On the Suitability of the Bandler–Kohout Subproduct as an Inference Mechanism

Fuzzy relational inference (FRI) systems form an important part of approximate reasoning schemes using fuzzy sets. The compositional rule of inference (CRI), which was introduced by Zadeh, has attracted the most attention so far. In this paper, we show that the FRI scheme that is based on the Bandler-Kohout (BK) subproduct, along with a suitable realization of the fuzzy rules, possesses all the important properties that are cited in favor of using CRI, viz., equivalent and reasonable conditions for their solvability, their interpolative properties, and the preservation of the indistinguishability that may be inherent in the input fuzzy sets. Moreover, we show that under certain conditions, the equivalence of first-infer-then-aggregate (FITA) and first-aggregate-then-infer (FATI) inference strategies can be shown for the BK subproduct, much like in the case of CRI. Finally, by addressing the computational complexity that may exist in the BK subproduct, we suggest a hierarchical inferencing scheme. Thus, this paper shows that the BK-subproduct-based FRI is as effective and efficient as the CRI itself

Data mining in soft computing framework: a survey

The present article provides a survey of the available literature on data mining using soft computing. A categorization has been provided based on the different soft computing tools and their hybridizations used, the data mining function implemented, and the preference criterion selected by the model. The utility of the different soft computing methodologies is highlighted. Generally fuzzy sets are suitable for handling the issues related to understandability of patterns, incomplete/noisy data, mixed media information and human interaction, and can provide approximate solutions faster. Neural networks are nonparametric, robust, and exhibit good learning and generalization capabilities in data-rich environments. Genetic algorithms provide efficient search algorithms to select a model, from mixed media data, based on some preference criterion/objective function. Rough sets are suitable for handling different types of uncertainty in data. Some challenges to data mining and the application of soft computing methodologies are indicated. An extensive bibliography is also included

Generalized Probabilistic Reasoning and Empirical Studies on Computational Efficiency and Scalability

Expert Systems are tools that can be very useful for diagnostic purposes, however current methods of storing and reasoning with knowledge have significant limitations. One set of limitations involves how to store and manipulate uncertain knowledge: much of the knowledge we are dealing with has some degree of uncertainty. These limitations include lack of complete information, not being able to model cyclic information and limitations on the size and complexity of the problems to be solved. If expert systems are ever going to be able to tackle significant real world problems then these deficiencies must be corrected. This paper describes a new method of reasoning with uncertain knowledge which improves the computational efficiency as well as scalability over current methods. The cornerstone of this method involves incorporating and exploiting information about the structure of the knowledge representation to reduce the problem size and complexity. Additionally, a new knowledge representation is discussed that will further increase the capability of expert systems to model a wider variety of real world problems. Finally, benchmarking studies of the new algorithm against the old have led to insights into the graph structure of very large knowledge bases

Fractional Order Fuzzy Control of Nuclear Reactor Power with Thermal-Hydraulic Effects in the Presence of Random Network Induced Delay and Sensor Noise having Long Range Dependence

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Nonlinear state space modeling of a nuclear reactor has been done for the purpose of controlling its global power in load following mode. The nonlinear state space model has been linearized at different percentage of reactor powers and a novel fractional order (FO) fuzzy proportional integral derivative (PID) controller is designed using real coded Genetic Algorithm (GA) to control the reactor power level at various operating conditions. The effectiveness of using the fuzzy FOPID controller over conventional fuzzy PID controllers has been shown with numerical simulations. The controllers tuned with the highest power models are shown to work well at other operating conditions as well; over the lowest power model based design and hence are robust with respect to the changes in nuclear reactor operating power levels. This paper also analyzes the degradation of nuclear reactor power signal due to network induced random delays in shared communication network and due to sensor noise while being fed-back to the Reactor Regulating System (RRS). The effect of long range dependence (LRD) which is a practical consideration for the stochastic processes like network induced delay and sensor noise has been tackled by optimum tuning of FO fuzzy PID controllers using GA, while also taking the operating point shift into consideration

Belief rule-base expert system with multilayer tree structure for complex problems modeling

Belief rule-base (BRB) expert system is one of recognized and fast-growing approaches in the areas of complex problems modeling. However, the conventional BRB has to suffer from the combinatorial explosion problem since the number of rules in BRB expands exponentially with the number of attributes in complex problems, although many alternative techniques have been looked at with the purpose of downsizing BRB. Motivated by this challenge, in this paper, multilayer tree structure (MTS) is introduced for the first time to define hierarchical BRB, also known as MTS-BRB. MTS- BRB is able to overcome the combinatorial explosion problem of the conventional BRB. Thereafter, the additional modeling, inferencing, and learning procedures are proposed to create a self-organized MTS-BRB expert system. To demonstrate the development process and benefits of the MTS-BRB expert system, case studies including benchmark classification datasets and research and development (R&D) project risk assessment have been done. The comparative results showed that, in terms of modelling effectiveness and/or prediction accuracy, MTS-BRB expert system surpasses various existing, as well as traditional fuzzy system-related and machine learning-related methodologie

Fuzzy in 3-D: Contrasting Complex Fuzzy Sets with Type-2 Fuzzy Sets

CCIComplex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, applications, definitions, and structures. In addition, pure complex fuzzy sets are compared with type-2 fuzzy sets in relation to their inferencing operations. Complex fuzzy sets and type-2 fuzzy sets differ in their roles and applications. Their definitions differ also, though there is equivalence between those of a pure complex fuzzy set and a type-2 fuzzy set. Structural similarity is evident between these three-dimensional sets. Complex fuzzy sets are represented by a line, and type-2 fuzzy sets by a surface, but a surface is simply a generalisation of a line. This similarity is particularly evident between pure complex fuzzy sets and type-2 fuzzy sets, which are both mappings from the domain onto the unit square. Type-2 fuzzy sets were found not to be isomorphic to pure complex fuzzy sets

Survey over Existing Query and Transformation Languages

A widely acknowledged obstacle for realizing the vision of the Semantic Web is the inability of many current Semantic Web approaches to cope with data available in such diverging representation formalisms as XML, RDF, or Topic Maps. A common query language is the first step to allow transparent access to data in any of these formats. To further the understanding of the requirements and approaches proposed for query languages in the conventional as well as the Semantic Web, this report surveys a large number of query languages for accessing XML, RDF, or Topic Maps. This is the first systematic survey to consider query languages from all these areas. From the detailed survey of these query languages, a common classification scheme is derived that is useful for understanding and differentiating languages within and among all three areas