We show the tight upperbound of the length of the minimum solution of a word equation L = R in one variable, in terms of the differences between the positions of corresponding variable occurrences in L and R. By introducing the notion of difference, the proof is obtained from Fine and Wilf’s theorem. As a corollary, it implies that the length of the minimum solution is less than N = |L|+ |R|.

Using a new scaling and a cut-off procedure, we show that φ theory on a deformed noncommutative R can be obtained from the corresponding theory on the fuzzy S × S. The star-product on this deformed R 4 is non-associative, and the theory naturally has an ultra-violet cut-off, Λ = 2/θ. We show that UV-IR mixing is absent to one loop, and that the β-function is the same as that of an ordinary φ th...

The present paper deals with formal concept analysis of data with fuzzy attributes. We clarify several points of a new approach of [S.Q. Fan, W.X. Zhang, Variable threshold concept lattice, Inf. Sci., accepted for publication] which is based on using thresholds in concept-forming operators. We show that the extentand intent-forming operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for p...

Fuzzy measures were introduced by M Sugeno in in order to express a grade of fuzziness in the same way that probability measures express a grade of random ness The Sugeno fuzzy integrals are the functionals with monotonicity de ned by using fuzzy measures Later on Murofushi and Sugeno proposed another type of fuzzy integral the Choquet integral based on the Capacity Theory developed by G Choque...

|||||||||||||||||||||||||||||||Abstract In this paper, the researcher proposes a modi ed new method to rank L-R fuzzy numbers. The modi ed method uses a defuzzi cation of parametrically represented fuzzy numbers that have been studied in [20]. This parameterized defuzzi cation can be used as a crisp approximation with respect to a fuzzy quantity. In this article, the researcher uses this defuzz...

We derive some of the basic properties of weighted variable exponent Lebesgue spaces L p(.) w (R) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W (L p(.) w , L q υ) is defined, where the local component is a weighted variable exponent Lebesgue space L p(.) w (R) and the global component is a weighted Lebesgue space Lυ (R) . We inves...

data envelopment analysis (dea) is a technique used to compare efficiency in various sectors such as hospitals, chain stores, and dealerships. it represents a set of linear programming techniques and uses deter-ministic data (inputs and outputs), in stable conditions. the dea technique cannot be used when there is data with indeterministic nature, or when there is an environment with dynamic co...

Fuzzy adaptive sliding mode control method is a good way to resolve the control problem when the system mathematic model is unknown. However, reaching condition must be satisfied in this method. In this paper, a kind of fuzzy adaptive variable structure control method is presented in which sliding mode doesn’t exist in closed-loop system. Dynamic fuzzy logical system (DFLS) is introduced to for...

Introduction and motivation To explain the motivation of our work we give a short glimpse into the history of Fuzzy Topology called more recently Lattice-Valued Topology or Many Valued Topology. In 1968, C. L. Chang [1] introduced the notion of a fuzzy topology on a set X as a subset τ ⊆ [0, 1] satisfying the natural counterparts of the axioms of topology: (1) 0X , 1X ∈ τ ; (2) U, V ∈ τ ⇒ U ∧ V...