Rule chaining in fuzzy expert systems

A fuzzy expert system must do rule chaining differently than a nonfuzzy expert system. In particular, any rule that can fire with a particular linguistic variable in its consequent must fire before any rule whose antecedent conditions depend upon the resultant fuzzy set value of the consequent linguistic variable is allowed to fire. The dependent rules would be considered in a chain with the fuzzy rules which generate or assert the needed fuzzy linguistic variable. A recent paper by J. Pan et al. (1998) points out that a version of the FuzzyCLIPS expert system shell does not operate with chained fuzzy rules as one would expect. They introduce FuzzyShell which is described as the only known shell to have the expected fuzzy rule chaining performance. We show several approaches to obtaining the desired behavior in FuzzyCLIPS. Further, a potential pitfall with the FuzzyShell approach to dealing with chaining is pointed out     

TALplanner: A temporal logic based forward chaining planner

We present TALplanner, a forward-chaining planner based on the use of domain-dependent search control knowledge represented as formulas in the Temporal Action Logic (TAL). TAL is a narrative based linear metric time logic used for reasoning about action and change in incompletely specified dynamic environments. TAL is used as the formal semantic basis for TALplanner, where a TAL goal narrative with control formulas is input to TALplanner which then generates a TAL narrative that entails the goal and control formulas. The sequential version of TALplanner is presented. The expressivity of plan operators is then extended to deal with an interesting class of resource types. An algorithm for generating concurrent plans, where operators have varying durations and internal state, is also presented. All versions of TALplanner have been implemented. The potential of these techniques is demonstrated by applying TALplanner to a number of standard planning benchmarks in the literature. This revised version was published online in June 2006 with corrections to the Cover Date.     

The real issues in fuzzy logic applications

The transition from Boolean Logic to Fuzzy Logic is shown by modifying a ladder diagram consisting of discrete variables with values of 0 and 1 to include intermediate values. Properties of membership functions are discussed as they influence the control output. The concept of compromise and output blending is shown. Important observations regarding the presence of rules are presented. The notions of “gain” and “time” are introduced, and a PID controller using Fuzzy Mechanisms is shown. In one example, the level and temperature of a tank are controlled; in another example the engine power and the turning of the wheels of an automobile are controlled as a function of the gas pedal and the steering wheel excitation.     

Complex fuzzy logic

A novel framework for logical reasoning, termed complex fuzzy logic, is presented in this paper. Complex fuzzy logic is a generalization of traditional fuzzy logic, based on complex fuzzy sets. In complex fuzzy logic, inference rules are constructed and "fired" in a manner that closely parallels traditional fuzzy logic. The novelty of complex fuzzy logic is that the sets used in the reasoning process are complex fuzzy sets, characterized by complex-valued membership functions. The range of these membership functions is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane, thus providing a method for describing membership in a set in terms of a complex number. Several mathematical properties of complex fuzzy sets, which serve as a basis for the derivation of complex fuzzy logic, are reviewed in this paper. These properties include basic set theoretic operations on complex fuzzy sets - namely complex fuzzy union and intersection, complex fuzzy relations and their composition, and a novel form of set aggregation - vector aggregation. Complex fuzzy logic is designed to maintain the advantages of traditional fuzzy logic, while benefiting from the properties of complex numbers and complex fuzzy sets. The introduction of complex-valued grades of membership to the realm of fuzzy logic generates a framework with unique mathematical properties, and considerable potential for further research and application.     

Forward chaining in HALO: An implementation strategy for history-based logic pointcuts

In aspect-oriented programming, pointcuts are formulated as conditions over the context of dynamic events in the execution of a program. Hybrid pointcut languages also allow this context to come from interactions between the pointcut language and the base program. While some pointcut languages only allow conditions on the current execution event, more recent proposals have demonstrated the need for expressing conditions over a history of join points. Such pointcut languages require means to balance the expressiveness of the language with the additional memory and runtime overhead caused by keeping a history of join point context data. In this paper, we introduce a logic-based pointcut language that allows interaction with the base program as well as pointcuts over a history of join points. We introduce forward chaining as an implementation model for this language, and discuss possible optimization strategies for the additional overhead.     

