Knowledge Based Systems And Fuzzy Boolean Programming

This paper discusses the applications of Fuzzy Boolean Programming (FBP) problems for representing and reasoning with Propositional Knowledge. The use of the models provided by the FBP are proposed to answer imprecise questions in precisely stated KBS. Also, the advantages of using Fuzzy Boolean Programming instead of classical ones are presented in the framework of Propositional Knowledge. Keywords. Approximate reasoning, fuzzy boolean programming, knowledge based systems. 1. Introduction In the last years, efficient methods performing automated reasoning have become increasingly important. Problems in automated reasoning in Artificial Intelligence (AI) are often represented in a language which is a derivation of the Predicate Calculus. By means of substituting constants and functions by variables (instantiation), statements in such a language are reduced to statements in the Propositional Calculus (Loveland, 1978; Nilsson, 1982). In Willians 1977 was shown that statements in the Pro..

Algunas formas de comparar números difusos (I).

Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEpu

An Algorithm For The Fuzzy Maximum Flow Problem

The problem of finding the maximum flow between a source and a destination node in a network with uncertainties in its capacities is an important problem of network flows, since it has a wide range of applications in different areas (telecommunications, transportations, manufacturing, etc) and therefore deserves special attention. However, due to complexity in working with this kind of problems, there are a few algorithms in literature, which demand that the user informs the desirable maximum flow, which is difficult when the network is the large scale. In this paper, an algorithm based on the classic algorithm of Ford-Fulkerson is proposed. The algorithm uses the technique of the incremental graph and it does not request that the decision-maker informs the desirable flow, in contrast of the main works of literature. The uncertainties of the parameters are resolved using the fuzzy sets theory. © 2007 IEEE.Ahuja, R.K., Magnanti, T.L., Orlin, J.B., Network flows: Theory, algorithms and applications (1993) Prendee HallBazaraa, M., Jarvis, J., Sherali, H.F., (1990) Linear programming and network flows, , John WileyGondran, M., Minoux, M., (1984) Graph and Algorithm, , New York, John Wiley & SonsChanas, S., Kolodziejczyk, W., Maximum flow in a network with fuzzy arc capacities (1982) Fuzzy Sets and Systems, 8, pp. 165-173Chanas, S., Kolodziejczyk, W., Real-valued flows in a network with fuzzy arc capacities (1984) Fuzzy Sets and Systems, 13, pp. 139-151Chanas, S., Kolodziejczyk, W., Integer flows in network with fuzzy capacity constraints (1986) Networks, 16, pp. 17-31Kim, K., Roush, F., Fuzzy flows on network (1982) Fuzzy Sets and System, 8, pp. 35-38Takahashi, M.T., Contribuções ao estudo de grafos fuzzy: Teoria e algoritmos (in Portuguese), (2004), Ph.D. thesis, Faculty. Elect Eng, Campinas Univ, Campinas, BrazilZadeh, L., Fuzzy sets (1965) Inf. and control, 8 (338 -3), p. 53Zadeh, L., Fuzzy algorithms (1968) Inf. and control, 12Zadeh, L., Fuzzy sets as a theory of possibility (1978) Fuzzy Sets and Systems, 1Chanas, S., Delgado, M., Verdegay, J.L., Vila, M., Fuzzy optimal flow on imprecise structures (1995) European Journal of Operational Research, 83 (3), pp. 568-580Delgado, M., Verdegay, J.L., Vila, M., On fuzzy tree definition (1985) European Journal of Operational Research, 22, pp. 243-249Malik, D., Moderson, J.N., (2001) Fuzzy discrete structures, 58. , Studies in Fuzziness and Soft Computing, Spring-VerlagBellman, R., Zadeh, L., Decision-making in a Fuzzy Environment (1970) Management Science, 17 (4), pp. B-141-B-16

Fuzzy Linear Programming Approach to Multi-mode Distribution Planning Problem

In this study we address the multi-product, multi-period, multi-mode distribution planning problem. The objective of this paper is to present a real distribution planning problem in which rail/road transportation is integrated within a whole focus on supply chain management. However, in real world problems, practical situations are often not well-defined and thus can not be described precisely. Therefore fuzzy mathematical programming becomes a valuable extension of traditional crisp optimization models. This paper also illustrates how a fuzzy linear programming approach be used to model and solve the multi-mode transportation problem