the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. The purpose of this paper is to introduce a generalization of ideas presented in [20]. Indeed, we study the concept of intuitionistic fuzzy interior ideals of a Γ-semigroup, by using Atanassov’s idea and investigate some of their important properties. Specially, we obtain a chara...

We construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement. In classical mathematics, the theory of closure operators and that of interior operators can be derived one from another. In fact, A...

In this paper we study the concept of Fuzzy-anti-n-normed linear operator as a generalization of Fuzzy-anti-2normed linear operator. Fuzzy-anti-n-continuous linear operator and three types (strongly, weakly, and sequentially) of Fuzzy-anti-n-continuous linear operators are defined and relation between strongly, weakly and sequentially Fuzzy-anti-n-continuous linear operator is developed. Also s...

We first give some useful characterizations of regular semigroups and right weakly regular semigroups by the properties of their bi-ideals, interior ideals, left ideals and right ideals. Based on these characterizations, we also characterize regular semigroups and right weakly regular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy (generalized) bi-ideals, (∈,∈ ∨qk)-fuzzy interior ideals,...

In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in...

in this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $h(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth banach spaces. it is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. this equivalence is used to define an iterative algorithm for solving fu...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

This paper presents a new fuzzy group decision-making approach by using probabilities and ordered weighted averages (OWA). Thus, we are able to assess the problem considering probabilistic information and the attitudinal character of the decision maker. For doing so, the fuzzy generalized probabilistic OWA (FGPOWA) operator is presented. It is an aggregation operator that unifies the probabilit...