013108","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"7076_CR28","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.fss.2013.03.009","volume":"232","author":"Z Matusiewicz","year":"2013","unstructured":"Matusiewicz Z, Drewniak J (2013) Increasing continuous operations in fuzzy max-* equations and inequalieties. Fuzzy Sets Syst 232:120\u2013133","journal-title":"Fuzzy Sets Syst"},{"key":"7076_CR29","doi-asserted-by":"publisher","first-page":"1240","DOI":"10.1016\/j.mcm.2010.01.006","volume":"51","author":"AA Molai","year":"2010","unstructured":"Molai AA (2010) Fuzzy linear objective function optimization with fuzzyvalued max-product fuzzy relation inequality constraints. Math Comput Model 51:1240\u20131250","journal-title":"Math Comput Model"},{"key":"7076_CR30","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.ins.2011.04.012","volume":"234","author":"AA Molai","year":"2013","unstructured":"Molai AA (2013) Resolution of a system of the max-product fuzzy relation equations using L$$\\circ $$U-factorization. Inf Sci 234:86\u201396","journal-title":"Inf Sci"},{"key":"7076_CR31","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.cie.2014.03.024","volume":"72","author":"AA Molai","year":"2014","unstructured":"Molai AA (2014) A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints. Comput Ind Eng 72:306\u2013314","journal-title":"Comput Ind Eng"},{"key":"7076_CR32","doi-asserted-by":"publisher","first-page":"3725","DOI":"10.1007\/s00500-020-05402-9","volume":"25","author":"B Mondal","year":"2021","unstructured":"Mondal B, Garai A, Mukhopadhyay A, Majumder SK (2021) Inventory policies for seasonal items with logistic-growth demand rate under fully permissible delay in payment: a neutrosophic optimization approach. Soft Comput 25:3725\u20133750","journal-title":"Soft Comput"},{"issue":"7","key":"7076_CR33","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1007\/s00500-006-0103-5","volume":"11","author":"K Peeva","year":"2007","unstructured":"Peeva K, Kyosev Y (2007) Algorithm for solving max-product fuzzy relational equations. Soft Comput 11(7):593\u2013605","journal-title":"Soft Comput"},{"key":"7076_CR34","doi-asserted-by":"publisher","first-page":"60811","DOI":"10.1109\/ACCESS.2020.2984095","volume":"8","author":"J Qiu","year":"2020","unstructured":"Qiu J, Xue H, Li G, Yang X (2020) Fuzzy relation bilevel optimization model in the wireless communication station system. IEEE Access 8:60811\u201360823","journal-title":"IEEE Access"},{"key":"7076_CR35","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.ins.2021.03.021","volume":"567","author":"J Qiu","year":"2021","unstructured":"Qiu J, Li G, Yang X (2021) Arbitrary-term-absent max-product fuzzy relation inequalities and its lexicographic minimal solution. Inf Sci 567:167\u2013184","journal-title":"Inf Sci"},{"issue":"11","key":"7076_CR36","doi-asserted-by":"publisher","first-page":"3374","DOI":"10.1109\/TFUZZ.2020.3021726","volume":"29","author":"J Qiu","year":"2021","unstructured":"Qiu J, Li G, Yang X (2021) Bilevel optimization problem with random-term-absent max-product fuzzy relation inequalities constraint. IEEE Trans Fuzzy Syst 29(11):3374\u20133388","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"7076_CR37","doi-asserted-by":"crossref","unstructured":"Ranjan A, Sahu HB, Misrab P (2020) Modeling and measurements for wireless communication networks in underground mine environments, Measurement 149, ID 106980","DOI":"10.1016\/j.measurement.2019.106980"},{"key":"7076_CR38","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/S0019-9958(76)90446-0","volume":"30","author":"E Sanchez","year":"1976","unstructured":"Sanchez E (1976) Resolution of composite fuzzy relation equations. Inf Control 30:38\u201348","journal-title":"Inf Control"},{"key":"7076_CR39","first-page":"221","volume-title":"Fuzzy automata and decision processes","author":"E Sanchez","year":"1977","unstructured":"Sanchez E (1977) Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Gupta MM, Saridis GN, Gaines BR (eds) Fuzzy automata and decision