Probabilistic dual hesitant fuzzy set is a more powerful and important tool to express
uncertain information. As we all know, the distance and similarity measures are very useful …

In this paper, a solution of the problem of the interval-valued fuzzy sets synthesis, is given.
The codomain is considered to be a lattice of intervals. The necessary and sufficient …

The membership function of a fuzzy set can be constructed from a family of subsets of a
universal set via the form of resolution identity assuming that the family is nested. In this …

The purpose of this paper is to propose a mechanical procedure to generate fuzzy data from
the observed real number data. The observed data may be imprecise owing to some …

A representation theorem of families of subsets by poset-valued fuzzy sets is presented.
Namely, necessary and sufficient conditions are given under which for a given family of …

This paper deals with the uniqueness of L-fuzzy sets in the representation of a given family
of subsets of a nonempty set. It first shows a formula of the number of L-fuzzy sets whose …

Given a pre-determined subset SS of (0, 1 (0, 1 and a solidly nested family MM of subsets of
a universal set UU, in this paper, we propose a methodology to construct a fuzzy subset of …

Generalized or relational-valued fuzzy sets are mappings from a set X to a relational system
S=(S, p). Representation of collections of subsets by relational-valued fuzzy sets in the …

A new methodology for constructing a fuzzy subset of a universal set U from a family of
subsets of U based on a pre-determined range S that is a subset of (0, 1] is proposed in this …

The main purpose of this paper is to establish a mechanical procedure to determine the
membership functions using the data collected from the economic and engineering …