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1

Linguistically defined clustering of data

Leski J. M., Kotas M. P.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

545--557

EN

This paper introduces a method of data clustering that is based on linguistically specified rules, similar to those applied by a human visually fulfilling a task. The method endeavors to follow these remarkable capabilities of intelligent beings. Even for most complicated data patterns a human is capable of accomplishing the clustering process using relatively simple rules. His/her way of clustering is a sequential search for new structures in the data and new prototypes with the use of the following linguistic rule: search for prototypes in regions of extremely high data densities and immensely far from the previously found ones. Then, after this search has been completed, the respective data have to be assigned to any of the clusters whose nuclei (prototypes) have been found. A human again uses a simple linguistic rule: data from regions with similar densities, which are located exceedingly close to each other, should belong to the same cluster. The goal of this work is to prove experimentally that such simple linguistic rules can result in a clustering method that is competitive with the most effective methods known from the literature on the subject. A linguistic formulation of a validity index for determination of the number of clusters is also presented. Finally, an extensive experimental analysis of benchmark datasets is performed to demonstrate the validity of the clustering approach introduced. Its competitiveness with the state-of-the-art solutions is also shown.

2

Numerical methods for analysis of mechanical systems with uncertain parameters

Vasko M., Saga M., Vasko A.

Production Engineering Archives

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2016

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Vol. 11, No. 2

18--21

EN

The paper presents new and improved numerical methods designed for analysis of mechanical systems with uncertain parameters. Uncertain parameters in mechanical systems are described using possibility theory. The main representatives of this theory are fuzzy and interval numbers. Algorithms using interval and fuzzy numbers are incorporated into the analysis. The possibilities and efficiency of suggested methods and algorithms are tested by programs created in the environment of the software package MATLAB.

3

Teoria możliwości jako narzędzie wspomagania decyzji inwestycyjnych

Banasik A

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2012

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z. 61

7--14

PL

Artykuł prezentuje możliwość zastosowania teorii możliwości w procesie podejmowania decyzji inwestycyjnych. Podstawowym celem pracy jest wskazanie kierunków aplikacyjnych wspomnianej wyżej teorii i efektów, jakie przypuszczalnie, wnosi do procesu decyzyjnego w inwestowaniu.

EN

Article presents a way of application of possibility theory to investment decision support. The main aim is to present application areas for above mentioned theory and probable effects which may be seen in decision making process in investment.

4

Rough Sets, Coverings and Incomplete Information

Couso I., Dubois D.

Fundamenta Informaticae

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2011

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Vol. 108, nr 3/4

223-247

EN

Rough sets are often induced by descriptions of objects based on the precise observations of an insufficient number of attributes. In this paper, we study generalizations of rough sets to incomplete information systems, involving imprecise observations of attributes. The precise role of covering-based approximations of sets that extend the standard rough sets in the presence of incomplete information about attribute values is described. In this setting, a covering encodes a set of possible partitions of the set of objects. A natural semantics of two possible generalisations of rough sets to the case of a covering (or a non transitive tolerance relation) is laid bare. It is shown that uncertainty due to granularity of the description of sets by attributes and uncertainty due to incomplete information are superposed, whereby upper and lower approximations themselves (in Pawlak’s sense) become ill-known, each being bracketed by two nested sets. The notion of measure of accuracy is extended to the incomplete information setting, and the generalization of this construct to fuzzy attribute mappings is outlined.

5

Convex sublattice based reliability theory

Pang Y., Huang H. Z., He L., Wang Z., Xiao N. C.

Eksploatacja i Niezawodność

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2011

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nr 3

56-61

EN

Classical probability theory has been widely used in reliability analysis; however, it is hard to handle when the system is lack of` adequate and sufficient data. Nowadays, alternative approaches such as possibility theory and fuzzy set theory have also been proposed to analyze vagueness and epistemic uncertainty regarding reliability aspects of complex and large systems. The model presented in this paper is based upon possibility theory and multistate assumption. Convex sublattice is addressed on congruence relation regarding the complete lattice of structure functions. The relations between the equivalence classes on the congruence relation and the set of all structure functions are established. Furthermore, important reliability bounds can be derived under the notion of convex sublattice. Finally, a numerical example is given to illustrate the results.

