Mathematical Foundation of Basic Algorithms of Fuzzy Reasoning

Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathe-~matical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.

Active suspension control of a one-wheel car model using single input rule modules fuzzy reasoning and a disturbance observer

This paper presents the construction of an active suspension control of a one-wheel car model using fuzzy reasoning and a disturbance observer. The one-wheel car model to be treated here can be approximately described as a nonlinear two degrees of freedom system subject to excitation from a road profile. The active control is designed as the fuzzy control inferred by using single input rule modules fuzzy reasoning, and the active control force is released by actuating a pneumatic actuator. The excitation from the road profile is estimated by using a disturbance observer, and the estimate is denoted as one of the variables in the precondition part of the fuzzy control rules. A compensator is inserted to counter the performance degradation due to the delay of the pneumatic actuator. The experimental result indicates that the proposed active suspension system improves much the vibration suppression of the car model. Key words One-wheel car model - Active suspension system - Single input rule modules fuzzy reasoning - Pneumatic actuator - Disturbance observer Document code A CLC number TH16

Pneumatic active suspension system for a one-wheel car model using fuzzy reasoning and a disturbance observer

This paper presents the construction of a pneumatic active suspension system for a one-wheel car model using fuzzy reasoning and a disturbance observer. The one-wheel car model can be approximately described as a nonlinear two degrees of freedom system subject to excitation from a road profile. The active control is composed of fuzzy and disturbance controls, and the active control force is constructed by actuating a pneumatic actuator. A phase lead-lag compensator is inserted to counter the performance degradation due to the delay of the pneumatic actuator. The experimental result indicates that the proposed active suspension improves much the vibration suppression of the car model.

CASCADED FUZZY SYSTEM AND ITS ROBUST ANALYSIS BASED ON SYLLOGISTIC FUZZY REASONING

Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is more robust than all other implication inferences for noise data and that CFS has better robustness than conventional fuzzy systems, which provide the solid foundation for CFS's potential application in fuzzy control and modeling and so on.

A Semantic Retrieval Method Based on the Fuzzy Reasoning

This paper gives a semantic fuzzy retrieval method of multimedia object, discusses the principle of fuzzy semantic retrieval technique, presents a fuzzy reasoning mechanism based on the knowledge base, and designs the relevant reasoning algorithms. Researchful results have innovative significance.

Universal triple I fuzzy reasoning algorithm of function model based on quotient space

Aiming at the deficiencies of analysis capacity from different levels and fuzzy treating method in product function modeling of conceptual design, the theory of quotient space and universal triple I fuzzy reasoning method are introduced, and then the function modeling algorithm based on the universal triple I fuzzy reasoning method is proposed. Firstly, the product function granular model based on the quotient space theory is built, with its function granular representation and computing rules defined at the same time. Secondly, in order to quickly achieve function granular model from function requirement, the function modeling method based on universal triple I fuzzy reasoning is put forward. Within the fuzzy reasoning of universal triple I method, the small-distance-activating method is proposed as the kernel of fuzzy reasoning; how to change function requirements to fuzzy ones, fuzzy computing methods, and strategy of fuzzy reasoning are respectively investigated as well; the function modeling algorithm based on the universal triple I fuzzy reasoning method is achieved. Lastly, the validity of the function granular model and function modeling algorithm is validated. Through our method, the reasonable function granular model can be quickly achieved from function requirements, and the fuzzy character of conceptual design can be well handled, which greatly improves conceptual design.

Power Transformer Fault Diagnosis Using Fuzzy Reasoning Spiking Neural P Systems

This paper presents an intelligent technique to fault diagnosis of power transformers dissolved and free gas analysis (DGA). Fuzzy Reasoning Spiking neural P systems (FRSN P systems) as a membrane computing with distributed parallel computing model is powerful and suitable graphical approach model in fuzzy diagnosis knowledge. In a sense this feature is required for establishing the power transformers faults identifications and capturing knowledge implicitly during the learning stage, using linguistic variables, membership functions with “low”, “medium”, and “high” descriptions for each gas signature, and inference rule base. Membership functions are used to translate judgments into numerical expression by fuzzy numbers. The performance method is analyzed in terms for four gas ratio (IEC 60599) signature as input data of FRSN P systems. Test case results evaluate that the proposals method for power transformer fault diagnosis can significantly improve the diagnosis accuracy power transformer.

