Cutello, V. and Montero de Juan, Francisco Javier and Yañez Gestoso, Francisco Javier
(1996)
*Structure functions with fuzzy states.*
Fuzzy Sets and Systems, 83
(2).
pp. 189-202.
ISSN 0165-0114

PDF
Restringido a Repository staff only hasta 2020. 780kB |

Official URL: http://www.sciencedirect.com/science/article/pii/0165011495003908

## Abstract

Systems are modeled in Reliability Theory by means of Structure Functions, which show how the system state of performance depends on the state of all its components. In this paper we consider that the space of states allowed for both the system and its components is an appropriate family of fuzzy numbers. Basic concepts in classical crisp binary and multistate models in Reliability Theory are in this way generalized. Some particular consequences relative to component importance are also analyzed.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Reliability theory; Structure functions; Fuzzy numbers |

Subjects: | Sciences > Mathematics > Operations research Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 16827 |

References: | R.E. Barlow and B. Proschan, Statistical Theory of Reliability and Life Testing (To Begin With, Silver Spring, MD, 1981). L.A. Baxter, Continuum structures I, J. Appl. Probab. 21 (1986) 802-815. H.W. Block and T.H. Savits, Continuous multistate structure functions, Oper. Res. 32 (1984) 703 714. G. Bortolan and R. Degani, A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems 15 (1985) 1 19. K.Y. Cai, C.Y. Wen and M.L. Zhang, Coherent systems in PROFUST reliability theory, in: T. Onisawa and J. Kacprzyk, Eds.,Reliability and Safety Analysis under Fuzziness (Physica-Verlag, Heidelberg, 1995) 81 94. B. Cappelle, Multistate structure functions and possibility: an alternative approach to reliability, in: E.E. Kerre, Ed., Introduction to the Basic Principles of Fuzzy Set Theory and some of its Applications (Communication and Cognition, Gent, 1991) 252 293. V. Cutello and J. Montero, Reliability structure functions based upon fuzzy numbers, Proc. IEEE Conf. on Fuzzy Systems, Orlando (June 1994) 1137 1139. D. Dubois and H. Prade, Decision-making under fuzziness, in: M.M. Gupta, R.K. Ragade and R.R. Yager, Eds., Advances in Fuzzy Set Theory and Applications (North-Holland, Amsterdam, 1979) 279 302. E. EI-Neweihi and F. Proschan, Degradable systems: a survey of multistate system theory, Commun. Statist. Theory Methods 13 (1984) 405 432. J. Endrenyi, Reliability Modeling in Electric Power Systems (Wiley, New York, 1978). ] H. Furuta and N. Shiraishi, Fuzzy importance in fault tree analysis, Fuzzy Sets and Systems 12 (1984) 205 213. S. Gäihler and W. Gäihler, Fuzzy real numbers, Fuzz), Sets and Systems 66 (1994) 137-158. O. Kaleva, Fuzzy performance of a coherent system. J. Math. Anal. Appl. 117 (1986) 234 246. A. Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic (Van Nostrand Reinhold, New York, 1985). E.E. Kerre, A deeper look on fuzzy numbers from a theoretical as well as from a practical point of view, in: M.M. Gupta and T. Yamakawa, Eds., Fuzzy Logic in Knowledge-Based Systems, Decision and Control (Elsevier, Amsterdam, 1979) 153 164. K.B. Misra and K.P. Soman, Multistate fault tree analysis using fuzzy probability vectors and resolution identity, in: T. Onisawa and J. Kacprzyk, Eds., Reliability and Safety Analysis under Fuzziness (Physica-Verlag, Heidelberg, 1995) 113 125. M. Mizumoto and K. Tanaka, Some properties of fuzzy sets of type 2, Inform. Control 31 (1976) 312 340. M. Mizumoto and K. Tanaka, Some properties of fuzzy numbers, in: M.M. Gupta, R.K. Ragade and R.R. Yager, Eds., Advances in Fuzzy Set Theory and Applications (North-Holland, Amsterdam, 1979) 153 164. J. Montero, B. Cappelle and E. Kerre, The usefulness of complete lattices in reliability analysis, in: T. Onisawa and J. Kacprzyk, Eds., Fuzz)' Sets and Possibility Theory in Reliability and Safety Analysis (Springer-Verlag, Heidelberg, 1995). J. Montero, J. Tejada and J. Yañezz, General structure functions, Kybernetes 23 (1994) 13 22. J. Montero, J. Tejada and J. Yañez, Structural properties of continuum systems, Eur. J. Oper. Res. 45 (1990) 231 240. J. Montero, J. Tejada and J. Yañez, Multivalued continuum systems, Eur. J. Oper. Res. 69 (1993) 55 64. D. Singer, A fuzzy set approach to fault tree and reliability analysis, Fuzzy Sets and Systems 34 (1990) 145 155. D. Singer and P.G. Singer, System identification based on linguistic variables, Fuzzy Sets and Systems 47 (1992) 141- 149. [25] P.V. Suresh, D. Chaudhuri and B. Rao, Fuzzy-set approach to select maintenance strategies for multistate equipment, IEEE Trans. Reliability 43 (1994) 451 456. R.R. Yager, A characterization of the extension principle, Fuzzy Sets and Systems 18 (1986) 205 217. J. Yañez and J. Montero, Barlow Wu continuum systems: a discussion on the model, Top 1 (1993) 117 125. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning 1, Inform. Sci. 8 (1975) 199-249. |

Deposited On: | 24 Oct 2012 09:26 |

Last Modified: | 07 Feb 2014 09:36 |

Repository Staff Only: item control page