In this paper we consider physical systems and the concept of their states in the context of the theory of fuzzy sets and systems. In section 1 we give a brief sketch on the fundamental difference between the theories of classical physics and quantum mechanics. In section 2 and 3 we introduce very shortly systems and their states in classical and quantum mechanics, respectively. Section 4 prese...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

In the field of pattern recognition, clustering is used to group the data into different clusters based on the similarity among them. There are a number of clustering techniques developed in the past using different distance/similarity measure. Due to the high versatility in data, researchers have used various distance measure like Hamming distance, Euclidean distance etc. to solve the clusteri...

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...

To have a real option means to have the possibility for a certain period to either choose for or against making an invetsment decision, without binding oneself up front. The real option rule is that one should invest today only if the net present value is high enough to compensate for giving up the value of the option to wait. Because the option to invest loses its value when the investment is ...

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...

holds (but which implies that the space is actually a Menger space). Z̆ikić [2] extended the existence part of their theorem showing that it is enough to consider the case of special sequence tn = 1/ n and that (1) holds for some x = x0 and y = f (x0). The error in her main theorem (and in all consequences) concerns the statement that, under the same conditions, also the uniqueness of fixed poin...

Chiclana, Herrera and Herrera-Viedma studied conditions under which the reciprocity property is maintained in the aggregation of reciprocal fuzzy preference relations using the OWA operator guided by a relative linguistic quantifier. In this note, we focus on the reciprocity in the aggregation of fuzzy preference relations (that is, the additive reciprocity is not assumed) using the OWA operato...

A. George and P. Veeramani, 1994. On some results in fuzzy metric space, Fuzzy Sets and Systems, vol. 64, 395-399. B. Schweizer, H. Sherwood, and R. M. Tardi®,1988. Contractions on PMspace examples and counter examples, Stochastica vol. 1, 5–17. D. Mihet, 2004. A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, vol. 144, 431–439. D. Mihet, 2008. Fuzzy -contractive mapp...