Uncertainty and fuzziness are involved in most of the real world problems. In present communication we have studied various advancements in fuzzy information theory and proposed a new measure of divergence between two fuzzy sets. Further, a measure of fuzzy directed divergence was developed based on the proposed divergence measure. Some properties of this fuzzy directed divergence measure were ...

State of the art approaches for modelling biological systems can be classified as qualitative or quantitative. Qualitative models are relatively simple and require only basic knowledge of the system, but may only be used to get a rough image about the system’s dynamics. On the other hand, quantitative models are able to mimic accurate dynamical properties of observed system, but require accurat...

Information from different sensors can be fused in various ways. It is often difficult to choose the most suitable method for solving a fusion problem. In a measurement situation, the measured signal is often corrupted by disturbances (noise, etc.). It is, therefore, meaningless to compare crisp values without the corresponding uncertainty intervals. This paper describes a toolbox including nin...

Uncertainty always exists in nature and real systems. It is known that probability has been used traditionally in modeling uncertainty. Since a belief function was proposed as an another type of measuring uncertainty, Dempster-Shafer theory (DST) has been widely studied and applied in diverse areas. Because of the advent of computer technology, the representation of human knowledge can be proce...

Ulrich Höhle was born on 6 December 1943 in Bad Oeynhausen, Germany. Being musically and mathematically gifted (among others), he could not decide between music and mathematics, so he began his studies in both directions: mathematics and music (piano) at Johannes-Gutenberg Universität in Mainz (1963–1966). After having realized his true vocation, he decided to become a mathematician and continu...

Fuzzy relational models have been widely investigated and found to be an efficient tool for the identification of complex systems. However, little attention has been given to the linguistic interpretation of these models. The use of relational models is recommended since their development follows a natural sequence based on the original ideas about fuzzy sets and fuzzy logic, involving the esti...

Fuzzy decision-making consists in making decisions under complex and uncertain environments where the information can be assessed with fuzzy sets and systems. The aim of this study is to review the main contributions in this field by using a bibliometric approach. For doing so, the article uses a wide range of bibliometric indicators including the citations and the h-index. Moreover, it also us...

Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets and Systems 61 (1994)] and we...

This paper generates a variety of general-systems theoretic concepts and a range of systems theories using a minimal set of primitives. The notion of a distinction is taken as primitive and the natural hierarchy of distinctions becomes the primitive structure. A number of system theories are then analysed in terms of these primitives: Zadeh’s fuzzy sets theory; Klir’s epistemological hierarchy ...

In this paper, we study countably compact fuzzy sets using the definition of C. K. Wong [10] and obtain its several properties. 1. Introduction The concept of fuzzy set and fuzzy set operations were first introduced by L. A. Zadeh [11] in1965. Several other mathematicians studied fuzzy sets in various areas in mathematics. Firstly, C. L. Chang [2] in 1968 developed the theory of fuzzy topologic...