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In this paper, we define the dominant set, zero divisor of the rough semiring (T, ∆, ∇). Also We prove that RS(X) is not a zero divisor for a dominant set X ⊆ U where U is the finite universal set on the set of all rough sets for the given information system together with the operations praba ∆ and praba ∇. We illustrate these concepts through examples.

In this paper, we define a Cayley graph corresponding to the Rough ideal J of the Rough semiring (T, ∆, ∇). The Domination number of the Rough Ideal based Rough Edge Cayley graphs  and )) where  contains the non-trivial elements of J are derived and illustrated through examples. Interpretation of a communication network is done in the form of Rough Ideal based Rough Edge Cayley Graph.

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Hidden Markov model (HMM) has become increasingly popular in the last several years. Real-world problems such as prediction of web navigation are uncertain in nature; in this case, HMM is less appropriate i.e., we cannot assign certain probability values while in fuzzy set theory everything has elasticity. In addition to that, a theory of possibility on fuzzy sets has been developed to handle uncertainity. Thus, we propose a fuzzy hidden Markov chain (FHMC) on possibility space and solve three basic problems of classical HMM in our proposed model to overcome the ambiguous situation. Client's browsing behavior is an interesting aspect in web access. Analysis of this issue can be of great benefit in discovering user's behavior in this way we have applied our proposed model to our institution's website ( www.ssn.edu.in ) to identify how well a given model matches a given observation sequence, next to find the corresponding state sequence which is the best to explain the given observation sequence and then to attempt to optimize the model parameters so as to describe best how a given observation sequence comes about. The solution of these problems help us to know the authenticity of the website.

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In this paper, the classical semi-Markov model in discrete time is extended to semi-Markov model with fuzzy transitions and fuzzy states. The definition and the basic equation for interval transitions of a semi-Markov model with fuzzy transitions are provided. Also the interval transitions for the above model with fuzzy states is provided for the homogeneous case and we apply this fuzzy technique to web based application and show this model gives the accessibility assessment that are based on uncertainties/imprecise. The definitions and results for the fuzzy model are provided by means of the fuzzy probabilities and are modeled by triangular fuzzy numbers.

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