Fuzzy Logic Operations Research Articles

Categorical Analysis of Logic Operators on Fuzzy Sets

Although the concept of Topos can lead naturally to the logic operations of the class of sets, SetH cannot be connected to the logic operations of fuzzy sets due to the fact that Sell-I has no subobject classifier. In thsi work, from category Fuz we introduce several concepts such as middle object, WSC and WTopos. It is shown that by the use of category Fuz which is a WTopos, the fuzzy logic operations can be obtained both logically and naturally.

Logic-based neural networks

Realization of two-valued or many-valued functions carried out by fuzzy set logical operations is studied. Two basic types of computational nodes performing generalized (weighted) AND and OR operations form generic components of neural networks. Their functional and numerical properties are carefully studied. The combination of these two nodes into a structure of logic processors is used to approximate manyinput-single-output logical relationships. Relevant learning algorithms are proposed and analyzed. Numerical considerations are included as well. Generalization aspects of this architecture are studied. A new interpretation of the paradigm of a fuzzy controller realized as a cerebellar model articulation controller structure with the aid of logic processors are discussed as well.

Fuzzy inference based on families of alpha -level sets

A fuzzy-inference method in which fuzzy sets are defined by the families of their alpha -level sets, based on the resolution identity theorem, is proposed. It has the following advantages over conventional methods: (1) it studies the characteristics of fuzzy inference, in particular the input-output relations of fuzzy inference; (2) it provides fast inference operations and requires less memory capacity; (3) it easily interfaces with two-valued logic; and (4) it effectively matches with systems that include fuzzy-set operations based on the extension principle. Fuzzy sets defined by the families of their alpha -level sets are compared with those defined by membership functions in terms of processing time and required memory capacity in fuzzy logic operations. The fuzzy inference method is then derived, and important propositions of fuzzy-inference operations are proved. Some examples of inference by the proposed method are presented, and fuzzy-inference characteristics and computational efficiency for alpha -level-set-based fuzzy inference are considered. >

A key to fuzzy-logic inference

Classically, whether to effect inference, one uses a small set of axioms and modus ponens, or a set of rules of inference including modus ponens, one is going beyond what can be derived with the explicit operations of logic alone. Carrying this concept over to fuzzy logic we construct a fuzzy modus ponens and other rules of inference that include modus tollens and reductio ad absurdum. These in turn are based on (and greatly facilitated by) a choice for the operation of implication that preserves the (logic) symmetry implicit in its definition. Extensions including conditional quantification, cut rules (single, multiple, and implicitory), and fuzzy mathematical induction are sketched. As an example, a fuzzy-logic treatment of the Yale shooting problem is discussed. The results suggest that the implicit processes of inference, as distinct from the explicit processes of decision (control) theory and systems theory, can be effected in fuzzy logic if, as in classical logic, one ventures outside the scope of (fuzzy) logic operations.

Fuzzy operator logic and fuzzy resolution

There have been only few attempts to extend fuzzy logic to automated theorem proving. In particular, the applicability of the resolution principle to fuzzy logic has been little examined. The approaches that have been suggested in the literature, however, have made some semantic assumptions which resulted in limitations and inflexibilities of the inference mechanism. In this paper we present a new approach to fuzzy logic and reasoning under uncertainty using the resolution principle based on a new operator, the fuzzy operator. We present the fuzzy resolution principle for this logic and show its completeness as an inference rule.

