In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from Chapter 1.

Interval-Valued Intuitionistic Fuzzy Sets

Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.

Hesitant fuzzy sets

An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.

Intuitionistic Fuzzy Aggregation Operators

In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

Soft set theory

What is modal logic

The exactitude of petroleum fluid molecular weight correlations affects significantly the precision of petroleum engineering calculations and can make process design and trouble-shooting inaccurate. Some of the methods in the literature to predict petroleum fluid molecular weight are used in commercial software process simulators. According to statements made in the literature, the correlations of Lee–Kesler and Twu are the most used in petroleum engineering, and the other methods do not exhibit any significant advantages over the Lee–Kesler and Twu correlations. In order to verify which of the proposed in the literature correlations are the most appropriate for petroleum fluids with molecular weight variation between 70 and 1685 g/mol, 430 data points for boiling point, specific gravity, and molecular weight of petroleum fluids and individual hydrocarbons were extracted from 17 literature sources. Besides the existing correlations in the literature, two different techniques, nonlinear regression and artificial neural network (ANN), were employed to model the molecular weight of the 430 petroleum fluid samples. It was found that the ANN model demonstrated the best accuracy of prediction with a relative standard error (RSE) of 7.2%, followed by the newly developed nonlinear regression correlation with an RSE of 10.9%. The best available molecular weight correlations in the literature were those of API (RSE = 12.4%), Goosens (RSE = 13.9%); and Riazi and Daubert (RSE = 15.2%). The well known molecular weight correlations of Lee–Kesler, and Twu, for the data set of 430 data points, exhibited RSEs of 26.5, and 30.3% respectively.

https://www.mdpi.com/2227-9717/11/2/426/pdf?version=1675159987

Prediction of Molecular Weight of Petroleum Fluids by Empirical Correlations and Artificial Neuron Networks

In a series of papers, Generalized Net (GN) models of the ways of functioning of the different systems and organs in the human body are described in general. Each GN model of a particular system or organ can be detailed and made more complex. In this paper a GN model of the abdominal aorta and its branches of the vascular system is proposed.

A Generalized Net Model of the Abdominal Aorta and Its Branches as a Part of the Vascular System

Research on intuitionistic fuzzy sets, 1990–1992

A first attempt for application of Intercriteria Analysis over patterns is described. Possible applications are discussed.

Intercriteria Analysis over Patterns

The research expounded in this paper is a continuation of previous investigations into the modelling of information flow with a typical university. A generalized net model which describes the process of creating and evaluation of educational content using a set of criteria is constructed. The example for education of medical students in diabetes mellitus and possibilities for venous thrombotic disease is given.

Krassimir T. Atanassov

Papers

Prediction of Molecular Weight of Petroleum Fluids by Empirical Correlations and Artificial Neuron Networks

A Generalized Net Model of the Abdominal Aorta and Its Branches as a Part of the Vascular System

Research on intuitionistic fuzzy sets, 1990–1992

Intercriteria Analysis over Patterns

Generalized Net Model for Creating and Evaluating of Educational Content