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EN
This paper presents a proposition of general reference model based on fuzzy set theory, model that allows defining and resolving structuring project teams decision problems. Proposed model combine precise and imprecise values of decision variables. The model allows formalising in mathematical way linguistic, rough assessment of human behaviour, competency, and psychological profile according to vacant posts, project and team requirements.
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Content available remote Bifuzzy sets and other generalizations of a fuzzy set
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EN
The article presents the new concept of a fuzzy set, namely bifuzzy set. In original papers [2]-[15] it is used the name „intuitionistic fuzzy set" but it is not really adequate. We describe the idea of such a set and basic definitions and theorems of bifuzzy set theory. At last we present some other concepts describing fuzzy objects and give a rich literature to them.
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Content available remote Fuzzy versus probabilistic benefit/cost ratio analysis for public work projects
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EN
The benefit/cost (B/C) ratio method is utilized in many government and public work projects to determine if the expected benefits provide an acceptable return on the estimated investment and costs. Many authors have studied probabilis- tic cash flows in recent years. They introduced some analytical methods which determine the probability distribution function of the net present value and in- ternal rate of return of a series of random discrete cash flows. They considered serially correlated cash flows and the uncertainty of future capital investment and reinvestment rates and they presented some formulae for the B/C ratio for probabilistic cash flows. In the paper, the expected value and the variance of a probabilistic cash flow are obtained by means of moments. Then a probabilistic B/C ratio is given. Fuzzy set theory has the capability of representing vague knowledge and allows mathematical operators and programming to be applied to the fuzzy domain. The theory is primarily concerned with quantifying the vagueness in human thoughts and perceptions. The fuzzy B/C ratios are devel- oped for a single investment project and for multiple projects having equal or different lives.
EN
In today´s competitive global markets, selection of a potential supplier plays an important role to cut production costs as well as material costs of the company. This leads to successful survival and sustainability in a competitive marketplace. Therefore, evaluation and selection of an appropriate supplier has become an important part of supply chain management. The nature of the supplier selection process is a complex multi-attribute group decision making (MAGDM) problem which deals with both quantitative and qualitative factors may be conflicting in nature as well as contain incomplete and uncertain information. In order to solve such a kind of MAGDM problems, the development of an effective supplier selection model is evidently desirable. In this paper, an application of the VIKOR method combined with fuzzy logic has been used to solve supplier selection problems with conflicting and non-commensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution. The decision maker wants a solution, which must be closest to the ideal, and the alternatives are evaluated according to all established criteria. Linguistic values are used to assess the ratings and weights for the conflicting factors. These linguistic ratings can be expressed in triangular fuzzy numbers. Then, a hierarchy MAGDM model based on fuzzy sets theory and the VIKOR method has been proposed to deal with the supplier selection problems in the supply chain system. A case study has been illustrated as an application of the proposed model.
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Content available Special functions in fuzzy analysis
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EN
In the treatment of Fuzzy Logic an useful tool appears: the membership function, with the information about the degree of completion of a condition which defines the respective Fuzzy Set or Fuzzy Relation. With their introduction, it is possible to prove some results on the foundations of Fuzzy Logic and open new ways in Fuzzy Analysis.
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Content available remote A new definition of the fuzzy set
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EN
The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
EN
The conventional Boolean logic models of land suitability assessment disregard the continuity concepts of the soil and landscape which might cause inaccurate evaluation and classification. To overcome this uncertainty and consequent constraints, the fuzzy set theories were introduced. Therefore, the current study was undertaken to estimate the optimum soil depth that is used in land suitability evaluation for irrigated rice through the fuzzy sets theory and analytic hierarchy process (fuzzy AHP) in Guilan Province, Iran. The square root and quantitative land suitability evaluation methods were employed to calculate traditional land suitability indices (for depths, 0-25, 0-50, 0-75, and 0-100 cm). Also, fuzzy and fuzzy AHP methods were used to explore new land indices. The Sarma similarity indices were used to compare the results of traditional and fuzzy methods for different soil depths. The results showed that the compatibility percentage between the representative pedons (0-100 cm) and the findings of this research (0-50 and 0-75 cm) were remarkable. Furthermore, the highest compatibility percentage of land suitability class was related to the comparison of these two former depths and 0 to 100 cm depths in each of the two used fuzzy methods. Besides, except for 0-25 cm depths, actual yield revealed a significant and positive correlation with the rest three soil pedon depths. These findings show that considering 0 to 50 cm soil depth might be a relevant alternative as the optimal depth to evaluate land suitability for rice in paddy fields in the Guilan rice-growing area. 