PL

Klasyczna teoria prawdopodobieństwa ma szerokie zastosowanie w analizie niezawodności, jednak trudno jest się nią posługiwać, kiedy brak jest wystarczających i odpowiednich danych na temat systemu. Obecnie, proponuje się alternatywne podejścia, takie jak teoria możliwości czy teoria zbiorów rozmytych, za pomocą których można analizować niepewność epistemiczną oraz nieostrość w odniesieniu do aspektów niezawodności złożonych i dużych systemów. Model przedstawiony w niniejszym artykule oparto na teorii możliwości oraz na założeniu wielostanowości. Podkratę wklęsłą opisano na relacji kongruencji, odnoszącej się do całej kraty funkcji struktury. Ustalono relacje pomiędzy klasami równoważności na relacji kongruencji a zbiorem wszystkich funkcji struktury. Ponadto posługując się pojęciem podkraty wypukłej można wyprowadzać istotne kresy niezawodności. Wyniki zilustrowano przykładem numerycznym.

6

Harmonogramowanie budowy z uwzględnieniem nieprecyzyjnie określonych ograniczeń planistycznych

Kulejewski J.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Wojsk Lądowych im. gen. T. Kościuszki

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2010

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Nr 3

350-365

PL

Przedmiotem referatu jest zagadnienie sporządzania harmonogramu budowy z uwzględnieniem nieprecyzyjnie określonych ograniczeń dostępności zasobów odnawialnych i nieprecyzyjnie określonego ograniczenia czasu na wykonanie robót. Do modelowania nieprecyzyjnie określonych ograniczeń wykorzystano trapezowe liczby rozmyte. Przedstawiono dwie metody oceny dotrzymania nieprecyzyjnie określonych ograniczeń. Metoda pierwsza polega na ocenie stopnia dotrzymania danego ograniczenia na podstawie założeń teorii możliwości. Metoda druga polega na wykorzystaniu koncepcji - przekrojów liczby rozmytej i miary probabilistycznej do oceny prawdopodobieństwa dotrzymania danego ograniczenia. Sformułowano wariantowe zadania optymalizacji harmonogramu budowy z uwzględnieniem obu metod oceny. Przedstawione przykłady liczbowe potwierdzają, że wykorzystanie miary probabilistycznej zapewnia neutralizację ocen dotrzymania rozmytych ograniczeń. Ponadto, polepsza wyniki optymalizacji harmonogramu budowy, pozwalając na zaplanowanie wykonania robót w krótszym czasie i przy niSszym poziomie zużycia zasobów odnawialnych, niż w przypadku wykorzystania teorii możliwości.

EN

The problem undertaken in this paper regards the scheduling of construction projects under imprecisely defined constraints of time and resources available for the execution of works. A single-point network model with finish-to-start relations between activities is adopted to represent the course of construction. Durations of works take account of the expected effects of possible interference (bad weather, equipment failures, etc.). The paper presents the principles of modeling imprecisely defined planning constraints using trapezoidal fuzzy numbers and the principles of assessing compliance with fuzzy restrictions using possibility theory. A probabilistic approach in conjunction with the concept of Α-cuts of fuzzy numbers is proposed for the neutralization of assessments to meet the fuzzy constraints. The paper also presents a numerical example showing the advantages of the use of probability measure to optimize the construction schedule in the terms of imprecisely defined planning constraints.

7

Outliers detection method in fuzzy regression

Gładysz B.

