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Abstract The hybrid knowledge‐based system proposed in this paper consists of a “stiff” segment, viz. the expert system based on the object‐oriented approach, and a flexible part, viz. the neural network. Some of the input parameters of the problem and output parameters of the “stiff” system are presented as the fuzzy numbers. Detailed information is also presented about the development of the neural network. The most evident advantages of the proposed introduction of a hybrid architecture of the knowledge‐based system are a faster evaluation and generation of design alternatives and support of systematic searches and storage of experience. In addition, the resulting ability to extrapolate results would be unattainable with separately acting stiff and flexible systems. A system for the estimation of the parameters of a mixing system for wastewater treatment is presented as an example to illustrate the principles of the hybrid system.
Approximate reasoning is about reasoning with imperfect information. Nowadays, a large diversity of approaches to approximate reasoning with fuzzy information and fuzzy type-2 information exists. It should be stressed, however, that real-world imperfect information is characterized by combination of fuzzy and probabilistic uncertainties, which is referred to as bimodal information. In view of this, Zadeh introduced the concept of a Z-number regarded as an ordered pair Z = (A, B) of fuzzy numbers A and B, where A is a linguistic value of a variable of interest, and B is a linguistic value of probability measure of A, playing a role of its reliability. Unfortunately, up to day, there is no research on approximate reasoning realized on the basis of if-then rules with Z-number-valued antecedents and consequents, briefly, Z- rules. Zadeh addressed this problem as related to an uncharted territory. In this paper, a new approach is developed to study approximate reasoning with Z-rules on a basis of linear interpolation. We provide an application of the approach to job satisfaction evaluation and to students' educational achievement evaluation problems related to psychological and perceptual issues naturally characterized by imperfect information. The obtained results show applicability and validity of the proposed approach.
The paper introduces an exclusion/inclusion fuzzy classification (EFC) neural network. The network is based on our general fuzzy min-max algorithm (GFMM [13]) and it allows for two distinct types of hyperboxes to be created: inclusion hyperboxes, that corresponds directly to those considered in GFMM, and exclusion hyperboxes that represent contentious areas of the patter space. The subtraction of the exclusion hyperboxes from the inclusion hyperboxes, implemented by EFC, provides for a more efficient coverage of complex topologies of data clusters
Develops a general framework for processes of matching fuzzy quantities. Indicates how different hierarchy levels of matching indices are constructed from a relational way of description of the matching process. Making use of max‐min and min‐max fuzzy relation equations, respectively, clarifies how the entire matching proceeds. Moreover formulates an inverse problem. The method provided here enables us to distinguish regions of the universe of discourse in which the quantities are specified, which are considered as fully supporting the given concept (completely matching observed); completely excluded with respect to this concept; and being of a borderline character. As a consequence the results of matching can have a thorough interpretation.