IF-DFT (Intuitionistic Fuzzy Decision Field Theory)

IF-DFT is a method for when you have a decision table in which expert opinions are given as degrees of support and rejection (intuitionistic fuzzy numbers) — "which investment target," "which country" — and you want to rank the options through a dynamic simulation that models how the human mind actually makes decisions. Most other ranking methods (TOPSIS, SAW, and the like) produce preference in a single instant, through a static calculation. IF-DFT is different: it is grounded in a psychological model called decision field theory, and assumes that preference forms as small comparisons between options accumulate over time. Its output is the preference value each option has accumulated by the end of the deliberation period, and the ranking that follows from it. Hao, Xu, Zhao and Zhang proposed the method in 2017, carrying classical decision field theory into an intuitionistic fuzzy setting; the paper's own application is choosing the most suitable country for investment in a development initiative.

The idea behind IF-DFT is that real decision-making is not an instantaneous calculation but a process that unfolds over time. The human mind does not compare options once and reach a definite conclusion; it shifts its attention between different criteria in turn, and each shift creates a small preference difference between the options, which accumulates over time. IF-DFT imitates this process mathematically: an instantaneous advantage pressure is computed for each option relative to the others, this pressure is added to the previous accumulation, the effects of competition between options and of memory are modelled through a feedback mechanism, and this cycle repeats until a set duration or a given threshold is reached. Because the intuitionistic fuzzy structure carries the expert's degree of rejection separately from their degree of support, the margin of indecision (the gap left between support and rejection) remains visible throughout the process from the start.

This idea carries a philosophical consequence: IF-DFT is a method of consistency and maturation. In static methods, a small score gap between two options and a large one are both reported the same way, as "first, second." In IF-DFT, by contrast, the process implicitly carries how robust the gap is: one option clearly overtaking the leader and one overtaking it by a margin close to zero carry a different level of confidence by the end of the process.

The method proceeds through six steps.

First, preparing the assessments. Every cell is an intuitionistic fuzzy number (a degree of support, a degree of rejection). If there is more than one decision-maker, their views are aggregated; if weights are known they are used directly, otherwise they are optimised. Cost-oriented ("lower is better") criteria are converted to a benefit orientation by swapping the degrees of support and rejection; this swap preserves the margin of indecision and only reverses that criterion's direction of scoring.

Second, distance between options. How different every pair of options is from each other is measured by a weighted distance between the intuitionistic fuzzy values (using support, rejection and the margin of indecision together), forming a distance table.

Third, the feedback mechanism. From this distance table, a contrast matrix (each option's comparison with itself is 1, its comparison with the others equal and negative) and a feedback matrix (its diagonal showing how much memory is retained, its off-diagonal entries showing the strength of competition between options) are constructed.

Fourth, instantaneous advantage pressure. Because direct subtraction of intuitionistic fuzzy numbers causes information loss, every pair of options is compared as a directional distance, and this is combined with the weights to compute each option's instantaneous relative advantage.

Fifth, accumulation over time. With a small time step, each option's preference value is updated by adding the feedback effect and the new advantage pressure to its previous value. This cycle repeats until a set deliberation period is reached or an option's preference value crosses a given threshold.

Sixth, the decision. At the end of the deliberation period, the option with the highest accumulated preference value is the best option; a selection probability can optionally also be derived from the preference values.

The formulas behind each step are given on the DecisionMind method page; this card carries no formulas.

The accumulated preference value tells you how far an option pulled ahead by the end of the deliberation process, and nothing more. A positive value shows the option stood out in the overall trend, a negative value shows it fell behind, but this is not a percentage or a probability; a selection probability optionally derived from the preference values is a separate figure and should not be confused with the preference value itself. The size of the value depends on the chosen deliberation period and the model parameters (memory effect, strength of competition).

Thus instead of writing:

"IF-DFT found the best option"

the report should read:

"With this deliberation period and these model parameters, the option accumulating the most preference is this one; only the ranking, not the size of the accumulated value, should be read as reliable"

IF-DFT works with intuitionistic fuzzy data: every cell holds not a single number but a pair made up of a degree of support and a degree of rejection; the sum of the two cannot exceed 1, and the remaining share is indecision. DecisionMind holds no extension of this method for other data types; it stands alone in its base form.

You need the following: options in rows, criteria in columns, a (support, rejection) pair in every cell; criterion weights (if unknown, the method can derive them from the data); and model parameters (memory effect, strength of competition, deliberation period, time step). If it is unclear how these parameters correspond to the real decision situation, working with default values affects the result; the choice of parameters should therefore be justified in the report.

IF-DFT is a suitable choice if your assessments are given as degrees of support and rejection (intuitionistic fuzzy) and you want the decision modelled not as a static calculation but as a process that matures over time. Its typical areas are strategic choices where human behaviour and deliberation are meant to be reflected more realistically (investment-target selection, resource-allocation decisions).

The situations in which it should not be used are as follows: if your data is already exact and there is no need to model the decision as a dynamic process, a simpler method (TOPSIS, SAW) is sufficient. If your assessments involve hesitation among more than one reasonable value (not a single support/rejection pair), its close relative HF-DFT may be more suitable. If you cannot justify the model parameters against the real decision situation, using IF-DFT without knowing how much these parameters affect the result can be misleading.

Support/rejection assessment available, decision process to be modelled dynamically → IF-DFT

Data exact, no need for a dynamic process → static methods such as TOPSIS, SAW

Hesitation among more than one reasonable value instead of support/rejection → HF-DFT

Model parameters cannot be justified → IF-DFT should not be used without a parameter sensitivity analysis

IF-DFT's greatest strength is that it models the decision not with a static formula but with a dynamic process imitating human deliberation; this draws on the strong experimental foundation classical decision field theory has in psychology (Busemeyer and Townsend, 1993; Roe, Busemeyer and Townsend, 2001). Working with intuitionistic fuzzy data lets an expert's support, rejection and indecision all be carried separately. The method has since been generalised to a hesitant fuzzy setting (Song et al., 2019), which shows that the original model offers an extensible framework.

Its limitations relate to the model's parameter burden and its process structure. First, the method requires several parameters (memory effect, strength of competition, deliberation period, time step); how these parameters correspond to the real decision situation is often unclear and can remain subjective. Second, classical decision field theory itself has been tested comparatively against some alternative models in psychology and is known not to explain every preference pattern with the same accuracy (Roe, Busemeyer and Townsend, 2001). Third, because direct subtraction causes information loss with intuitionistic fuzzy numbers, the method is forced into an indirect comparison such as directional distance; this is a less intuitive step than standard arithmetic operations. Fourth, the size of the result depends on the chosen deliberation period; if the period is cut too short, the process may not yet have matured.

The most common mistake is reading the size of the accumulated preference value as a percentage or a degree of certainty; the value only shows relative position at the end of the process.

A second mistake is leaving the model parameters (memory effect, strength of competition, deliberation period) at their defaults without justification; these parameters can seriously change the size of the result, though they do not always change the ranking. A third mistake is forgetting that the margin of indecision does not change when a cost criterion is converted by taking its complement, and misreading the score's direction as a result. A fourth mistake is keeping the deliberation period too short and deciding at a point when the process has not yet matured. A fifth mistake is confusing the preference value with the optionally derived selection probability; the two are on different scales.

The governing principle is this:

An IF-DFT result is a summary of a preference process accumulated with the chosen model parameters and deliberation period; if the parameters change, the size of the accumulated value changes, while the ranking generally remains robust in the examples studied.