processes. North-Holland, Amsterdam, pp 221\u2013234"},{"key":"7076_CR40","doi-asserted-by":"publisher","first-page":"3766","DOI":"10.1016\/j.ins.2008.05.030","volume":"178","author":"B-S Shieh","year":"2008","unstructured":"Shieh B-S (2008) Deriving minimal solutions for fuzzy relation equations with max-product composition. Inf Sci 178:3766\u20133774","journal-title":"Inf Sci"},{"key":"7076_CR41","first-page":"29","volume":"1","author":"Y-K Wu","year":"2004","unstructured":"Wu Y-K, Guu S-M (2004) Finding the complete set of minimal solutions for fuzzy relational equations with max-product composition. Int J Oper Res 1:29\u201336","journal-title":"Int J Oper Res"},{"key":"7076_CR42","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.aeue.2019.01.025","volume":"101","author":"D Xu","year":"2019","unstructured":"Xu D, Li Q (2019) Resource allocation in OFDM-based wireless powered communication networks with SWIPT. AEU-Int J Electron Commun 101:69\u201375","journal-title":"AEU-Int J Electron Commun"},{"key":"7076_CR43","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1109\/TSMC.1987.289361","volume":"17","author":"C-W Xu","year":"1987","unstructured":"Xu C-W, Lu Y-Z (1987) Fuzzy model identification and self-learning for dynamic systems. IEEE Trans Syst Man Cybernet 17:683\u2013689","journal-title":"IEEE Trans Syst Man Cybernet"},{"key":"7076_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.08.005","author":"XP Yang","year":"2019","unstructured":"Yang XP (2019) Resolution of bipolar fuzzy relation equations with max-\u0141ukasiewicz composition. Fuzzy Sets Syst. https:\/\/doi.org\/10.1016\/j.fss.2019.08.005","journal-title":"Fuzzy Sets Syst"},{"key":"7076_CR45","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.fss.2019.04.029","volume":"384","author":"XG Yang","year":"2020","unstructured":"Yang XG (2020) Solutions and strong solutions of min-product fuzzy relation inequalities with application in supply chain. Fuzzy Sets Syst 384:54\u201374","journal-title":"Fuzzy Sets Syst"},{"key":"7076_CR46","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.ins.2016.04.014","volume":"358\u2013359","author":"X-P Yang","year":"2016","unstructured":"Yang X-P, Zhou X-G, Cao B-Y (2016) Latticized linear programming subject to max-product fuzzy relation inequalities with application in wireless communication. Inf Sci 358\u2013359:44\u201355","journal-title":"Inf Sci"},{"key":"7076_CR47","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.fss.2017.08.001","volume":"341","author":"X-P Yang","year":"2018","unstructured":"Yang X-P, Yuan D-H, Cao B-Y (2018) Lexicographic optimal solution of the multi-objective programming problem subject to max-product fuzzy relation inequalities. Fuzzy Sets Syst 341:92\u2013112","journal-title":"Fuzzy Sets Syst"},{"key":"7076_CR48","doi-asserted-by":"publisher","first-page":"71306","DOI":"10.1109\/ACCESS.2018.2878748","volume":"6","author":"X Zhou","year":"2018","unstructured":"Zhou X, Zhong X, Lin H, Qin Z, Yang X (2018) Lexicographic maximum solution of min-product fuzzy relation inequalities for modeling the optimal pricing with fixed priority grade in supply chain. IEEE Access 6:71306\u201371316","journal-title":"IEEE Access"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07076-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07076-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07076-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T22:09:02Z","timestamp":1652479742000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07076-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,17]]},"references-count":48,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["7076"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07076-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2022,4,17]]},"assertion":[{"value":"17 February 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Xiaopeng Yang has received research grants from the National Natural Science Foundation of China. Xiaopeng Yang declares that he has no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}