Abstract: Fuzzy sets theory affirmed that the linguistic value for
every contraries relation is complementary. It was stressed in the
intuitionistic fuzzy sets (IFS) that the conditions for contraries
relations, which are the fuzzy values, cannot be greater than one.
However, complementary in two contradict phenomena are not
always true. This paper proposes a new idea condition for conflicting
bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets.
Here, we will critically forward examples using triangular fuzzy
number in formulating a new condition for conflicting bifuzzy sets
(CBFS). Evaluation of positive and negative in conflicting
phenomena were calculated concurrently by relaxing the condition in
IFS. The hypothetical illustration showed the applicability of the new
condition in CBFS for solving non-complement contraries
intuitionistic evaluation. This approach can be applied to any
decision making where conflicting is very much exist.
Abstract: Decision making preferences to certain criteria
usually focus on positive degrees without considering the negative
degrees. However, in real life situation, evaluation becomes more
comprehensive if negative degrees are considered concurrently.
Preference is expected to be more effective when considering both
positive and negative degrees of preference to evaluate the best
selection. Therefore, the aim of this paper is to propose the
conflicting bifuzzy preference relations in group decision making by
utilization of a novel score function. The conflicting bifuzzy
preference relation is obtained by introducing some modifications on
intuitionistic fuzzy preference relations. Releasing the intuitionistic
condition by taking into account positive and negative degrees
simultaneously and utilizing the novel score function are the main
modifications to establish the proposed preference model. The
proposed model is tested with a numerical example and proved to be
simple and practical. The four-step decision model shows the
efficiency of obtaining preference in group decision making.