Motivated by interval matrix multiplication we consider (matrix) polytopes A ⊆ R, B ⊆ R, m,n, k ∈ N, and investigate the boundary shape of their pointwise product AB := {AB | A ∈ A, B ∈ B}. We prove that AB cannot have outward curved boundary sections while inward curved sections may exist. This is achieved by a simple local extreme point analysis. Results are proved in a more general abstract ...

*Corresponding address: [email protected] Received 14 September, 2010; Revised 29 April, 2011 ABSTRACT Ever since the introduction of fuzzy sets by Zadeh [1] , the fuzzyness invaded almost all the branches of crisp mathematics. Deng [3] kaleva and Seikalla [2] and Kramosil and Michalek [5]Have introduced the concept of fuzzy metric space, George and Veeramani [4] modified the concept of...

H. Akbar-Zadeh has recently proposed (J Geom Phys 17 (1995) 342) a new geometric formulation of Einstein–Maxwell system with source in terms of what are called “Generalized Einstein manifolds”. We show that, contrary to the claim, Maxwell equations have not been derived in this formulation and that, the assumed equations can be identified only as sourcefree Maxwell equations in the proposed geo...

Fuzzy logics in Zadeh’s ‘narrow sense’ (Zadeh, 1988), i.e., truth functional logics referring to the real closed unit interval [0,1] as set of truth values, are often motivated as logics for ‘reasoning with imprecise notions and propositions’ (see, e.g., (Hájek, 1998)). However the relation between these logics and theories of vagueness, as discussed in a prolific discourse in analytic philosop...

Editor's Note: These short reviews of a recent paper in the Journal, written exclusively by graduate students or postdoctoral fellows, are intended to mimic the journal clubs that exist in your own departments or institutions. For more information on the format and purpose of the Journal Club, please see Review of Aziz-Zadeh et al. In the premotor cortex of the macaque there are neurons whose f...

Stability of a fuzzy control system is closely related to the analytical structure of the fuzzy controller, which is determined by its components such as input and output fuzzy sets and fuzzy rules. We first characterize the mathematical input–output structure of fuzzy controllers and then utilize the structure characteristics to advance stability analysis. We study how the components of a gene...

Fuzzy logic emerged in 1965 with the work of Lotfi Zadeh that aims rigorously deal with the uncertainty inherent in the definition of notions and inaccurate or vague properties in several everyday situations, such as high temperature, sharp drop, etc. For this, Zadeh considered a degree (a value in the range [0,1]) in order to express how much an element belongs to a set, i.e. satisfies a given...

This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well a comprehensive overview of major contributions in the domain soft computing methods fuzzy environment. part special reverential volume, Centenary Birth Lotfi A. Zadeh, whom considered be mentor, and he showed gratitude many times innumerable ways, including by being Guest Editor...

Most existing context reasoning approaches implicitly assume that contexts are precise and complete. This assumption cannot be held in pervasive computing environments, where contexts are often imprecise and incomplete due to unreliable connectivity, user mobility and resource constraints. To this end, we propose an approach called CRET: Context Reasoning using extended Evidence Theory. CRET ap...

The commonly accepted theory of fuzzy numbers (Czogała and Pedrycz, 1985) is that set up by Dubois and Prade (1978), who proposed a restricted class of membership functions, called (L,R)–numbers with shape functions L and R. However, approximations of fuzzy functions and operations are needed if one wants to follow Zadeh’s (Zadeh 1975; 1983) extension principle. It leads to some drawbacks that ...