**1. Introduction**

The scientific contribution of this paper is setting up a novel framework for making decisions that stems from the first cross-fertilization of two features: (a) intertemporal aspects of choice; and (b) extended fuzzy set models. We also give a novel adjustable algorithm that prioritizes alternatives with the aforementioned features.

Decisions whose consequences extend across multiple time periods are called intertemporal choices. The entry "Intertemporal choice" in the Palgrave Dictionary of Economics states: "Most choices require decision-makers to trade-off costs and benefits at different points in time. Decisions with consequences in multiple time periods are referred to as intertemporal choices. Decisions about savings, work effort, education, nutrition, exercise, and health care are all intertemporal choices" [1]. Although its analysis is preeminent in the standard crisp literature, to the best of our knowledge, the problem of intertemporal choice has never been modeled when the data are imprecise, uncertain or subjective in the sense of the extended fuzzy set theories. In this paper, we first put forward a model that fills this important gap. To prove that it can be used to make decisions, we propose a flexible mechanism that provides a ranking of the alternatives that are characterized by these characteristics. We also present some examples that illustrate the application of our decision making procedure.

To achieve our goals, we have selected the successful setting of fuzzy soft sets. (Other models of imprecise knowledge would require an ad hoc analysis, which we postpone for subsequent investigations to avoid confusions.) The new model that arises (from the amalgamation of the intertemporal setting of choice and data in the form of fuzzy soft sets) is called intertemporal fuzzy soft sets. We put forward various equivalent and complementary definitions of this concept. Some are more convenient for the purpose of algebraic manipulations and intuitions. Some are better suited to describe the computational machinery that produces the results from which the decisions are achieved.

In relation with the latter issue, the gist of standard intertemporal problems is that the consequences of a decision span along an infinite number of periods. However, to decide among various alternatives, their consequences across time are summarized by an amount called their respective Net Present Values. In this fashion, the infinite expansion that characterizes an alternative is summarized by a unique number, for example through a discounted sum. By inspiration of this widely accepted position, we propose to condense the information of intertemporal fuzzy soft sets into fuzzy soft sets in order to make optimal decisions. The tool that we introduce to achieve this target is called a reduction mechanism. Reduction mechanisms can both indicate symmetry in the valuation of a reward irrespective of the period when it is obtained, or a preference for earlier rewards (i.e., violation of the symmetric treatment of the periods). We provide several noteworthy examples of both behaviors. Once this reduction to a fuzzy soft set has been performed, our decision can rely on widely accepted solutions stated for that setting.

Actually, the main reason for choosing fuzzy soft sets in our pioneering approach is that there is a fully-developed theory for fuzzy soft set based decision making. To further assess the importance of this setting, in the next section, we review some general background about soft computing models with a more explicit explanation about soft set based modelizations and their decision making. We also dwell on the fundamentals of the intertemporal problem of choice and its applications.

This paper is organized as follows. In Section 2, we give some general background about the main notions that are used in our research. A fully developed real example helps to clarify the application of the discounted utility aggregation model. Section 3 recalls some terminology and definitions. In Section 4, we define our new model of intertemporal fuzzy soft sets and we also offer alternative formalizations. In Section 5, we define the notion of a reduction mechanism, which we use to state the decision algorithm that prioritizes alternatives in the framework of intertemporal fuzzy soft sets. We also illustrate the model with a numerical application to the selection of alternative portfolios of public projects. Finally, we conclude in Section 6.
