Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middle-point and the spread of each $gamma$-cut of a fuzzy number, respectively. We use the value of a as the weight of the signal/noise ratio of each $gamma$-cut of a fuzzy number to calcula...

the purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $delta$ and give some inclusion relations.

With respect to multiple attribute group decision making problem with triangular fuzzy linguistic information, in which the attribute weights and expert weights take the form of real numbers, and the preference values take the form of triangular fuzzy linguistic variables, some operators for aggregating triangular fuzzy linguistic variables, such as the fuzzy linguistic harmonic mean (FLHM) ope...

Intuitionistic fuzzy linguistic numbers (IFLNs) are an extension of the linguistic variables and the intuitionistic fuzzy sets, which are proposed by Wang and Li (Wang J.Q., Li J.J. (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science & Technology Information (33), 8-9.). In this paper, we introduced some operational laws of IFL...

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...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

in this work, we define a fuzzy soft set theory and its related properties. we then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) $L-R$, or flat (semi) $L-R$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using $gamma$-cuts of fuzzy coefficients. Then, we consider a fix $g...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with interval-valued dual hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic operation, we have developed some aggregation operators for aggregating interval-valued dual hesitant fuzzy linguistic information: i...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...