Survey of theory and applications of Łukasiewicz-Pavelka fuzzy logic (Q2784605)

The paper is a short survey of propositional fuzzy logic with evaluated syntax, which has been initiated by \textit{J. Pavelka} [Z. Math. Logik Grundlagen Math. 25, 45-52 (1979; Zbl 0435.03020), ibid. 25, 119-134 (1979; Zbl 0446.03015), and ibid. 25, 447-464 (1979; Zbl 0446.03016)]. This logic is based on Łukasiewicz MV-algebra of truth values and it was proved that no other MV-algebra can be used. The paper has 4 sections, where the first 3 sections provide an overview of the main results in this logic. Section 4 is devoted to demonstrations of some applications. First, similarity-based reasoning is introduced as well as an algorithm for constructing fuzzy inference systems. The main idea is to find a number of fuzzy similarities and to construct from them a global one which is proved to be also a fuzzy similarity. Then 4 applications, namely multi-phase vehicle control, determination of an athlete's anaerobic thresholds, classification and case-based reasoning are briefly described. The paper, unfortunately, lacks references to some other relevant literature on this topic, among them especially the book: \textit{V. Novák, I. Perfilieva} and \textit{J. Močkoř}: Mathematical principles of fuzzy logic. Kluwer, Boston (1999; Zbl 0940.03028).NEWLINENEWLINEFor the entire collection see [Zbl 0970.00009].