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...

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving...

In this paper we develop a new method for 2-tuple linguistic multiple attribute decision making, namely the 2-tuple linguistic generalized ordered weighted averaging distance (2LGOWAD) operator. This operator is an extension of the OWA operator that utilizes generalized means, distance measures and uncertain information represented as 2-tuple linguistic variables. By using 2LGOWAD, it is possib...

In practice, it is often necessary to combine information from different sources. For this task, one of aggregation operators can be used. Probably the best-known of them are the weighted average and the OWA (ordered weighted average) operator. The weighted average makes it possible to assign importances to the individual information sources. On the other hand, with the OWA operator, the import...

Motivated by intuitionistic fuzzy sets and fzzy linguistic approach, this article proposes the concept of linguistic intuitionistic fuzzy numbers (LIFNs) where membership and and nonmembership are represented as linguistic terms. In order to process the multiple attribute decision making (MADM) with LIFNs, we introduce the linguistic score index and linguistic accuracy index of the LIFN. Simult...

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-m...

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...

− The fuzzy weighted average (FWA) is used in many engineering problems where aggregation of fuzzy information is dealt with. In this framework, many algorithms have been proposed to compute efficiently the FWA according to Zadeh's extension principle. However, due to fuzzy interval calculus, the exact solution presents a characteristic that may be viewed as an important drawback. Indeed, repla...

In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.

Yager @IEEE Trans Syst Man Cybern B 2004;34:1952–1963# introduced a continuous interval argument OWA ~C-OWA! operator, which extends the ordered weighted averaging ~OWA! operator, introduced by Yager @IEEE Trans Syst Man Cybern B 1988;18:183–190#, to the case in which the given argument is a continuous valued interval rather than a finite set of values. In this article, we utilize the C-OWA ope...