Fuzzy Reasoning Methods by Choosing Different Fuzzy Counters and Analysis of Effect

Different fuzzy reasoning methods were gave by choosing different fuzzy counters.This article generally introduced the basic structure of fuzzy controller,and compared and analysised the reasoning effect of fuzzy reasoning methods and the effect of computer simulating control basicly on different fuzzy counters.

Knowledge Representation and Fuzzy Reasoning of an Agricultural Expert System

The design scheme of an agricultural expert system based on longan and cauliflower planting techniques is presented. Using an object-oriented design and a combination of the techniques in multimedia, database, expert system and artificial intelligence, an in-depth analysis and summary are made of the knowledge features of die agricultural multimedia expert system and data models involved. According to the practical problems in agricultural field, the architectures and functions of the system are designed, and some design ideas about the hybrid knowledge representation and fuzzy reasoning are proposed.

Moldability Evaluation for Molded Parts Based on Fuzzy Reasoning

Moldability evaluation for molded parts, which is the basis of concurrent design, is a key design stage in injection molding design. By moldability evaluation the design problems can be found timely and an optimum plastic part design achieved. In this paper, a systematic methodology for moldability evaluation based on fuzzy logic is proposed. Firstly, fuzzy set modeling for six key design attributes of molded parts is carried out respectively. Secondly, on the basis of this, the relationship between fuzzy sets for design attributes and fuzzy sets for moldability is established by fuzzy rules that are based on domain experts’ experience and knowledge. At last the integral moldability for molded parts is obtained through fuzzy reasoning. The neural network based fuzzy reasoning approach presented in this paper can improve fuzzy reasoning efficiency greatly, especially for system having a large number of rules and complicated membership functions. An example for moldability evaluation is given to show the feasibility of this proposed methodology.

FUZZY REASONING IN CYCLES

By the similarity between the syllogism in logic and a path proposition in graph theory,a new concept,fuzzy reasoning graph G has been given in this paper. Transitive closure has been studied and used to do reasoning related to self-loop in G,and an algorithm has been designed to cope with reasoning in other cycles in G. Both approaches are applicable and efficient.

An Intelligent System for a Resource Allocation Problem Based on Fuzzy Reasoning

The development of the assistive abilities regarding the decision-making process o fan Intelligent Control System （ICS） like a fuzzy expert system implies the development of its functionality and its ability of specification. Fuzzy expert systems can model fuzzy controllers, i.e., the knowledge representation and the abilities of making decisions corresponding to fuzzy expert systems are much more complicated that in the case of standard fuzzy controllers. The expert system acts also as a supervisor, creating meta-level reasoning on a set of fuzzy controllers, in order to choose the best one for the management of the process. Knowledge Management Systems （KMSs） is a new development paradigm of Intelligent Systems which has resulted from a synergy between fuzzy sets, artificial neural networks, evolutionary computation, machine learning, etc., broadening computer science, physics, economics, engineering, mathematics. This paper presents, after a synergic new paradigm of intelligent systems, as a practical case study the fuzzy and temporal properties of knowledge formalism embedded in an ICS. We are not dealing high with level reasoning methods, because we think that real-time problems can only be solved by rather low-level reasoning. Solving the match-time predictability problem would allow us to build much more powerful reasoning techniques.

A FUZZY REASONING PETRI NET MODEL AND ITS REASONING ALGORITHM

This paper compared the difference between the traditional Petri nets and reasoning Petri nets(RPN),and presented a fuzzy reasoning Petri net(FRPN) model to represent the fuzzy production rules of a rule based system.Based on the FRPN model,a formal reasoning algorithm using the operators in max algebra was proposed to perform fuzzy reasoning automatically.The algorithm is consistent with the matrix equation expression method in the traditional Petri net.Its legitimacy and feasibility were testified through an example.

A NOVEL TEMPORAL ERROR CONCEALMENT METHOD BASED ON FUZZY REASONING FOR H.264

In this paper,a fuzzy reasoning based temporal error concealment method is proposed. The basic temporal error concealment is implemented by estimating Motion Vector (MV) of the lost MacroBlock (MB) from its neighboring MVs. Which MV is the most proper one is evaluated by some criteria. Generally,two criteria are widely used,namely Side Match Distortion (SMD) and Sum of Absolute Difference (SAD) of corresponding MV. However,each criterion could only partly describe the status of lost block. To accomplish the judgement more accurately,the two measures are considered together. Thus a refined measure based on fuzzy reasoning is adopted to balance the effects of SMD and SAD. Terms SMD and SAD are regarded as fuzzy input and the term ‘similarity’ as output to complete fuzzy reasoning. Result of fuzzy reasoning represents how the tested MV is similar to the original one. And k-means clustering technique is performed to define the membership function of input fuzzy sets adaptively. According to the experimental results,the concealment based on new measure achieves better performance.

