Different languages that are offered to model vague preferences are reviewed and an interval-valued language is proposed to resolve a particular difficulty encountered with other languages. It is shown that interval-valued languagesare well definedfor De Morgan triples constructedby continuoustriangular norms, conorms and a strong negation function. A new transitivity condition for vague prefer...

In order to encourage the use of public transportation, it is necessary make more appealing commuters by conducting frequent Service Quality (SQ) evaluations and modifications. Understanding passengers’ expectations transportation are important, evaluating SQ an essential tool for assessing overall performance system. The purpose present study was examine perceptions core passengers regarding i...

Abstract Cubic Pythagorean fuzzy (CPF) set (CPFS) is a hybrid that can hold much more information and be used to describe both an interval-valued (IVPFS) (PFS) at the same time handle data uncertainties. Based on it, present study classified into three phases. The first phase modify existing operational laws aggregation operators (AOs) in article presented by Abbas et al. (Journal of Intelligen...

The Pythagorean theorem can be proven geometrically through the use of dissections of squares and triangles. Four of these decompositions are paired into two compound dissections, which are used to create novel images. Pythagorean Theorem Many proofs of the Pythagorean theorem are given in the literature, for example, at the MathWorld web site [1]. Of particular interest to this work are dissec...

This paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, we discuss the notions of variance and covariance of set-valued and interval-valued random variables. Then, we give the definition of the intervalvalued linear model and its le...

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs.

It was John Maynard Keynes [13] who first forcibly argued that probabilities cannot be simply ordered. There are cases, he argued, in which the probability of the hypothesis h can be regarded neither as greater than that of hypothesis k, nor less than that of hypothesis k, nor yet equal to that of hypothesis k. Although he did not provide a mathematical structure for his probability values, he ...

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

The aim of this work is to analyze the interval canonical representation for fuzzy QL-implications and automorphisms. Intervals have been used to model the uncertainty of a specialist’s information related to truth values in the fuzzy propositional calculus: the basic systems are based on interval fuzzy connectives. Thus, using subsets of the real unit interval as the standard sets of truth deg...