On fuzzy equality and approximation in fuzzy logic

The paper is a contribution to the theory of fuzzy logic in narrow sense with evaluated syntax (FLn). We show that the concepts of fuzzy equality and the provability degree enable to generalize the concept of fuzzy approximation. In the second part of the paper we return to the Mamdani-Assilian formula, which is formed on the basis of the so called totally bounded fuzzy equality and using which we can approximate any function with the prescribed accuracy.This paper has been supported by Grant A1187901/99 of the GA AV R and the project VS96037 of MMT of the Czech Republic.     

Knowledge representation in fuzzy logic

The author presents a summary of the basic concepts and techniques underlying the application of fuzzy logic to knowledge representation. He then describes a number of examples relating to its use as a computational system for dealing with uncertainty and imprecision in the context of knowledge, meaning, and inference. It is noted that one of the basic aims of fuzzy logic is to provide a computational framework for knowledge representation and inference in an environment of uncertainty and imprecision. In such environments, fuzzy logic is effective when the solutions need not be precise and/or it is acceptable for a conclusion to have a dispositional rather than categorical validity. The importance of fuzzy logic derives from the fact that there are many real-world applications which fit these conditions, especially in the realm of knowledge-based systems for decision-making and control     

On contradiction in fuzzy logic

 We clarify which space of functions in [0, 1] ^E would be reasonable in fuzzy logic in order to avoid self-contradiction.     

Implication operators in fuzzy logic

The choice of fuzzy implication as well as other connectives is an important problem in the theoretical development of fuzzy logic, and at the same time, it is significant for the performance of the systems in which fuzzy logic technique is employed. There are mainly two ways in fuzzy logic to define implication operators: (1) an implication operator is considered as the residuation of conjunction operator; and (2) it is directly defined in terms of negation, conjunction, and disjunction operators. The purpose of this paper is to determine the number of implication operators defined in the second way for some usual negation, conjunction and disjunction operators in fuzzy logic     

Neural fuzzy logic programming

A foundational development of propositional fuzzy logic programs is presented. Fuzzy logic programs are structured knowledge bases including uncertainties in rules and facts. The precise specifications of uncertainties have a great influence on the performance of the knowledge base. It is shown how fuzzy logic programs can be transformed to neural networks, where adaptations of uncertainties in the knowledge base increase the reliability of the program and are carried out automatically.     

Concepts and fuzzy logic

Weights are used to measure relative importance of multiple attributes or objectives, which influence evaluation or decision results to a great degree. Thus, analyzing weight sensitivity is an important work for a multi-attribute evaluation or decision. A measuring method based on the inclined angle of two vectors is proposed in this paper in order to solve the weight sensitivity of a multi-attribute evaluation with isotonicity characteristic. This method uses the cosine of the inclined angle to measure the weight sensitivity based on preferences or preference combinations. Concepts of sensitivity space, degree, and angle are given, and the relevant measurement method is discussed and proved. Also, this method is used for the choice of the water environment protection projects in Heyuan City.     

概率逻辑、不确定逻辑和模糊逻辑之比较

通过一个实例分析比较了概率逻辑、主观概率逻辑、不确定逻辑和模糊逻辑的思想方法。提出了自己的观点：基于数据统计的概率逻辑是最科学的。不确定逻辑比主观概率逻辑更科学。当具有不确定性的原子命题具有独立性时,不确定逻辑和模糊逻辑的观点是一致的。而对于处理带有不确定性的相关性命题,不确定逻辑比模糊逻辑更科学。但是模糊逻辑在建立推理理论方面见长。     

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     

Prolog-ELF incorporating fuzzy logic

Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness. Prolog-ELF inherits all the desirable basic features of Prolog. In addition to assertions with truth-values between 1.0 and 0.5 (0 for exceptional cases), fuzzy sets can be very easily manipulated. An application of fuzzy logical database is illustrated.     

