# zbMATH — the first resource for mathematics

$$R _{0}$$ implication: Characteristics and applications. (English) Zbl 1015.03034
$$R_0$$ implication is an important fuzzy implication determined by the standard nilpotent minimum t-norm. In this paper, this implication is further studied, its main properties are pointed out, some of its characteristics and its independence are discussed, and its applications in fuzzy logic and fuzzy reasoning are also reviewed.

##### MSC:
 03B52 Fuzzy logic; logic of vagueness
Full Text:
##### References:
 [1] Dubois, D.; Prade, H., Fuzzy sets in approximate reasoning, part 1, Fuzzy sets and systems, 40, 143-202, (1991) · Zbl 0722.03017 [2] Esteva, F.; Godo, L., Monoidal t-norm based logictowards a logic for left-continuous t-norms, Fuzzy sets and systems, 124, 271-288, (2001) · Zbl 0994.03017 [3] Fodor, J.C., Contrapositive symmetry of fuzzy implications, Fuzzy sets and systems, 69, 141-156, (1995) · Zbl 0845.03007 [4] Hajek, P., Metamathematics of fuzzy logic, (1998), Kluwer Academic Publishers Dordrecht · Zbl 0937.03030 [5] Klement, E.P.; Navara, M., A survey on different triangular norm-based fuzzy logics, Fuzzy sets and systems, 101, 241-251, (1999) · Zbl 0945.03032 [6] Pavelka, J., On fuzzy logic (II), Z. math. logik grundl. math., 25, 119-134, (1979) · Zbl 0446.03015 [7] D.W. Pei, The first order system K* and its completeness, Chinese Ann. Math., to appear. · Zbl 1027.03508 [8] D.W. Pei, On the equivalence between two formal systems and related algebras based on the nilpotent minimum, submitted for publication. [9] D.W. Pei, G.J. Wang, The completeness of the formal system $$L\^{}\{*\}$$, J. Symbolic Logic, to appear. [10] D.W. Pei, G.J. Wang, The extensions $$Ln\^{}\{*\}$$ of the formal system $$L\^{}\{*\}$$ and their completeness, Internat. J. Inform. Sci., to appear. [11] Turksen, I.B.; Kreinovich, V.; Yager, R.R., A new class of fuzzy implications, axioms of fuzzy implication revisited, Fuzzy sets and systems, 100, 267-272, (1998) · Zbl 0939.03030 [12] Wang, G.J., A formal deductive system for fuzzy propositional calculus, Chinese sci. bull., 42, 1521-1526, (1997) · Zbl 0889.03017 [13] Wang, G.J., Theory of σ-(α-tautologies) in revised Kleene systems, Science in China (series E), 41, 188-195, (1998) [14] Wang, G.J., On the logic foundation of fuzzy reasoning, Inf. sci., 117, 47-88, (1999) · Zbl 0939.03031 [15] Wang, G.J., Full implication triple I method for fuzzy reasoning, Science in China (series E), 29, 43-53, (1999) [16] Wang, G.J., Non-classical mathematical logic and approximate reasoning, (2000), Science Press Beijing, (in Chinese) [17] Wang, G.J.; Wang, H., Non-fuzzy versions of fuzzy reasoning in classical logics, Inf. sci., 138, 211-236, (2001) · Zbl 0994.03014 [18] Wu, W.M., Principles and methods of fuzzy reasoning, (1994), Guizhou Science and Technology Press Guiyang, (in Chinese) [19] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE trans. S.M.C., 3, 28-44, (1974) · Zbl 0273.93002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.