In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum ...

From both a theoretical and a practical point of view, the study of the concept of independence has great importance in any formalism that manages uncertainty. In Independence Concepts in Possibility Theory: Part I (de Campos and Huete, Fuzzy Sets and Systems 103 (1999) 127-152) several independence relationships were proposed, using different comparison criteria between conditional possibility...

An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce $L$-multi-fuzzy and$L$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

Over the past few years, fuzzy set theory has become a well-established mathematical theory that has been applied in many practical applications. In this paper, we elaborate on the use of fuzzy sets in the context of music information retrieval. First, we demonstrate that music objects like artists and songs can straightforwardly be represented as fuzzy sets, and then we explain why it is benef...

Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft se...

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, andbackward-forwardbisimulations) between fuzzyautomatahavebeen introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of th...

New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatović, M. Ćirić, S. Bogdanović, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081–3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relati...

In this paper, we firstly defined neutrosophic parameterized neutrosophic soft sets(npn−soft sets) which is combination of a neutrosophic sets and a soft sets. Our npn−soft sets generalizes the concept of the other soft sets such as; fuzzy soft sets, intuitionistic fuzzy soft sets, neutrosophic soft sets, fuzzy parameterized soft sets, intuitionistic fuzzy parameterized soft sets, neutrosophic ...

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic ...