Many problems of practical interest can be modeled and solved by using graph algorithms. In general, graph theory has a wide range of applications in diverse fields. In this paper, the intuitionistic fuzzy organizational and neural network models, intuitionistic fuzzy neurons in medical diagnosis, intuitionistic fuzzy digraphs in vulnerability assessment of gas pipeline networks, and intuitionistic fuzzy digraphs in travel time are presented as examples of intuitionistic fuzzy digraphs in decision support system. We have also designed and implemented the algorithms for these decision support systems.

Type-II fuzzy sets are used to convey the uncertainties in the membership function of type-I fuzzy sets. Linguistic information in expert rules does not give any information about the geometry of the membership functions. These membership functions are mostly constructed through numerical data or range of classes. But there exists an uncertainty about the shape of the membership, that is, whether to go for a triangle membership function or a trapezoidal membership function. In this paper we use a type-II fuzzy set to overcome this uncertainty, and develop a fuzzy decision support system of fertilizers based on a type-II fuzzy set. This type-II fuzzy system takes cropping time and soil nutrients in the form of spatial surfaces as input, fuzzifies it using a type-II fuzzy membership function, and implies fuzzy rules on it in the fuzzy inference engine. The output of the fuzzy inference engine, which is in the form of interval value type-II fuzzy sets, reduced to an interval type-I fuzzy set, defuzzifies it to a crisp value and generates a spatial surface of fertilizers. This spatial surface shows the spatial trend of the required amount of fertilizer needed to cultivate a specific crop. The complexity of our algorithm isO(mnr), wheremis the height of the raster,nis the width of the raster, andris the number of expert rules.