In this paper, we use L-fuzzy preopen operator to introduce the degree of pre-separatedness and the degree of preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of preconnectedness are presented in L-fuzzy topological spaces.

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language compose...

Closure (interior) operators and closure systems are important tools in many mathematical environments. Considering the logical sense of a complete residuated lattice L, this paper aims to present concepts L-closure (L-interior) by means infimums (supremums) L-families L-subsets show their equivalence categorical sense. Also, two types fuzzy relations between corresponding L-interior proposed, ...

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations meet, multiplication, fuzzy equality and a unit element. They open the door to an alternative development of fuzzy (manyvalued) logic with the basic connective being fuzzy e...

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...

Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the ...

We study interior operators and interior structures in a fuzzy setting. We investigate systems of “almost open” fuzzy sets and the relationships to fuzzy interior operators and fuzzy interior systems.

In many applied disciplines like computer science, coding theory and formal languages, the use of fuzzified algebraic structures play a remarkable role. In this paper, we introduced some new types of generalization of an intuitionistic fuzzy interior ideal, called (α, β)-intuitionistic interior ideals of an ordered semigroup S. The important milestone of this paper is to link the ordinary inter...

in this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $m$-hyponormal operator‎. ‎we show that every analytic extension of a $n$th roots of $m$-hyponormal operator is subscalar of order $2k+2n$‎. ‎as a consequence‎, ‎we get that if the spectrum of such operator $t$ has a nonempty interior in $mathbb{c}$‎, ‎then $t$ has a nontrivial invariant subspace‎. ‎finally‎, ‎w...