Toward complex fuzzy logic

Complex fuzzy logic is a postulated logic system that is isomorphic to the complex fuzzy sets recently described in a previous paper. This concept is analogous to the many-valued logics that are isomorphic to type-1 fuzzy sets, commonly known as fuzzy logic. As with fuzzy logics, a complex fuzzy logic would be defined by particular choices of the conjunction, disjunction and complement operators. In this paper, an important assertion from a previous paper, that only the modulus of a complex fuzzy membership should be considered in set theoretic (or logical) operations, is examined. A more general mathematical formulation (the property of rotational invariance) is proposed for this assertion, and the impact of this property on the form of complex fuzzy logic operations is examined. All complex fuzzy logics based on the modulus of a vector are shown to be rotationally invariant. The case of complex fuzzy logics that are not rotationally invariant is examined using the framework of vector logic. A candidate conjunction operator was identified, and the existence of a dual disjunction was proven. Finally, a discussion on the possible applications of complex fuzzy logic focuses on the phenomenon of regularity as a possible fuzzification of stationarity.     

经典逻辑公理在模糊逻辑系统中的真度分析

对经典逻辑中的公理在Gödel系统、Lukasiewicz以及R₀系统中的真度大小进行了分析,得到了一系列深刻而有趣的结果。     

Medical diagnosis with the aid of using fuzzy logic and intuitionistic fuzzy logic

The objective of the present study is to develop/establish a web-based medical diagnostic support system (MDSS) by which health care support can be provided for people living in rural areas of a country. In this respect, this research provides a novel approach for medical diagnosis driven by integrating fuzzy and intuitionistic fuzzy (IF) frameworks. Subsequently, based on the proposed approach a web-based MDSS is developed. The proposed MDSS comprises of a knowledge base (KB) and intuitionistic fuzzy inference system (IFIS). Based on the observation that medical data cannot be described with both precision and certainty, a medical KB is constructed in the form of a set of if-then decision rules by employing both fuzzy and IF logics. After constructing the medical KB, a new set of patients is considered for diagnosing the diseases. For each patient, linguistic values of the patients’ symptoms are considered as inputs of the proposed IFIS and modeled by using the generalized triangular membership functions. Subsequently, integrated fuzzy and IF rule-based inference system is used to find a valid conclusion for the new set of patients. In a nutshell, in this paper fuzzy rule-based and IFS based inference systems are combined for better and more realistic representation of uncertainty of the medical diagnosis problem and for more accurate diagnostic result. The method is composed of following four steps: (1) the modeling of antecedent part of the rules, which consist of linguistic assessments of the patients’ symptoms provided by the doctors/medical experts with their corresponding confidence levels, by using generalized fuzzy numbers; (2) the modeling of consequent part, which reveals the degree of association and the degree of non-association of diseases into the patient, by using IFSs; (3) the use of IF aggregation operator in inference process; (4) the application of relative closeness function to find the final crisp output for a given diagnosis. Finally, the applicability of the proposed approach is illustrated with a suitable case study. This article has also justified the proposed approach by using similarity measurement.     

Fuzzy XNOR connectives in fuzzy logic

In this paper, a generalized XNOR connective called fuzzy XNOR connective is introduced. First, the definition of fuzzy XNOR connective is proposed and its properties are analyzed. Then, two forms of fuzzy XNOR connectives are obtained by the composition of t-norms, t-conorms and fuzzy negations. Moreover, the relationships between fuzzy XNOR connectives and fuzzy Xor connectives introduced in Bedregal et al. (Electron Notes Theor Comput Sci 247:5–18, 2009) are discussed. At last, two new kinds of fuzzy implications are constructed by fuzzy XNOR connectives and other connectives, their main properties are also studied.     

Self-reference and chaos in fuzzy logic

Investigates a range of phenomena from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0,1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and in three dimensions in the graphing of mutually referential triples