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.

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.

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.

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.

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.

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.

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.

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.

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.

Parameterized continuous models of fuzzy reasoning

In this paper,the ideas of universal logic is introduced into fuzzy systems.After giving the definitions of the softened fuzzy reasoning models based on Schweizer-Sklar t-norms and Schweizer-Sklar implications,i.e.,α-models andβ-models,we give the sufficient and necessary conditions for these models to be continuous,and discuss the continuity of some commonly used models.We also prove that when anα-model or aβ-model is used as a fuzzy controller,it has universal property with respect to function approximation.The results we obtained show thatα-models andβ-models are more flexible than the existing models in applications.

High-Speed Railway Train Timetable Conflict Prediction Based on Fuzzy Temporal Knowledge Reasoning

Trains are prone to delays and deviations from train operation plans during their operation because of internal or external disturbances. Delays may develop into operational conflicts between adjacent trains as a result of delay propagation, which may disturb the arrangement of the train operation plan and threaten the operational safety of trains. Therefore, reliable conflict prediction results can be valuable references for dispatchers in making more efficient train operation adjustments when conflicts occur. In contrast to the traditional approach to conflict prediction that involves introducing random disturbances, this study addresses the issue of the fuzzification of time intervals in a train timetable based on historical statistics and the modeling of a high-speed railway train timetable based on the concept of a timed Petri net. To measure conflict prediction results more comprehensively, we divided conflicts into potential conflicts and certain conflicts and defined the judgment conditions for both. Two evaluation indexes, one for the deviation of a single train and one for the possibility of conflicts between adjacent train operations, were developed using a formalized computation method. Based on the temporal fuzzy reasoning method, with some adjustment, a new conflict prediction method is proposed, and the results of a simulation example for two scenarios are presented. The results prove that conflict prediction after fuzzy processing of the time intervals of a train timetable is more reliable and practical and can provide helpful information for use in train operation adjustment, train timetable improvement, and other purposes.

General Expressions of Triple Ⅰ Restriction Methods for Fuzzy Soft Reasoning

The aim of this paper is to discuss the Triple Ⅰ restriction reasoning methods for fuzzy soft sets. Triple Ⅰ restriction principles for fuzzy soft modus ponens(FSMP) and fuzzy soft modus tollens(FSMT) are proposed, and then, the general expressions of the Triple Ⅰ restriction reasoning method for FSMP and FSMT with respect to residual pairs are presented respectively. Finally, the optimal restriction solutions for Lukasiewicz and Godel implication operators are examined.

Upper and Lower Bounds of the α-Universal Triple I Method for Unified Interval Implications

Theα-universal triple I(α-UTI)method is a recognized scheme in the field of fuzzy reasoning,whichwas proposed by our research group previously.The robustness of fuzzy reasoning determines the quality of reasoning algorithms to a large extent,which is quantified by calculating the disparity between the output of fuzzy reasoning with interference and the output without interference.Therefore,in this study,the interval robustness(embodied as the interval stability)of theα-UTI method is explored in the interval-valued fuzzy environment.To begin with,the stability of theα-UTI method is explored for the case of an individual rule,and the upper and lower bounds of its results are estimated,using four kinds of unified interval implications(including the R-interval implication,the S-interval implication,the QL-interval implication and the interval t-norm implication).Through analysis,it is found that theα-UTI method exhibits good interval stability for an individual rule.Moreover,the stability of theα-UTI method is revealed in the case of multiple rules,and the upper and lower bounds of its outcomes are estimated.The results show that theα-UTI method is stable for multiple rules when four kinds of unified interval implications are used,respectively.Lastly,theα-UTI reasoning chain method is presented,which contains a chain structure with multiple layers.The corresponding solutions and their interval perturbations are investigated.It is found that theα-UTI reasoning chain method is stable in the case of chain reasoning.Two application examples in affective computing are given to verify the stability of theα-UTImethod.In summary,through theoretical proof and example verification,it is found that theα-UTImethod has good interval robustness with four kinds of unified interval implications aiming at the situations of an individual rule,multi-rule and reasoning chain.