The factor complexity function C w (n) of a finite or infinite word w counts the number of distinct factors of w of length n for each n ≥ 0. A finite word w of length |w| is said to be trapezoidal if the graph of its factor complexity C w (n) as a function of n (for 0 ≤ n ≤ |w|) is that of a regular trapezoid (or possibly an isosceles triangle); that is, C w (n) increases by 1 with each n on so...

fuzzy newton-cotes method for integration of fuzzy functions that was proposed by ahmady in [1]. in this paper we construct error estimate of fuzzy newton-cotes method such as fuzzy trapezoidal rule and fuzzy simpson rule by using taylor's series. the corresponding error terms are proven by two theorems. we prove that the fuzzy trapezoidal rule is accurate for fuzzy polynomial of degree one and...

The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) ar...

How to maximize the efficiency of X-ray Talbot interferometry (XTI) is discussed for X-ray phase imaging. Shape parameters of an amplitude grating used in XTI strongly affect the efficiency. We calculated efficiencies assuming rectangular and trapezoidal patterns for an absorption grating. As a result, a rectangular absorption grating of a duty ratio of 1:1 is optimal. But, a trapezoidal patter...

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New algorithms for calculating the proper trapezoidal approximation of fuzzy numbers with respect to the distance based on bi-symmetrical weighted functions are proposed. It is shown that the adequate approximation operator is chosen with respect both to the global spread of a fuzzy numbe...

In this paper we explore various interconnections between rich words, Sturmian words, and trapezoidal words. Rich words, first introduced by the second and third authors together with J. Justin and S. Widmer, constitute a new class of finite and infinite words characterized by having the maximal number of palindromic factors. Every finite Sturmian word is rich, but not conversely. Trapezoidal w...

Standard intuitionistic fuzzy arithmetic operations have certain problems in division and subtraction operations. Ezzati et al. (2014) defined a new operation on symmetric trapezoidal intuitionistic fuzzy numbers in which the properties ≈ 1 and ≈ 0 are satisfied. In this paper, the new operations according to Ezzati et al. (2014) are extended to symmetric trapezoidal intuitionistic fuzzy number...

This letter presents a new directional dual-band slotted trapezoidal inverted-F antenna (IFA) for indoor Wireless Local Area Network (WLAN) applications. The dual-band performance can be obtained by tuning the lengths of the inner symmetrical trapezoidal slots and the outer trapezoidal arms in a nearly independent manner. The measured results show that the proposed antenna can provide two separ...

In this study, a new modeling method based on trapezoidal fuzzy number FAHP has been proposed to solve the problem of risk element transmission in enterprise project evaluation chain. We firstly put forward enterprise project chain risk element transmission and constructs enterprise project chain risk element transmission tetrahedron model and then proposed the theory of enterprise project eval...

In general fuzzy linear regression, the coefficients of the fuzzy regression model are symmetric triangular fuzzy numbers, while we try to replace them by more general ones, which are asymmetric trapezoidal fuzzy numbers. Possibility of equality between two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models are presented in this paper. Furthermor...