IJSRSET1621517 | Received : 12Sep. 2016 | Accepted :18Sep. 2016 | September-October-2016 [(2)5: 86-90] © 2016 IJSRSET | Volume 2 | Issue 5 | Print ISSN: 2395-1990 | Online ISSN : 2394-4099 Themed Section: Engineering and Technology 86 Some Special Types of Type-2 Triangular Fuzzy Number K. Latha* *P.G. and Research Department of Mathematics, Poompuhar College (Autonomous), Melaiyur, Tamil Nadu, India ABSTRACT Type-2 fuzzy sets are fuzzy sets whose membership values are fuzzy sets on the interval [0, 1]. Zadeh, as an extension of fuzzy sets, proposed this concept. Type-2 fuzzy sets possess a great expressive power and are conceptually quite appealing. In this paper, some special types of type-2 triangular fuzzy number are proposed. Arithmetic operations and numerical examples are also included. Keywords: Triangular fuzzy number, Trapezoidal fuzzy number, Pentagonal fuzzy number, Type-2 fuzzy set, Type-2 fuzzy number, Type-2 triangular fuzzy number. I. INTRODUCTION Uncertainty is an attribute of information. For systems being controlled using the type-1 fuzzy logic systems, such uncertainty leads to fuzzy rules whose antecedents or consequents are uncertain, which in turn translates into uncertain antecedent or consequent membership functions. Type-1 fuzzy sets are not able to directly model such uncertainties because their membership functions are totally crisp. On the other hand, type-2 fuzzy sets are able to model such uncertainties because their membership functions are themselves fuzzy. Membership functions of type-1 fuzzy sets are two-dimensional, whereas membership functions of type-2 fuzzy sets are three-dimensional. It is the new third-dimension of type-2 fuzzy sets that provides additional degrees of freedom that make it possible to directly model uncertainties. Type-2 fuzzy sets are difficult to understand and use because: (1) the three-dimensional nature of type-2 fuzzy sets makes them very difficult to draw; (2) there is no simple collection of well-defined terms that let us effectively communicate about type-2 fuzzy sets, and then be mathematically precise about them; and (3) using type-2 fuzzy sets is computationally more complicated than using type-1 fuzzy sets. The concept of a type-2 fuzzy set, which is an extension of the concept of an ordinary fuzzy set, was introduced by Zadeh [8]. A fuzzy relation of higher type has been regarded as one way to increase the fuzziness of a relation and, according to Hisdal [1], “Increased fuzziness in a description means increased ability to handle in exact information in a logically correct manner”. According to Jhon [2], “Type-2 fuzzy sets allow for linguistic grades of membership, thus assisting in knowledge representation, and they also offer improvement on inferring with type-2 fuzzy sets”. Type-2 fuzzy sets have already been used in a number of applications. Stephen Dinagar and Anbalagan [4] presented new ranking function and arithmetic operations on generalized type-2 trapezoidal fuzzy numbers. Stephen Dinagar and Latha [5] introduced type-2 triangular fuzzy matrices. This paper is organized as follows. In section-II, some basic definitions are given. In section-III, the definition of some special types of type-2 triangular fuzzy number, proposed ranking function and arithmetic operations on some special types of type-2 triangular fuzzy number are presented. In section-IV, relevant numerical examples are presented. In section- V, conclusion is also included. II. METHODS AND MATERIAL 1. Preliminaries A. Definition: Fuzzy Set A fuzzy set is characterized by a membership function mapping the elements of a domain, space or universe of discourse X to the unit interval [0,1].