Very and more or less in non-commutative fuzzy logic

In this paper we consider fuzzy subsets of a universe as L-fuzzy subsets instead of [ 0, 1 ]-valued, where L is a complete lattice. We enrich the lattice L by adding some suitable operations to make it into a pseudo-BL algebra. Since BL algebras are main frameworks of fuzzy logic, we propose to consider the non-commutative BL-algebras which are more natural for modeling the fuzzy notions. Based on reasoning with in non-commutative fuzzy logic we model the linguistic modifiers such as very and more or less and give an appropriate membership function for each one by taking into account the context of the given fuzzy notion by means of resemblance L-fuzzy relations.     

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.     

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.     

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.     

A graph-theoretic characterization theorem for multiplicative fragment of non-commutative linear logic

It is well known that every proof net of a non-commutative version of MLL (multiplicative fragment of commutative linear logic) can be drawn as a plane Danos–Regnier graph (drawing) satisfying the switching condition of Danos–Regnier [3]. In this paper, we study the reverse direction; we introduce a system MNCLL which is logically equivalent to the multiplicative fragment of cyclic linear logic introduced by Yetter [9], and show that any plane Danos–Regnier graph drawing with one terminal edge satisfying the switching condition represents a unique non-commutative proof net (i.e., a proof net of MNCLL). In the course of proving this, we also give the characterization of the non-commutative proof nets by means of the notion of strong planarity, as well as the notion of a certain long-trip condition, called the stack-condition, of a Danos–Regnier graph, the latter of which is related to Abrusci's balanced long-trip condition [2].     

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.     

基于模糊逻辑的汽车障碍物探测系统设计

近些年交通事故频频发生,不仅造成大量的经济损失,而且还使很多人失去了生命。除人为因素减少交通事故外,研发更为高效、智能的障碍物探测系统具有更重要的现实意义。此设计方案中利用6个超声波传感器组成探测器网络,通过多次反射法采集障碍物的位置信息数据,并利用模糊逻辑和数据融合的算法思想,不仅可以采集车辆周围障碍物的距离信息,还可以对障碍物方位进行分析,解决了单一超声波传感器只能测障碍物距离的缺陷,从而可以及时提醒驾驶员进行减速、避障等操作,有利于减少交通事故的发生。     

Intelligent e-learning system based on fuzzy logic

Neural Computing and Applications - In this technological world demanding latest updations in the domain knowledge, it is no surprise that e-learning has become a more viable option to a range of...     

基于模糊逻辑的信用评判模型

为了解决个人对个人(C2C)交易平台信用评价体系不能正确识别信用炒作行为导致交易数据不能真实反映卖方信用的问题,设计了一种基于模糊逻辑的可信度评判模型.该模型为信用影响因素建立论域以及论域上的模糊集,通过隶属度函数对各个时段交易进行模糊评价,得到信用可信度评判结果.实例数据分析表明:该模型完善了信用评价系统,为用户的交易决策提供了较可靠的评判依据,降低了交易中的信用风险.     

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.     

A complementary fuzzy logic system

This article discusses complementary (C) fuzzy logic system that is one of continuous multiary logic systems that satisfies a complementary law differently from usual fuzzy logic systems. This article includes formulation of the C fuzzy logic system, derivation of tautologies, and mentions an example that typically shows a difference in inference computation between the C fuzzy logic system and a usual fuzzy logic system.     

Soft computing and fuzzy logic

What is soft computing? What is fuzzy computing? What is the relationship between them? This paper intends to provide clear answers to these questions. We focus on exploring the notions of the fuzzy coordinate system and the related transformations between qualitative and quantitative information. These notions are considered to be the core ideas of fuzzy computing. Then the three novel theories of fuzzy computing and soft computing developed by the first author of this paper, namely, the Falling Shadow Representation of fuzzy theory, the Factors Space theory and the Truth Value Flow Inference theory are introduced.     

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     

Basic fuzzy logic and BL-algebras

 The many-valued propositional logic BL (basic fuzzy logic) is investigated. It is known to be complete for tautologies over BL-algebras (particular residuated lattices). Each continuous t-norm on [0,1] determines a BL-algebra; such algebras are called t-algebras. Two additional axioms B1, B2 are found such that BL+(B1,B2) is complete for tautologies over t-algebras. It remains open whether B1, B2 are provable in BL.     

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.