Learning control using fuzzified self-organizing radial basis function network

This note describes an approach to integrating fuzzy reasoning systems with radial basis function (RBF) networks and shows how the integrated network can be employed as a multivariable self-organizing and self-learning fuzzy controller. In particular, by drawing some equivalence between a simplified fuzzy control algorithm (SFCA) and a RBF network, we conclude that the RBF network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks, referred to as FBFN, with a variety of basis functions (not necessarily globally radial) synthesized from each dimension by fuzzy logical operators. On the other hand, as a result of natural generalization from RBF to SFCA, we claim that the fuzzy system like RBF is capable of universal approximation. Next, the FBFN is used as a multivariable rule-based controller but with an assumption that no rule-base exists, leading to a challenging problem of how to construct such a rule-base directly from the control environment. We propose a simple and systematic approach to performing this task by using a fuzzified competitive self-organizing scheme and incorporating an iterative learning control algorithm into the system. We have applied the approach to a problem of multivariable blood pressure control with a FBFN-based controller having six inputs and two outputs, representing a complicated control structure. >

A fuzzy controller for generator excitation control

An approach based on fuzzy set theory is proposed for the design of an excitation controller for a synchronous generator. In the proposed fuzzy expert system, generator speed deviation and acceleration are taken as controller inputs. These input signals are first characterized by linguistic variables using fuzzy set notations. A fuzzy relation matrix is built to give the relationship between controller input and controller output. A set of fuzzy logic operations are performed by the fuzzy excitation controller using controller inputs and fuzzy relation matrix to get the desired controller output. To demonstrate the effectiveness of the fuzzy excitation controller, digital simulations of a power system subject to a three-phase fault under different operating conditions are performed. It is found that the fuzzy excitation controller can improve the dynamic performance of a power system over a wide range of operating conditions. Since the fuzzy excitation controller does not require model identification, it can be easily implemented on a microcomputer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Process Planning Knowledge Acquisition

In this paper, a method for acquiring manufacturing planning knowledge is presented. Emphasis is placed on eliciting, analyzing and interpreting the knowledge of cutting parameter selection which a human expert uses when solving a particular problem and then transforming this knowledge into suitable machine representation. The approach is based on repertory grid analysis and fuzzy logic operations. Production rules are automatically generated upon the successful acquisition of the relevant knowledge.

Categories Fuz and Fuzzy Semantics

Although SetH is not a Topos, subcategory Fuz of SetH can make a WTopos because Fuz has two special objects----Middle Object and WSC. By the use of WTo-pos Fuz , the fuzzy logic operations and a fuzzy power set of the fuzzy set (A,α) can be o be ained naturally, and a new Semantics-Fuzzy Semantics is introduced logically.

λ-Resolution and interpretation of λ-implication in fuzzy operator logic

The concepts of implication between two formulas in fuzzy operator logic are discussed and the Λ-resolution method is introduced. It is proved that, given two clauses, the Λ-resolvent of these clauses is a logical consequence of the two clauses. The concepts of Λ-inconsistency and Λ-validity are also introduced, and it is proved that Λ-resolution is complete in fuzzy operator logic.

Reasoning under uncertainty in fuzzy operator logic

The authors present an approach to fuzzy logic and reasoning using the resolution principle based on a novel operator, the fuzzy operator. After presenting the fuzzy resolution principle, a general methodology for reasoning under uncertainty, based on resolution in this fuzzy logic, is discussed. The calculus presented is referred to as fuzzy operator logic or FOL. Some simple examples illustrating the reasoning process using FOL are included. >

Angular fuzzy set models for linguistic values

Abstract In this paper, an angular fuzzy set model is introduced. The model uses an angle to determine a line that represents a linguistic value. Therefore, the membership value is a function of the angle a. This angular fuzzy set model can be applied to fuzzy logic modusponensand modus tollensdeduction techniques. In relation to these techniques, we employ fuzzy logic operations, such as the truth functional modification and inverse truth functional modification. A relatively simple calculation procedure is required to perform these operations. The conventional models that are represented graphically could pose difficulties during the interpretation of the graphs. The angular models, on the other hand, depend only on the angle. They are solved numerically, and therefore are easier to interpret. Illustrations using this model and comparison with conventional models are presented in this paper.

