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We define $$2n+1$$ 2 n + 1 and 2 n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2 n fuzzy numbers. When the data is representable in terms of $$2n+1$$ 2 n + 1 fuzzy number, we generalize the FMCDM (f...
In this paper, we present applications of Markov rough approximation framework (MRAF). The concept of MRAF is defined based on rough sets and Markov chains. MRAF is used to obtain the probability distribution function of various reference points in a rough approximation framework. We consider a set to be approximated together with its dynamacity an...
In this paper, we present the notion of perfect ideal of a seminearring S and prove that the kernel of a seminearring homomorphism is a perfect ideal. We show that the quotient structure S/I is isomorphic to the structure ST(I). Finally, we prove isomorphism theorems in seminearrings by using tame condition.
In this paper, we present a link between markov chains and rough sets. A rough approximation framework (RAF) gives a set of approximations for a subset of universe. Rough approximations using a collection of reference points gives rise to a RAF. We use the concept of markov chains and introduce the notion of a Markov rough approximation framework (...