Prediction of Multivariable Properties of Reservoir Rocks by Using Fuzzy Clustering

AbstractForecasting of geological parameters is very important for decision making on investment to exploration of new hydrocarbon structures and fields. On the one hand, the complexity of this problem is originated from the nonlinearity and uncertainty of behavior of an ensemble of interrelated parameters changing with respect to the depth. This phenomenon is considered analogously to time series, where the depth plays the role of time. On the other hand, the available data are irregular over the depth, as represent different geological bodies with distinct properties. These features mandate necessity to consider multivariable time series of geological parameters with irregular intervals. In this paper, we consider multilag forecasting of five geological parameters over the depth. As a model of forecasting, fuzzy c-means based fuzzy if-then rules are used and this allows better capture of high complexity of the considered phenomena than the classical precise forecasting model. The experimental data show validity of the suggested approach

Supplier Selection Problem under Z-information

AbstractSupplier selection problem is a very important element of Supply Chain Management systems. The existing works are devoted to solving this problem under deterministic, stochastic, interval-based and fuzzy information. Unfortunately, up today no systematic research on supplier selection under partial reliability of information is proposed. In this paper we suggest new method for solving supplier selection problem under fuzzy and partially reliable information formalized by using Z-numbers. The method is based on determination of Z-number valued ideal and negative ideal solutions. A numerical example is provided to illustrate validity of the proposed approach to supplier selection problem

Z

Decision making, reasoning, and analysis in real-world problems are complicated by imperfect information. Real-world imperfect information is mainly characterized by two features. In view of this, Professor Zadeh suggested the concept of a Z-number as an ordered pair Z=(A,B) of fuzzy numbers A and B, the first of which is a linguistic value of a variable of interest, and the second one is a linguistic value of probability measure of the first one, playing a role of its reliability. The concept of distance is one of the important concepts for handling imperfect information in decision making and reasoning. In this paper, we, for the first time, apply the concept of distance of Z-numbers to the approximate reasoning with Z-number based IF-THEN rules. We provide an example on solving problem related to psychological issues naturally characterized by imperfect information, which shows applicability and validity of the suggested approach

Fuzzy Logic for Incidence Geometry

The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid’s first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points