On continuity of the entropy-based differently implicational algorithm

Tang, Yiming; Pedrycz, Witold

doi:10.14736/kyb-2019-2-0307

Cited by 3 publications

(3 citation statements)

References 34 publications

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“…This contradicts (21). Consequently (8) holds, and thus C is an α(x,y)-symmetric I* restriction solution.…”

Section: Optimal Solutionsmentioning

confidence: 91%

“…The variable differently implicational algorithm was further researched focusing on the FMT problem, in which the differently implicational principle for FMT was improved [20]. The continuous and uniformly continuous properties of the entropy-based differently implicational algorithm were demonstrated for the Tchebyshev and Hamming metrics [21]. The robustness becomes a hot research point to analyze the triple I method [22][23].…”

Section: Introductionmentioning

confidence: 99%

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Symmetric I* Restriction Method of Fuzzy Inference

Tang¹,

Bao²

2019

MCS

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As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications.

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“…This contradicts (21). Consequently (8) holds, and thus C is an α(x,y)-symmetric I* restriction solution.…”

Section: Optimal Solutionsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Symmetric I* Restriction Method of Fuzzy Inference

Tang¹,

Bao²

2019

MCS

Self Cite

View full text Add to dashboard Cite

show abstract

“…Fuzzy systems are composed of the fuzzy reasoning method [95][96][97] and fuzzier, defuzzier, and fuzzy rule bases. They can deal with fuzzy information processing problems, which are difficult to be solved using conventional mathematical methods that imitate human's comprehensive inference [98][99][100][101][102] . They enable computer applications to be extended to the fields of humanities, social sciences, and complex systems.…”

Section: Many Other Methods Have Also Been Proposedmentioning

confidence: 99%

State-of-the-Art Development of Complex Systems and Their Simulation Methods

Tang

Liu

2021

Complex Syst. Model. Simul.

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The research on complex systems is different from that on general systems because the former must consider self-organization, emergence, uncertainty, predetermination, and evolution. As an important method to transform the world, a simulation is one of the most important skills to discover complex systems. In this study, we provide a survey on complex systems and their simulation methods. Initially, the development history of complex system research is summarized from two main lines. Then, the eight common characteristics of the most complex systems are presented. Furthermore, the simulation methods of complex systems are introduced in detail from four aspects, namely, meta-synthesis methods, complex networks, intelligent technologies, and other methods. From the overall point of view, intelligent technologies are the driving force, and complex networks are the advanced structure. Meta-synthesis methods are the integration strategy, and other methods are the supplements. In addition, we show three complex system simulation examples: digital reactor simulation, simulation of a logistics system in the industrial site, and crowd evacuation simulation. The examples show that a simulation is a useful means and an important method in complex system research.Finally, the future development prospects for complex systems and their simulation methods are suggested.

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