Operations Research and Decisions

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2010

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Vol. 20, No. 2

26-39

EN

In this article we propose a method for identifying outliers in fuzzy regression. Outliers in a sample may have an important influence on the form of the regression equation. For this reason there is great scientific interest in this issue. The method presented is analogous to the method of finding outliers based on the studentized distribution of residuals. In order to identify outliers, regression models are constructed with an additional explanatory variable for each observation. Next, the significance of a fuzzy regression coefficient is analysed considering this additional explanatory variable. Illustrative examples are presented.

8

A Framework for Iterated Belief Revision Using Possibilistic Counterparts to Jeffrey's Rule

Benferhat S., Dubois D., Prade H., Williams M-A.

Fundamenta Informaticae

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2010

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Vol. 99, nr 2

147-168

EN

Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey’s rule, which extends conditioning to probabilistic inputs, is appropriate for revising probabilistic epistemic states when new information comes in the form of a partition of events with new probabilities and has priority over prior beliefs. This paper analyses the expressive power of two possibilistic counterparts to Jeffrey's rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover several existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, and the revision of an epistemic state by another epistemic state. In addition, we also show that some recent forms of revision, called improvement operators, can also be recovered in our framework.

9

A Comparative Analysis of Possibilistic Variances and Covariances of Fuzzy Numbers

Zhang W-G., Wang Y-L.

Fundamenta Informaticae

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2007

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Vol. 79, nr 1-2

257-263

EN

In this paper, we introduce a new crisp possibilistic variance and a new crisp possibilistic covariance of fuzzy numbers, which are different from those introduced by Carlsson and Fullér. We show that the possibilistic variance and covariance preserve many properties of variance and covariance in probability theory. Furthermore, we investigate the relationship between several crisp possibilistic variances and covariances of fuzzy numbers.

10

Parking demand assignment by means of possibility theory based procedure

Sassanelli D.

Archives of Transport

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2002

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Vol. 14, iss.2

85--94

EN

The paper presents a new approach to parking demand assignment. It is shown how the Theory of Possibility can be a valid mathematical approach to deal with uncertainty in transportation modelling. In particular, it is appropriate when available data are inaccurate, uncertain and/or approximate, or they are represented by linguistic proposition. In addition, on the contrary to traditional approaches to transportation systems modelling the Possibility Theory allows to preserve the uncertainty related to both available data and the user's costs perception. In this work the theoretical framework of the user's choice modelling is presented and then the application to parking demand assignment is proposed. On the basis of the principie of invariance of uncertainty it is also shown the procedure to derive the user's choice probability from choice possibility.

PL

Artykuł przedstawia nowe podejście do zagadnienia wyznaczania zapotrzebowania miejsc podstawowych. Pokazano ważną rolę matematycznych metod teorii możliwości w modelowaniu niepewności w transporcie, w szczególności ich przydatność, gdy dostępne dane są niedokładne, niepewne i/lub są one reprezentowane przez lingwistyczne twierdzenia. W przeciwieństwie do tradycyjnych metod modelowania systemów transportowych teoria możliwości pozwala uwzględnić niepewność odnoszącą się zarówno do dostępnych danych, jak i do postrzegania kosztów użytkownika. W artykule przedstawiono opis teoretyczny modelowania wyboru użytkownika i zastosowanie do wyznaczania zapotrzebowania miejsc postojowych. Na podstawie zasady niezmienności niepewności przedstawiono także procedurę wyznaczania prawdopodobieństwa wyboru użytkownika.

11

Using possibilistic logic for modeling qualitative decision: ATMS-based algorithms

Dubois D., Le Berre D., Prade H., Sabbadin R.

Fundamenta Informaticae

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1999

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Vol. 37, Nr 1,2

1-30

EN

This paper describes a logical machinery for computing decision, where the available knowledge on the state of the world is described by a possibilistic prepositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels), and where the preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities. Two attitudes are allowed for the decision maker: a pessimistic risk-averse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to the classical theory of expected utility, recently developed by three of the authors. A link is established between this logical view of qualitative decision making and an ATMS-based computation procedure. Efficient algorithms for computing pessimistic and optimistic optimal decisions are finally given in this logical setting (using some previous work of the fourth author).