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There exists little investigation on multiattribute decision making under intuitionistic fuzzy environments although both crisp and fuzzy multiattribute decision making have achieved a great progress. In this paper, multiattribute decision making problems using intuitionistic fuzzy sets are investigated and the TOPSIS is further extended to develop one new methodology for solving such problems. In this methodology, an interval fractional programming model is constructed on the basis of the relative closeness coefficient using the TOPSIS. Comprehensive evaluation of each alternative, which may be described as an intuitionistic fuzzy set or interval number, is calculated using two auxiliary mathematical programming problems derived from the interval fractional programming model proposed in this paper. Optimal degrees of membership for alternatives are calculated to determine their ranking order using the concept of likelihood based on the ranking method of interval numbers. Implementation process of the method proposed in this paper is illustrated with a numerical example.

The paper investigates the dynamic hybrid multi-attribute group decision making problems, in which the decision information, provided by multiple decision makers at different periods, is expressed in real numbers, interval numbers or linguistic labels (linguistic labels can be described by triangular fuzzy numbers), respectively. We define the concepts of argument variable and dynamic weighted geometric aggregation (DWGA) operator, etc., and give an approach to determining the weights of periods based on the basic unit-interval monotonic (BUM) function, and then propose a dynamic hybrid multi-attribute group decision making method based on the hybrid geometric aggregation (HGA) operator and the DWGA operator. The method first utilizes three different TOPSISs (real-valued TOPSIS, interval-valued TOPSIS and fuzzy-valued TOPSIS) to calculate the individual closeness coefficient of each alternative to the positive and negative ideal alternatives based on the decision information expressed in real numbers, interval numbers and linguistic labels, respectively, provided by each decision maker at each period, and then employs the HGA operator to aggregate all individual closeness coefficients into the collective closeness coefficient corresponding to each alternative at each period. After doing so, the method uses the DWGA operator to fuse the collective closeness coefficients at different periods into the overall closeness coefficient corresponding to each alternative. These overall closeness coefficients are then used to rank and select the given alternatives. We can also reduce the above method to solve the dynamic multi-attribute group decision making problems, in which the decision information, provided by multiple decision makers at different periods, is expressed by means of values from the same type, either real numbers, or interval numbers or linguistic labels. Finally, the developed method is applied to multi-period investment decision making.

Hesitant fuzzy linguistic term set (HFLTS) is a set with ordered consecutive linguistic terms, and is very useful in addressing the situations where people are hesitant in providing their linguistic assessments. Wang [H. Wang, Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making, International Journal of Computational Intelligence Systems8(1) (2015) 14–33.] removed the consecutive condition to introduce the notion of extended HFLTS (EHFLTS). The generalized form has wider applications in linguistic group decision-making. By introducing distance measures for EHFLTSs, in this paper we develop a novel multi-criteria group decision making model to deal with hesitant fuzzy linguistic information. The model collects group linguistic information by using EHFLTSs and avoids the possible loss of information. Moreover, it can assess the importance weights of criteria according to their subjective and objective information and rank alternatives based on the rationale of TOPSIS. In order to illustrate the applicability of the proposed algorithm, two examples are given and comparisons are made with the other existing methods.