Design of fuzzy power system stabilisers for multimachine power systems

A new type of power system stabiliser based on fuzzy set theory is proposed to improve the dynamic performance of a multimachine power system. To have good damping character istic over a wide range of operating conditions, speed deviation (δω) and acceleration (δω) of a machine are chosen as the input signals to the fuzzy stabiliser on that particular machine. These input signals are first characterised by a set of linguistic variables using fuzzy set notations. The fuzzy relation matrix, which gives the relationship between stabiliser inputs and stabiliser output, allows a set of fuzzy logic operations that are per formed on stabiliser inputs to obtain the desired stabiliser output. Since only local measurements are required by the fuzzy stabiliser on each generating unit, the proposed stabiliser is of decentralised output feedback form and is easy for practical implementation. The effectiveness of the proposed fuzzy stabiliser is demonstrated by a multimachine system example.

Optical implementation of parallel fuzzy logic

A multiple-imaging scheme with area-coding of input fuzzy variables and negations and thresholding of output intensity is proposed to perform basic fuzzy logic operations in parallel. Thus the pattern fuzzy logic described by a fuzzy logic function in disjunctive or conjunctive normal form can be easily realized in a two-stage optica system. The access of the required fuzzy logic function can be achieved by programming the lens-arrays and the thresholding devices. Simulations and experimental results are given, too.

Logical analysis of assumptions in code calibration

A logical model of the process of calibrating a new code of practice has been developed. The hierarchical system of statements was derived from an initial statement that structures built in the future should be no less reliable, on average, than existing structures. The other statements which are connected by fuzzy logical operators and are necessary conditions on the first statement, cover random hazards, human controls on tolerance and quality, human systems such as design and construction and the process of code calibration itself. Data were acquired for input to the model from two individuals who were involved in the calibration of BS 5400 against BS 153, the new and old codes for steel bridge design in the U.K. These data were intended only for use in illustrating the potential of the fuzzy logic modelling. However, the analysis showed that both donors felt that statements outside the detailed calibration process were less dependable than those inside, particularly those concerned with the human activities of design and construction. Within the calibration process the quality of data and the loading model was considered to be the least dependable part of the analysis. The fuzzy logic method described in this paper, with some development of consistent ways of obtaining subjective estimates from various sources, could be used to report a consensus on this type of complex process.

Outline of a fuzzy logic approach to information retrieval

An information retrieval method based on fuzzy logic is presented. The method described takes into account in a straightforward way the varying importance of descriptors which reflect the content of the information system documents as well as the varying formal relevance grades of documents in relation to a given query. The use of the simple operations of fuzzy logic allows retrieval of documents with the highest grades of formal relevance (in a given information system).

A fuzzy set approach to modifiers and vagueness in natural language.

SUMMARY Recent developments in semantic theory, such as the work of Labov (1973) and Lakoff (1973), have brought into question the assumption that meanings are precise. It has been proposed that the meanings of all terms are to a lesser or greater degree vague, such that, the boundary of the application of a term is never a point but a region where the term gradually moves from being applicable to nonapplicable. Developments in fuzzy set theory have made it possible to offer a formal treatment of vagueness of natural language concepts. In this article, the proposition that natural language concepts are represented as fuzzy sets of meaning components and that language operators—adverbs, negative markers, and adjectives— can be considered as operators on fuzzy sets was assessed empirically. In a series of experiments, we explored the application of fuzzy set theory to the meaning of phrases such as very small, sort of large, and so on. In Experiment 1, subjects judged the applicability of the set of phrases to a set of squares of varying size. The results indicated that the group interpretation of the phrases can be characterized within the framework of fuzzy set theory. Similar results were obtained in Experiment 2, where each subject's responses were analyzed individually. Although the responses of the subjects, in general, could be interpreted in terms of fuzzy logical operations, one subject responded in a more idiomatic style. Experiments 3 and 4 were attempts to influence the logical-idiomatic distinction in interpretatio n by (a) varying the presentation mode of the phrases and by (b) giving subjects only a single phrase to judge. Overall, the results were consistent with the hypothesis that natural language concepts and operators can be described more completely and more precisely using the framework of fuzzy set theory.