In group decision making with linguistic information, the decision makers (DMs) usually provide their assessment information by means of linguistic variables. In some situations, however, the DMs may provide fuzzy linguistic information because of time pressure, lack of knowledge, and their limited attention and information processing capabilities. In this paper, we introduce the concepts of tr...

Environmental indices (EI) are common communication tool used to describe the overall status of environmental systems (e.g. air, water, soil). Development of EI entails the use of mathematical operators to aggregate various non-commensurate input parameters in a logical manner. Ordered weighted averaging (OWA) operator is a general mean type operator that provides flexibility in the aggregation...

Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation o...

* Correspondence author. Abstract The fuzzy multi-attribute decision making problems are investigated, in which the attribute values are given as intervalvalued intuitionistic fuzzy numbers and the attribute weight information is incomplete. Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers...

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respec...

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the Land Rmembership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which...

The use of geographical entities with fuzzy spatial extent, called here fuzzy geographical entities (FGE’s), in Geographical Information Systems requires the existence of operators capable of processing them. This paper focuses on the computation of areas of FGE’s. Two methods are considered, one crisp due to Rosenfeld (1984), which will be shown to be limited in its applicability, and the othe...

We develop the fuzzy generalized ordered weighted averaging distance (FGOWAD) operator. It is a new aggregation operator that uses the main characteristics of the generalized OWA (GOWA), the ordered weighted averaging distance (OWAD) and uncertain information represented as fuzzy numbers. This operator includes a wide range of distance measures and aggregation operators such as the fuzzy maximu...