interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

The fuzzy rule based inference is known to be a useful tool to capture the behavior of an approximate system in transportation. One of the obstacles of implementing the fuzzy rule based inference, however, has been to calibrate the membership functions of the fuzzy sets used in the rules. This paper proposes a way to calibrate the membership function when a set of input and output data is given...

Multiple attributes group decision making problems aim to find the best alternative for the experts from a solution set of alternatives. Because the attribute value and decision-makers evaluation with respect to the alternatives are usually vague and imprecise, fuzzy multiple attributes group decision making have been widely investigated, in which, ordering fuzzy evaluation results in fuzzy dec...

This paper examines type-2 fuzzy arithmetic using interval analysis. It relies heavily on alpha-cuts and alpha-planes. Furthermore, we discuss the use of quasi type-2 fuzzy sets proposed by Mendel and Liu and define quasi type-2 fuzzy numbers. Arithmetic operations of such numbers are defined and a worked example is presented. Keywords— Fuzzy Arithmetic, Type-2 Fuzzy Arithmetic, Type-2 Fuzzy Nu...

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

In this article, we propose a new approach to the virus DNA–based evolutionary algorithm (VDNA-EA) to implement self-learning of a class of Takagi-Sugeno (T-S) fuzzy controllers. The fuzzy controllers use T-S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear pro...

A novel approach to fuzzy modeling based on the tuning of parametric conjunction operations is proposed. First, some novel methods for the construction of parametric generalized conjunction operations simpler than the known parametric classes of conjunctions are considered and discussed. Second, several examples of function approximation by fuzzy models, based on the tuning of the parameters of...

It is argued that inference procedures of fuzzy models do not always require commutativity and associativity of the operations used. This raises the possibility of considering nonassociative and noncommutative conjunction and disjunction operations. Such operations are investigated in this paper and different methods for their generation are proposed. A number of new types of conjunction operat...

We have presented trapezoidal intuitionistic fuzzy number. Arithmetic operations of trapezoidal intuitionistic fuzzy number is presented based on (α, β)-cuts. We have presented intuitionistic fuzzy fault tree analysis using trapezoidal intuitionistic fuzzy number. In application of intuitionistic fuzzy fault tree analysis, we have computed failure of fire protection system taking failure of eac...

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some...