Artificial Intelligence Embedded Object-Oriented Methodology For Model Based Decision Support

The paper presents the coupling of artificial intelligence-AI and Object-oriented methodology applied for the construction of the model-based decision support system MBDSS.The MBDSS is designed for support the strategic decision making lead to the achievemellt of optimal path towardsmarket economy from the central planning situation in China. To meet user's various requirements,a series of innovations in software development have been carried out, such as system formalization with OBFRAMEs in an object-oriented paradigm for problem solving automation and techniques of modules intelligent cooperation, hybrid system of reasoning, connectionist framework utilization,etc. Integration technology has been highly emphasized and discussed in this article and an outlook to future software engineering is given in the conclusion section.

Threat Assessment Method Based on Intuitionistic Fuzzy Similarity Measurement Reasoning with Orientation

The aim of this paper is to propose a threat assessment method based on intuitionistic fuzzy measurement reasoning with orientaion to deal with the shortcomings of the method proposed in [Ying-Jie Lei et al., Journal of Electronics and Information Technology 29(9)(2007)2077-2081] and [Dong-Feng Chen et al., Procedia Engineering 29(5)(2012)3302-3306] the ignorance of the influence of the intuitionistic index's orientation on the membership functions in the reasoning, which caused partial information loss in reasoning process. Therefore, we present a 3D expression of intuitionistic fuzzy similarity measurement, make an analysis of the constraints for intuitionistic fuzzy similarity measurement, and redefine the intuitionistic fuzzy similarity measurement. Moreover, in view of the threat assessment problem, we give the system variables of attribute function and assessment index, set up the reasoning system based on intuitionistic fuzzy similarity measurement with orientation, and design the reasoning rules, reasoning algorithms and fuzzy-resolving algorithms. Finally, through the threat assessment, some typical examples are cited to verify the validity and superiority of the method.

Reverse triple Ⅰ method of fuzzy reasoning

A theory of reverse triple I method with sustention degree is presented by using the implication operator R0 in every step of the fuzzy reasoning. Its computation formulas of supremum for fuzzy modus ponens and infimum for fuzzy modus tollens are given respectively. Moreover, through the generalization of this problem, the corresponding formulas of α-reverse triple I method with sustention degree are also obtained. In addition, the theory of reverse triple I method with restriction degree is proposed as well by using the operator R0, and the computation formulas of infimum for fuzzy modus ponens and supremum for fuzzy modus tollens are shown.

Reasoning complexity for extended fuzzy description logic with qualifying number restriction

To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ reasoning results are reused to prove the complexity of EFALCQ reasoning problems. The ALCQ simulation method for the consistency of EFALCQ is proposed. This method reduces EFALCQ satisfiability into EFALCQ consistency, and uses EFALCQ satisfiability to discretely simulate EFALCQ satdomain. It is proved that the reasoning complexity for EFALCQ satisfiability, consistency and sat-domain is PSPACE-complete.

A Fuzzy Reasoning System and Its Heuristic Inference Algorithm

Based on a presented inference algorithm of fuzzy reasoning, a fuzzy reasoning system is made up. A method of modeling the fuzzy reasoning system, and the setting up of the reasoning knowledge based and reasoning rules are studied in this paper. Then a heuristic inference algorithm is presented according to the system.

Truth-value transmittal fuzzy reasoning inter-polator

In this paper, we firstly associate fuzzy reasoning algorithm with the interpolation algorithm and discuss the limitation of defuzzification methods used commonly in the fuzzy reasoning algorithm. Secondly, we give a new fuzzy reasoning algorithm in case of single input, called the truth-value transmittal method, and discuss its properties. Finally, we analyze the rationality to adopy the truth-value transmittal method as the defuzzification method of full implication triple I method, and show that although CRI and triple I fuzzy reasoning method are different from fuzzy output set, they are uniform finally under the truth-value transmittal defuzzification method.