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...

In 1965, in his pioneer paper L.A. Zadeh [9] introduced the concept of fuzzy set to handle the uncertainties in our daily life. After that many generalizations of fuzzy sets are presented, for example, interval valued fuzzy sets [10] and intuitionistic fuzzy sets [1]. Fuzzy sets are extremely useful to solve many problems in applied mathematics, information sciences and theory of automata [2]. ...

Information theory was introduced by Shannon in 1948 and it includes the study of uncertainty measures. Analogous to information theory which is founded on probability theory, notion of fuzzy sets was established by Zadeh in 1965 which is a mechanism to manage uncertainty. The pedestal for present study is information theory with intuitionistic fuzzy sets. Atanassov (1986) devised Intuitionisti...

The uncertain nonlinear systems can bemodeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations.We use the neural networks to approximate the coefficients of the fuzzy equations.The approximation theory for ...

We discuss an emerging group of successful parties in Central and Eastern "Concept Structures and Fuzzy Set Theory: A Proposal for Concept. Applying the fuzzy set theory is a good example of meaning. When viewing the areas of decision making in marketing, decision making in the business. A conceptual formulation emphasizes on the meaning and interpretation of the formulations makes an in-depth ...

Gradual concepts abound in many web-related domains, ranging from the notion of relevance in information retrieval, to the strength of connection in online social networks. As a result, fuzzy set theory is often a natural choice in implementing web systems. In this chapter, we give an overview of applications of fuzzy set theory in this area, focusing in particular on information retrieval, the...

The concept of the strongest path plays a crucial role in fuzzy graph theory. In classical graph theory, all paths in a graph are strongest, with a strength value of one. In this article, we introduce Menger’s theorem for fuzzy graphs and discuss the concepts of strengthreducing sets and t-connected fuzzy graphs. We also characterize t-connected and t-arc connected fuzzy graphs. 2012 Elsevier I...

In Spain, the first paper on fuzzy set theory was published by Trillas and Riera (1978). From 1978 to the present, more than 1,500 papers on the topic have been published by the Spanish fuzzy set research community, as shown by the ISI Web of Science. The Spanish fuzzy set community ranks seventh in the “top-ten” ranking of the most productive countries on fuzzy set theory research, and it is t...

To avoid self-contradictions in Fuzzy Set Theory, it is needed to consider only fuzzy sets that are not selfcontradictory and whose complements are also not selfcontradictory. This paper deals with a subset Fnc(E) in [0, 1] , where the above conditions are satisfied. A particular Fuzzy Set Theory is defined in Fnc(E) with adequate logical connectives. Finally, which classical properties hold in...