The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms

We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomial-size fuzzy circuits composed of fuzzy gates. We also introduce fuzzy proof verification systems to model the fuzzification of nondeterminism. Those models help us identify four complexity classes: Fuzzy-FPA of fuzzy functions, Fuzzy-PA and Fuzzy-NPA of fuzzy decision problems, and Fuzzy-NPAO of fuzzy optimization problems. Based on a relative approximation scheme targeting fuzzy membership degree, we formulate two notions of "reducibility" in order to compare the computational complexity of two fuzzy problems. These reducibility notions make it possible to locate the most difficult fuzzy problems in Fuzzy-NPA and in Fuzzy-NPAO.Comment: A4, 10pt, 10 pages. This extended abstract already appeared in the Proceedings of the Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS 2014) and 15th International Symposium on Advanced Intelligent Systems (ISIS 2014), December 3-6, 2014, Institute of Electrical and Electronics Engineers (IEEE), pp. 29-35, 201

Representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n-cell number spaces

In this paper, we discuss the problem of characterization for uncertain multichannel digital signal spaces, propose using fuzzy n-cell number space to represent uncertain n-channel digital signal space, and put forward a method of constructing such fuzzy n-cell numbers. We introduce two new metrics and concepts of certain types of difference values on fuzzy n -cell number space and study their properties. Further, based on the metrics or difference values appropriately defined, we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment, and we also give practical examples to show the application and rationality of the proposed technique

A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production

This paper addresses the problem of the optimal design of batch plants with imprecise demands and proposes an alternative treatment of the imprecision by using fuzzy concepts. For this purpose, we extended a multiobjective genetic algorithm (MOGA) developed in previousworks, taking into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The former is computed by comparing the fuzzy computed production time to a given fuzzy production time horizon and the latter is based on the additional fuzzy demand that the plant is able to produce. The methodology provides a set of scenarios that are helpful to the decision’s maker and constitutes a very promising framework for taken imprecision into account in new product development stage

Fuzzy-based Propagation of Prior Knowledge to Improve Large-Scale Image Analysis Pipelines

Many automatically analyzable scientific questions are well-posed and offer a variety of information about the expected outcome a priori. Although often being neglected, this prior knowledge can be systematically exploited to make automated analysis operations sensitive to a desired phenomenon or to evaluate extracted content with respect to this prior knowledge. For instance, the performance of processing operators can be greatly enhanced by a more focused detection strategy and the direct information about the ambiguity inherent in the extracted data. We present a new concept for the estimation and propagation of uncertainty involved in image analysis operators. This allows using simple processing operators that are suitable for analyzing large-scale 3D+t microscopy images without compromising the result quality. On the foundation of fuzzy set theory, we transform available prior knowledge into a mathematical representation and extensively use it enhance the result quality of various processing operators. All presented concepts are illustrated on a typical bioimage analysis pipeline comprised of seed point detection, segmentation, multiview fusion and tracking. Furthermore, the functionality of the proposed approach is validated on a comprehensive simulated 3D+t benchmark data set that mimics embryonic development and on large-scale light-sheet microscopy data of a zebrafish embryo. The general concept introduced in this contribution represents a new approach to efficiently exploit prior knowledge to improve the result quality of image analysis pipelines. Especially, the automated analysis of terabyte-scale microscopy data will benefit from sophisticated and efficient algorithms that enable a quantitative and fast readout. The generality of the concept, however, makes it also applicable to practically any other field with processing strategies that are arranged as linear pipelines.Comment: 39 pages, 12 figure