USA.: International Journal of Computer Applications (IJCA) (0975 โ 8887), Vol. 61, No.7 (Jan., 2013), pp. 35-39, English. (OCR-ัะปะพะน).
[Supriya Raheja. ITM University. Gurgaon, India.
Reena Dhadich. Govt. Engg. College. Ajmer, India].
Abstract. Many-Valued logics have been developed to represent mathematical model of imprecision, vagueness, uncertainty and ambiguity in the information. In real world each and every species is vague, human knowledge and the natural languages have a bunch of vagueness or imprecise information. This paper attempts to present three main theories of many-valued logics to treat the vagueness: Fuzzy Logic, Vague Logic and Neutrosophic Logic. Author touches the various perspectives logical, algebraic operation, graphical representations and the practical usage. This paper addresses the modeling of vagueness. Author introduces the framework, Vague Inference System (VIS) for modeling the vagueness using vague logic.
Introduction. In the Classical Set Theory introduced by Cantor, values of elements in a set are only two possibilities: either exists or not exist in the set. The theory cannot handle the ambiguity and uncertainty. Theories of Fuzzy sets, Vague sets and Neutrosophic sets are the generalizations of Classical Set Theory for treating vagueness and uncertainty. A sentence is vague if and only if the sentence is neither absolutely true nor absolutely false. Fuzzy logic has been essential means of implementing machine intelligence. Therefore, Fuzzy Logic cannot be ignored in order to bridge the gap between natural language and machine language.
Fuzzy Logic (FL), one form of many-valued logic was conceived by Prof. Lotfi Zadeh [1]. It deals with the imprecise information, as a way of treating data by permitting partial set membership rather than crisp set membership. In FL the value (degree) for the Linguistic variables can be ranging between 0 and 1. When the Linguistic variables are used, these degrees may be dealt by specific functions called membership functions.
Introduction.Basic concept. Definitions.
Graphical Representation of Membership Functions.
Algebraic operations.Fuzzy Set Operations.
Vague Set Operations.
Neutrosophic Set Operations.
Vagueness in practical usage. Modeling of vagueness. Modeling of Vagueness Using FL (Fuzzy Logic).
Modeling of Vagueness Using NL (Neutrosophic Logic).
Modeling of Vagueness Using VL (Vague Logic).
Conclusion. References.