Lopez, Victoria and Montero de Juan, Francisco Javier and Garmendia , Luis and Resconi, Germano
(2008)
*Specification and computing states in fuzzy algorithms.*
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16
(3).
pp. 301-336.
ISSN 0218-4885

PDF
Restringido a Repository staff only hasta 2020. 366kB |

Official URL: http://www.worldscinet.com/ijufks/16/1603/S0218488508005303.html

## Abstract

Since many complex decision making problems can be solved solely by means of an ap-propriate algorithm, checking the quality of such algorithm is a key issue, even more relevant in the presence of fuzzy uncertainty. In this paper we postulate that the de-sign and formal specication of algorithms can be translated into a fuzzy framework introducing fuzzy rst order logic and assert transformations. Following the classical crisp scheme we rst formalize the concepts of a fuzzy algorithm specication and a fuzzy computing state, and then a new fuzzy computational logic is presented, so we can derive a computational reasoning for correctness of algorithms. A proposal for the evaluation and setting of suitable degrees of truth to computing states is also introduced.

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

Uncontrolled Keywords: | Fuzzy algorithms; Fuzzy specication; Decision making. |

Subjects: | Sciences > Computer science > Artificial intelligence |

ID Code: | 16192 |

References: | R. Lorentz and D. B. Benson, Deterministic and nondeterministic ow-chart interpretations,J. Comput. System Sci. 27 (1983) 400{433. M. J. Beeson, Foundations of Constructive Mathematics (Springer, Berlin, 1985). K. L. Clark, Negations as failure, in Logic and Data Bases, eds. H. Gallaire and J. Winker (Plenum Press, New York, 1973) pp. 293{306. M. Joliat, A simple technique for partial elimination of unit productions from LR(k) parsers, IEEE Trans. Comput. 27 (1976) 753{764. D. Dolve, Unanimity in an unknown and unreliable environment, Proc. 22nd Annual Symposium on Foundations of Computer Science, Nashville, TN, Oct. 1981, pp. 159{168. R. Tamassia, C. Batini and M. Talamo, An algorithm for automatic layout of entity relationship diagrams, in Entity-Relationship Approach to Software Engineering, Proc. 3rd Int. Conf. on Entity-Relationship Approach, eds. C. G. Davis, S. Jajodia, P. A. Ng and R. T. Yeh (North-Holland, Amsterdam, 1983) pp. 421{439. W. L. Gewirtz, Investigations in the theory of descriptive complexity, Ph.D. Thesis, New York University, 1974. A. Amo. D. G_omez, J. Montero and G. Biging, Improving fuzzy classi_cation by means of a segmentation algorithm, in H. Bustince, F. Herrera and J. Montero (eds.), Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, Springer, Berlin, in press. A. Amo, J. Montero and E. Molina, Representation of consistent recursive rules, European J. Operations Research 130 (2001) 29{53. H. K. Berg, Formal Methods of Program Veri_cation and Speci_cation (Prentice Hall, New Jersey, 1982). M. Broy and B. Krieg, Derivation of invariant assertions during program development by transformation, ACM Transactions on Programming Languages and Systems 2 (1980) 321{327. T. Calvo, A. Kolesarova, M. Komornikova and R. Mesiar, Agreggation operators: properties, classes and construction methods, in T. Calvo, G. Mayor and R. Mesiar (eds.), Aggregation Operators (Physica-Verlag, Heidelberg, 2002), pp. 3{104. T. Calvo and A. Pradera, Double aggregation operators, Fuzzy Sets and Systems 142 (2004) 15{33. J. L. Castro, M. Delgado and E. Trillas, Inducing implication relations, Int. J. Approximate Reasoning 10 (1994) 235{250. J. L. Castro, E. Trillas and S. Cubillo, On consequence in aproximate reasoning, J. Applied Non-Classical Logics 4 (1994) 91{103. V. Cutello and J. Montero, Recursive connective rules, Int. J. Intelligent Systems 14 (1999) 3{20. E. W. Dijkstra, A Discipline of Programming (Prentice Hall, 1976). E. W. Dijkstra and W. H. J. Feijen, A Method of Programming (Addison-Wesley, 1988). H. B. Enderton, A Mathematical Introduction to Logic (Academic Press, 2001). R. Fuller and P. Majlender, An analytic approach for obtaining maximal entropy OWA operator weights, Fuzzy Sets and Systems 124 (2001) 53{57. D. G_omez and J. Montero, A discussion on aggregation operators, Kybernetika 40 (2004) 107{120. C. A. R. Hoare, An axiomatic basis for computer programming, Communications ACM 12 (1969) 89{100. B. J. Kim, R. R. Bishu, Uncertainty of human error and fuzzy approach to human reliability analysis, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 14(1,1) (2006) 111{129. E. Klement, R. Mesiar and E. Pap, Triangular Norms. Trends in Logic (Kluwer Academic Publishers, Dordrecht, 2000). V. L_opez, Dise~no y veri_caci_on de algoritmos para el tratamiento difuso de im_agenes digitales en teledetecci_on y seguridad, Ph.D. Thesis, Politechnic University of Madrid, Spain, 2004 (in Spanish). V. L_opez, J. M. Cleva and J. Montero, A functional tool for fuzzy _rst order logic evaluation, in D. Ruan, P. D'hont, P. F. Fantoni, M. De Cock, M. Nachtegael and E. E. Kerre (eds.), Applied Arti_cial Intelligence (World Scienti_c, New Jersey, 2006), pp. 19{26. T. Marchant, Maximal orness weights with a _xed variability for OWA operators, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 14(3) (2006) 271{276. J. Montero, Classi_ers and decision makers, in D. Ruan et al. (eds.), Applied Compu-tational Intelligence (World Scienti_c, Singapore, 2003), pp. 19{24. J. Montero, Comprehensive fuzziness, Fuzzy Sets and Systems 20 (1986) 89{86. J. Montero, Extensive fuzziness, Fuzzy Sets and Systems 21 (1987) 201{209. J. Montero, V. L_opez and D. G_omez, The role of fuzziness in decision making, in D. Ruan et al. (eds.), Fuzzy Logic: A Spectrum of Applied and Theoretical Issues, Springer, in press. J. Montero and M. Mendel, Crisp acts, fuzzy decisions, in S. Barro et al. (eds.), Advances in Fuzzy Logic (Universidad de Santiago de Compostela, 1998), pp. 219{238. A. Pradera, E. Trillas and S. Cubillo, On modus ponens generating functions, J. Uncertaintly, Fuzziness and Knowledge-Based Systems 8 (2000) 7{20. G. Resconi, Intelligent agents: theory and applications, Studies in Fuzziness and Soft Computing, 155 (Springer, 2004). G. Resconi and B. Kovalerchuk, The logic of uncertainty with irrational agents, Joint Conference on Information Sciences, Kaohsiung, Taiwan, October 8{11, 2006. B. Schweizer and A. Sklar, Probabilistic Metric Spaces (North-Holland, New York, 1984). H. Xingui, Fuzzy computational reasoning and neural networks, IEEE Tools for Arti_cial Intelligence (1990) 706{711. L. A. Zadeh, Similarity relations and fuzzy orderings, Information Science 3 (1971) 177{200. L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338{353. |

Deposited On: | 10 Sep 2012 11:51 |

Last Modified: | 06 Feb 2014 10:39 |

Repository Staff Only: item control page