With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of intuitionistic fuzzy linguistic variables, a decision analysis approach is proposed. In this paper, we develop an intuitionistic fuzzy linguistic induce OWA (IFLIOWA) operator and analyze the properties of it by utilizing some operational laws of intuitionistic fuzzy linguistic variables. A new method based on the IFLIOWA operator for multiple attribute group decision making (MAGDM) is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method. Keywords: Intuitionistic fuzzy linguistic variable; operations laws; induce OWA operator; intuitionistic fuzzy linguistic induce OWA operator; group decision making. * Corresponding author. 627 Int. J. Unc. Fuzz. Knowl. Based Syst. 2015.23:627-648. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/21/15. For personal use only., sr (2)

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Entropy, a basic concept of measuring the amount of information and the degree of confusion, has been applied in many weighted averaging operators in the linguistic group decision making. In the paper, we construct an intuitionistic fuzzy linguistic entropy based on the intuitionistic fuzzy entropy and the intuitionistic fuzzy linguistic variable. Then, inspired by operations of concentration and dilation (De SK, Biswas R, and Roy AR, Fuzzy Sets Syst. 2000;114(3):477ȓ484), we extend the intuitionistic fuzzy linguistic entropy to the intuitionistic fuzzy interval‐valued linguistic entropy. After that, the intuitionistic fuzzy interval‐valued linguistic entropic combined weighted averaging (IFIVLECWA) operator is proposed for multiple attribute linguistic group decision making. Finally, a numerical example about the selection of optimal alternative(s) is presented to illustrate the applicability and effectiveness of the proposed method.

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Multicriteria decision making (MCDM) has been attracting attention in recent years. There are two essential directions in the research territory, one direction is the research of representation of evaluation information and another is the construction of ranking function. In this paper, we consider some nonstandard fuzzy sets, intuitionistic, and interval‐valued fuzzy sets. Especially, the Pythagorean membership grade and Pythagorean fuzzy set receive much attention. Then, to reflect the importance of principal value, we shall propose the principal‐value Pythagorean fuzzy number (p‐PFN) and principal‐value Pythagorean fuzzy set. Furthermore, a novel ranking function is constructed to select the ideal alternative(s) based on p‐PFNs in MCDM. Finally, an investment strategy decision‐making problem is proposed to reveal the availability and practicability of the function under the new environment.