Alizadeh Sigarpich, Leila; Allahviranloo, Tofigh; Hosseinzadeh Lotfi, Farhad; Aftab Kiani, Narsis Degeneracy in fuzzy linear programming and its application. (English) Zbl 1250.90117 Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 19, No. 6, 999-1012 (2011). Summary: In this paper, by a definite linear function for ranking symmetric triangular fuzzy numbers, in a Fuzzy Linear Programming problem (FLP) model, we introduced a Fuzzy Degenerate Solution (FDS). In the physical meaning, occurrence of degeneracy in a Fuzzy Minimal Cost Flow Network is investigated. To prevent of falling into Cycling phenomenon in optimization process, we defined two new techniques of Cycling prevention proper to fuzzy environment. Cited in 3 Documents MSC: 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming Keywords:symmetric triangular fuzzy number; fuzzy numbers ranking; fuzzy linear programming; fuzzy degeneracy; cycling prevention PDFBibTeX XMLCite \textit{L. Alizadeh Sigarpich} et al., Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 19, No. 6, 999--1012 (2011; Zbl 1250.90117) Full Text: DOI References: [1] Maleki H. R., Far East J. Appl. Math. 4 pp 283– [2] Luenberger D. C., Linear and Nonlinear Programming (1984) · Zbl 0571.90051 [3] Mahdavi-Amiri N., Appl. Math. Comput. 180 pp 206– [4] Bazaraa M. S., Linear Programming and Network Flows (1990) · Zbl 0722.90042 [5] DOI: 10.1287/mnsc.17.4.B141 · Zbl 0224.90032 [6] DOI: 10.1016/S0165-0114(83)80104-3 · Zbl 0517.90073 [7] DOI: 10.1016/0165-0114(94)00172-4 · Zbl 0844.03011 [8] DOI: 10.1007/978-94-017-3602-2 [9] DOI: 10.1016/0165-0114(89)90133-4 · Zbl 0662.90049 [10] DOI: 10.1007/s10479-006-7390-1 · Zbl 1101.90091 [11] DOI: 10.1016/0165-0114(93)90184-J · Zbl 0804.90137 [12] Herrera F., Interactive Fuzzy Optimization (1991) [13] Jahanshahloo G. R., Operations Research 2 (2002) [14] Li Ch., Inform. Sci. 158 pp 313– [15] Allahviranloo T., Appl. Math. Comput. 155 pp 493– [16] Bazaraa M. S., Linear Programming and Network Flows (2004) [17] Allahviranloo T., Int. J. Contemp. Math. Sci. 2 pp 167– · Zbl 1115.90069 [18] DOI: 10.1016/S0165-0114(98)00066-9 · Zbl 0956.90068 [19] Negoita C. V., Fuzziness in Management (1970) [20] DOI: 10.1016/0377-2217(95)00008-9 · Zbl 0914.90265 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.