In this paper, we introduce the concept of fuzzy congruence relations on a pseudo BE-algebra and some of properties are investigated. We show that the set of all fuzzy congruence relations is a modular lattice and the quotient structure induced by fuzzy congruence relations is studied.

No abstract

No abstract

The aim of this paper is to investigate several operators on quantum B-algebras. At first, we introduce closure and interior operators on quantum B-algebras and consider their relations on bounded quantum B-algebras. Furthermore, we discuss very true operators on quantum B-algebras by three cases via the unit element, and present some similar conclusions and different results. Finally, by constructing a very true operator on a quotient very true perfect quantum B-algebra, we establish a homomorphism theorem on very true perfect quantum B-algebras.

Inducing information and bi-polar preference-based weights allocation and relevant decision-making are one important branch of Yager’s decision theory. In the context of basic uncertain information environment, there exist more than one inducing factor and the relative importance between them should be determined. Some subjective methods require decision makers to indicate the bi-polar preference extents for each inducing factor as well as the relative importance between all the involved inducing factors. However, although the bi-polar preference extents for inducing factors can often be elicited, sometimes decision makers cannot provide the required relative importance. This work presents some approaches to address such problem in basic uncertain information environment. From the mere bi-polar preference extents offered by decision makers, we propose three methods, statistic method, distance method and linguistic variable method, to derive relative importance between different inducing factors, respectively. Each of them has advantages and disadvantages, and the third method serves as a trade-off between the first two methods. The rationale of preference and uncertainty involved evaluation is analyzed, detailed evaluation procedure is presented, and numerical example is given to illustrate the proposals.