5] has shown that the intersection of any two fuzzy subgroups is also a fuzzy subgroup and we now show that the intersection of any two anti fuzzy subgroups is also an anti fuzzy subgroup. More over, we state and prove the anti fuzzy version the work of 6] in characterizing union of fuzzy subgroups. Besides, 2] and 7] have worked on the set of all fuzzy symmetric subgroup of the symmetric group F (S_n).
The theory of rough sets found wider applications in knowledge discovery and datamining. This paper deals with indexing the records of an information system by using afuzzy decision attribute. The method of indexing is obtained by using the hedges of thefuzzy attribute.
The aim of this paper is to solve a multi-objective mathematical programming problem where fuzziness and randomness are observed under one umbrella. In the present mathematical problem some parameters are considered as fuzzy random variable. In first step of the solution procedure, fuzziness is removed by using alpha-cut technique to obtain multi-objective stochastic problem. By using the chance constrained technique, the multi-objective stochastic problem is transformed to equivalent crisp multi-objective mathematical problem. Then, introducing the concept of membership function, multi-objective deterministic mathematical problem is converted into single objective mathematical programming problem. Finally, it is solved with the help of existing technique. Two numerical examples are provided in order to illustrate the methodology.
In our work we have used the model with exponential relative growth rate derived by Chakrabarty and Baruah with fuzzy data to calculate the total population of a region in fuzzy intervals. This model is based on the assumption that the relative growth rate of the population concerned decreases exponentially over time. We will also see the effect of fuzziness on the model with exponential relative growth rate. The fuzzy model developed will be applied to the situation prevailing in India as India is with large population.
We introduce a fuzzy model to describe the process of learning a subject matter bystudents. Our model is presented in contrast to a probabilistic model, introduced in anearlier paper. A classroom experiment, that was performed in order to illustrate the useof the probabilistic model in practice, was repeated twice during the teaching process ofthe same cognitive object, with the same didactic material, the same conditions and thesame method of teaching. The outputs of these two repetitions of the experiment areinterpreted here in terms of the fuzzy model, so that the conclusions obtained from theapplication of the two models become easily comparable to each other.