Recently, Bourne constructed a system of three-valued logic that he supposed to replace à Lukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to à Lukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original...

This paper presents mathematical foundtions of the Overlap Resolution Number System (ORNS) which employs signed Continuous Valued Digits (CVD’s). ORNS is a redundant Number System employing residue arithmetic. In contrast to the implementation of arithmetic by binary or multiple-valued logic circuits, arithmetic operations in this novel number system are performed by analog digit manipulation c...

Recently, Bourne constructed a system of three-valued logic that he supposed to replace à Lukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to à Lukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

We introduce new and interesting model of system of generalized set-valued equilibrium problems which generalizes and unifies the system of set-valued equilibrium problems, the system of generalized implicit vector variational inequalities, the system of generalized vector and vector-like variational inequalities introduced by Ansari et al. (2002), the system of generalized vector variational i...