scholarly journals Fuzzy Reasoning Method Based on Distance Measure and Its Reductive Property

2020 ◽  
Vol 8 ◽  
pp. 73-89
Author(s):  
Sonil Kwak ◽  
Unha Kim ◽  
Kumju Kim ◽  
Ilmyong Son ◽  
Chonghan Ri
Keyword(s):  
Fuzzy Control ◽  
Fuzzy Systems ◽  
Distance Measure ◽  
Fuzzy Reasoning ◽  
Modus Ponens ◽  
Information Loss ◽  
Modus Tollens ◽  
Criterion Function ◽  
Human Thinking ◽  
Fuzzy Modus Ponens

This paper shows a basic and original fuzzy reasoning method that can draw a novel study direction of the approximate inference in fuzzy systems with uncertainty. Firstly we propose a criterion function for checking of the reductive property about fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). Secondly unlike fuzzy reasoning methods based on the similarity measure, we propose a principle of new fuzzy reasoning method based on distance measure and then present two theorems for FMP and FMT. Thirdly through the several computational experiments, we show that proposed method is simple and effective, and in accordance with human thinking. Finally we pointed out conclusion that proposed method does satisfy the convergence of the fuzzy control and has not information loss.

Observer-based proportional derivative fuzzy control for singular Takagi-Sugeno fuzzy systems

2021 ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Wen-Jer Chang ◽  
Ming-Hsuan Tsai ◽  
Yi-Chen Lee
Keyword(s):  
Fuzzy Control ◽  
Fuzzy Systems ◽  
Takagi Sugeno

Pythagorean fuzzy full implication multiple I method and corresponding applications

2021 ◽  
pp. 1-15
Author(s):  
TaiBen Nan ◽  
Haidong Zhang ◽  
Yanping He
Keyword(s):  
Decision Making ◽  
Modus Ponens ◽  
Pythagorean Fuzzy Set ◽  
Implication Operator ◽  
Continuity Properties ◽  
Fuzzy Implication ◽  
Decision Making Problem ◽  
Fuzzy Implication Operator ◽  
Degree Of Similarity ◽  
Fuzzy Modus Ponens

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

scholarly journals Finite-Time Adaptive Fuzzy Control for Nonlinear Systems with Unknown Backlash-Like Hysteresis

2021 ◽  
Author(s):  
Shuzhen Diao ◽  
Wei Sun ◽  
Le Wang ◽  
Jing Wu
Keyword(s):  
Fuzzy Control ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Tracking Error ◽  
Adaptive Fuzzy Control ◽  
Finite Time Stability ◽  
Adaptive Fuzzy ◽  
Intermediate Variable ◽  
Control Scheme ◽  
Theoretical Results

AbstractThis study considers the tracking control problem of the nonstrict-feedback nonlinear system with unknown backlash-like hysteresis, and a finite-time adaptive fuzzy control scheme is developed to address this problem. More precisely, the fuzzy systems are employed to approximate the unknown nonlinearities, and the design difficulties caused by the nonlower triangular structure are also overcome by using the property of fuzzy systems. Besides, the effect of unknown hysteresis input is compensated by approximating an intermediate variable. With the aid of finite-time stability theory, the proposed control algorithm could guarantee that the tracking error converges to a smaller region. Finally, a simulation example is provided to further verify the above theoretical results.

scholarly journals On Basic Probability Logic Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Marija Boričić Joksimović
Keyword(s):  
Probability Theory ◽  
Inference Rule ◽  
Modus Ponens ◽  
Probability Logic ◽  
Modus Tollens ◽  
Short Overview ◽  
Basic Probability ◽  
Probabilistic Version ◽  
Hypothetical Syllogism

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

Development of Intelligent Frequency Drum Washing Machine Based on Fuzzy Control Technology

2014 ◽  
Vol 701-702 ◽  
pp. 697-703
Author(s):  
Li Zong Lin ◽  
Jian Feng Chen ◽  
Shuai Han ◽  
Chao Huang ◽  
Zi Li Ke
Keyword(s):  
Fuzzy Control ◽  
Frequency Control ◽  
Fuzzy Reasoning ◽  
Development Trend ◽  
Structure Design ◽  
Control Technology ◽  
Body Structure ◽  
Washing Machine ◽  
The Development Trend ◽  
Current Energy

Aiming at the current energy efficiency of washing machine is not high. The smart inverter washing machine based on fuzzy control technology is designed. Drum washing machine including a content body structure design, programmable controller and the overall program and frequency control module is highlighted. And the generation and fuzzy reasoning process SPWM signals and other issues are discussed in detail. The results show that the use of fuzzy control technology frequency control can not only save water and energy, but also meet the modern requirements of a variety of special laundry, in line with the development trend of the washing machine technology.

Indirect Adaptive Fuzzy Control for a Class of Uncertain Nonlinear Systems with Unknown Control Direction

2013 ◽  
pp. 139-154
Author(s):  
Salim Labiod ◽  
Hamid Boubertakh ◽  
Thierry Marie Guerra
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Fuzzy Control ◽  
Fuzzy Systems ◽  
Control Algorithm ◽  
Adaptive Fuzzy Control ◽  
Control Schemes ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction

In this paper, the authors propose two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time single-input single-output (SISO) nonlinear dynamic systems with known and unknown control direction. Within these schemes, fuzzy systems are used to approximate unknown nonlinear functions and the Nussbaum gain technique is used to deal with the unknown control direction. This paper first presents a singularity-free indirect adaptive control algorithm for nonlinear systems with known control direction, and then this control algorithm is generalized for the case of unknown control direction. The proposed adaptive controllers are free from singularity, allow initialization to zero of all adjustable parameters of the used fuzzy systems, and guarantee asymptotic convergence of the tracking error to zero. Simulations performed on a nonlinear system are given to show the feasibility of the proposed adaptive control schemes.

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