Motivated by important applications, the theory of mathematical programming has been extended to the case of infinitely many restrictions. At the same time, this theory knew remarcable developments since invexity and its further generalizations have been introduced as substitute of convexity. Here, we consider the multiobjective programming with a set of restrictions indexed in a compact. We ob...

The connections between variational inequalities and optimization problems is well known, and many investigators have discussed them along many years; see, for instance, [1, 8, 10, 13]. This last article, which was authored by Giannessi, in particular, is one of the main works that study these connections in the finite-dimensional context. In recent years, the interest in the investigation on t...

We address the problem of identifying a useful set of mutually compatible separation axioms for each category T-FNS of T-neighbourhood spaces. It should contain one of T-complete regularity that characterizes T-uniformizability, as indeed we achieve here. This seems to necessitate the parameterization of most separation axioms by the triangular norm T, with the exception of the two axioms T0 an...

We study computably enumerable equivalence relations (ceers), under the reducibility R ≤ S if there exists a computable function f such that x R y if and only if f(x) S f(y), for every x, y. We show that the degrees of ceers under the equivalence relation generated by ≤ form a bounded poset that is neither a lower semilattice, nor an upper semilattice, and its first order theory is undecidable....

Welcome to the Journal of Intelligent and Fuzzy Systems’s special issue for “FUZZYSS’2011: 2nd International Fuzzy Systems Symposium”. Since its introduction by Prof. Dr. Lotfi A. Zadeh fuzzy logic, fuzzy sets and systems have been applied to various problems in many diverse areas. As everything try to evolve towards better states, the fuzzy theory and its applications are also evolving to mode...

Bijective transformations play an important role in generating fuzzy implications from fuzzy implications. In [Representations through a Monoid on the set of Fuzzy Implications, Fuzzy Sets and Systems, 247, 5167], Vemuri and Jayaram proposed a monoid structure on the set of fuzzy implications, which is denoted by I, and using the largest subgroup S of this monoid discussed some group actions on...

Li and Yu (Fuzzy Sets and Systems 101 (1999) 109) argued that the model of Yang et al. for fuzzy programming (Fuzzy Sets and Systems 41 (1991) 39) is correct only for a speci2c type of piecewise linear membership function and proposed their model for other type of membership functions. This study generalizes the model of Yang et al. A numerical example indicates that the model of Li and Yu is i...

When 60 years ago Shannon established “A Mathematical Theory of Communication” nobody could know the consequences for science and technology in the second half of the century. Shannon published his article in two parts in the July and October 1948 editions of the Bell System Technical Journal. However, it is very probable that this article wouldn’t have become famous without the help of Weaver,...

Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilisticmean, variance and covariance of fuzzy numbers and Fuller andMajlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the...

Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as de1ned by Atanassov (Instuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999), give us a way to...