Bipolar Fuzzy Matrices

In the fuzzy set, only the membership value of an element is considered, and it represents the degree of acceptance or the degree of belongingness of an element. But, in the real world, in many situations have both positive and negative sides. For example, in a mechanical system, there are sources of forces and sinks of forces, in a water supply line source of water and sinks of water. In both cases, sources and sinks are acting as positive and negative sides of the system, respectively. In these systems, bipolar (positive and negative) information is available. Many other problems are available in reality, such as cooperation and competition, common interests and conflict of interests, effect and side effect, friendship and hostility, likelihood and unlikelihood, etc. These types of situations mainly occur in multi-criteria decision making, psychology, qualitative reasoning, artificial intelligence, and many others.