This paper focuses on modelling fuzzy numbers with meaningful membership functions. More precisely, it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data. In many applications, input information is numerical, and therefore, particular fuzzy sets, such as fuzzy numbers, hold great interest and relevance in managing data imprecision and vagueness. The pr...

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...

We present a solution procedure for a quadratic programming problem with some probabilistic constraints where the model parameters are either triangular fuzzy number or trapezoidal fuzzy number. Randomness and fuzziness are present in some real-life situations, so it makes perfect sense to address decision making problem by using some specified random variables and fuzzy numbers. In the present...

Ranking fuzzy numbers plays an important role in data analysis, decision making optimization, forecasting etc. The last few decades have seen a large number of methods investigated for ranking fuzzy numbers. In this paper, a new approach is proposed for the ranking of generalized trapezoidal fuzzy numbers namely Haar ranking and is based on the approximate coefficients and detailed coefficients...

Trapezoidal words are words having at most n+1 distinct factors of length n for every n ≥ 0. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration. We then separate trapezoidal words into two disjoint classes: open and closed. A trapezoidal word is closed if it has a factor that occurs only as a p...

Class Sm variable transformations with integer m, for accurate numerical computation of finite-range integrals via the trapezoidal rule, were introduced and studied by the author. A representative of this class is the sinm -transformation. In a recent work of the author, this class was extended to arbitrary noninteger values of m, and it was shown that exceptionally high accuracies are achieved...

We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.