Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains

In the real-world manufacturing/distribution planning decision (MDPD) integration problems in supply chains, the environmental coefficients and parameters are normally imprecise due to incomplete and/or unavailable information. This work presents a fuzzy linear programming approach based on the possibility theory. It applies this approach to solve multi-product and multi-time period MDPD problems with imprecise goals and forecast demand by considering the time value of money of related operating cost categories. The proposed approach attempts to minimize the total manufacturing and distribution costs by considering the levels of inventory, subcontracting and backordering, the available machine capacity and labor levels at each source, forecast demand and available warehouse space at each destination. This study utilizes an industrial case study to demonstrate the feasibility of applying the proposed approach to practical MDPD problems. The primary contribution of this paper is a fuzzy mathematical programming methodology for solving the MDPD integration problems in uncertain environments.     

Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint

The work examines the feasibility of minimizing a linear objective function subject to a max-t fuzzy relation equation constraint, where t is a continuous/Archimedean t-norm. Conventional methods for solving this problem are significantly improved by, first separating the problem into two sub-problems according to the availability of positive coefficients. This decomposition is thus more easily handled than in previous literature. Next, based on use of the maximum solution of the constraint equation, the sub-problem with non-positive coefficients is solved and the size of the sub-problem with positive coefficients reduced as well. This step is unique among conventional methods, owing to its ability to determine as many optimal variables as possible. Additionally, several rules are developed for simplifying the remaining problem. Finally, those undecided optimal variables are obtained using the covering problem rather than the branch-and-bound methods. Three illustrative examples demonstrate that the proposed approach outperforms conventional schemes. Its potential applications are discussed as well.     

Enhancing the semantics of UML association redefinition

Association redefinition is a UML construct that permits us to define an association end more specifically in a particular context. Concretely, it allows specifying some additional participation and cardinality constraints on the association. Association refinements, which have been studied and used by many authors in conceptual modelling languages prior to UML, are closely related to association redefinitions. They also permit to refine the ends of an association adding participation and cardinality constraints. In this paper, we analyze and compare the semantics of both concepts and propose to extend the semantics of association redefinitions in UML to cover all the constraints that may be expressed by association refinements in other conceptual modelling languages. Additionally, we present how to integrate previous results on validation of association refinements to UML and how to generate code for a relational technology platform. Finally, we provide a prototype tool to verify the feasibility of the approach.     

Model-based cognitive diagnosis

This paper considers the problem of cognitive diagnosis as an instance of general diagnosis, as studied in artificial intelligence. Cognitive diagnosis is the process of inferring a cognitive state from observations of performance. It is thus a key component of any system which attempts to build a dynamic model of the user of that system. Many issues in cognitive diagnosis, previously discussed informally, are mapped onto formal techniques, with consequent increased clarity and rigour. But it is concluded that the general theories for diagnosis must be broadened to fully encompass the problems of cognitive diagnosis.     

Using immune genetic algorithm based hybrid techniques for short-term unit commitment problem

This paper presents a hybrid chaos search (CS), immune algorithm (IA)/genetic algorithm (GA), and fuzzy system (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shut-down schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve, and individual units. First, we combined the IA and GA, then we added the CS and the FS approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20, and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional Tabu search (TTS). A comparison with an immune genetic algorithm (IGA) combined with the CS and FS was carried out. The results show that the CS and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

Practical implementation of possibilistic probability mass functions

 Probability assessments of events are often linguistic in nature. We model them by means of possibilistic probabilities (a version of Zadeh's fuzzy probabilities with a behavioural interpretation) with a suitable shape for practical implementation (on a computer). Employing the tools of interval analysis and the theory of imprecise probabilities we argue that the verification of coherence for these possibilistic probabilities, the corrections of non-coherent to coherent possibilistic probabilities and their extension to other events and gambles can be performed by finite and exact algorithms. The model can furthermore be transformed into an imprecise first-order model, useful for decision making and statistical inference.     

The uses of fuzzy logic in autonomous robot navigation

 The development of techniques for autonomous navigation in real-world environments constitutes one of the major trends in the current research on robotics. An important problem in autonomous navigation is the need to cope with the large amount of uncertainty that is inherent of natural environments. Fuzzy logic has features that make it an adequate tool to address this problem. In this paper, we review some of the possible uses of fuzzy logic in the field of autonomous navigation. We focus on four issues: how to design robust behavior-producing modules; how to coordinate the activity of several such modules; how to use data from the sensors; and how to integrate high-level reasoning and low-level execution. For each issue, we review some of the proposals in the literature, and discuss the pros and cons of fuzzy logic solutions. Received: 31 March 1997 / Accepted: 24 September 1997