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Content available remote A Granular Computing Method for OWL Ontologies
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EN
We propose a method to extract and integrate fuzzy information granules from a populated OWL ontology. The purpose of this approach is to represent imprecise knowledge within an OWL ontology, as motivated by the fact that the Semantic Web is full of imprecise and uncertain information coming from perceptual data, incomplete data, data with errors, etc. In particular, we focus on Fuzzy Set Theory as a means for representing and processing information granules corresponding to imprecise concepts usually expressed by linguistic terms. The method applies to numerical data properties. The values of a property are first clustered to form a collection of fuzzy sets. Then, for each fuzzy set, the relative σ-count is computed and compared with a number of predefined fuzzy quantifiers, which are therefore used to define new assertions that are added to the original ontology. In this way, the extended ontology provides both a punctual view and a granular view of individuals w.r.t. the selected property. We use a real-world ontology concerning hotels and populated with data of the Italian city of Pisa, to illustrate the method and to test its implementation. We show that it is possible to extract granular properties that can be described in natural language and smoothly integrated in the original ontology by means of annotated assertions.
PL
W pracy została przedstawiona metoda analizy drzewa uszkodzeń (FTA) poszerzona o elementy teorii zbiorów rozmytych. Zdarzenia nieokreślone drzewa uszkodzeń nie są rozwijane w analizie FTA z powodu braku wystarczającej ilości informacji, funduszy lub czasu na oszacowanie podstawowych ich parametrów. Teoria zbiorów rozmytych jest jednym z narzędzi umożliwiających opis tego typu zdarzeń. W artykule zaprezentowano hipotetyczny przykład drzewa uszkodzeń ze zdarzeniami nieokreślonymi i próbę ich ilościowego opisu.
EN
In this paper a FT A (fault tree analysis) method with elements of fuzzy set has been presented. Undeveloped events in FT A method are not taken into consideration in qualitative analysis because of too less information about element, not enough money or time to research, but they are important in context of operation of system. Fuzzy set theory is one of tool which can be used for describing undeveloped events. In this article hypothetical example of fault tree with undeveloped events and fault tree of 20 Pm gear have been shown.
EN
This paper adopts a probabilistic fuzzy analytic network process (PROFUZANP) approach in developing a sustainable manufacturing strategy. In this hybrid method, analytic network process handles the complexity of the problem structure under consideration, fuzzy set theory is used to describe vagueness in individual decision-making and probability theory is used to handle randomness in group decision-making. This holistic methodological approach addresses complexity and uncertainty both in individual and group decision-making which is useful in modeling group decisions such as developing a sustainable manufacturing strategy. In this work, an inclusive approach of integrating traditional manufacturing strategy concepts and sustainable manufacturing principles is proposed as a unifying decision model. The proposed decision structure adopts the hierarchical structure of manufacturing strategy and explores the presence of strategic responses and stakeholders’ interests as significant components of sustainability. Using PROFUZANP, the decision model identifies the content policies of sustainable manufacturing strategy. This content strategy is expected to address both competitiveness and sustainability of manufacturing firms. Results are reported in this paper along with insights and future work. The contribution of this work is the integration of manufacturing strategy and sustainability into a coherent decision framework that requires the use of PROFUZANP in dealing with complex and uncertain group decision-making problem.
EN
The paper presents construction of the fuzzy logic system to analog circuits parametric fault diagnosis. The classical dictionary construction is replaced by fuzzy rule system. The first part refers to analog fault diagnosis, its techniques, approaches and goals. It clarifies common strategy and define differences between detecting, locating and identifying a fault in analog electronic circuit. The second part is focused on a creation of fuzzy rule expert system with use of sensitivity functions and known circuit topology. To detect, locate and identify a faulty element in a circuit the sensitivity matrix is used. The advantage of the method is its utilization in all, AC, DC and time domain. The fuzzy system, like the classical fault dictionary, can detect and locate single catastrophic faults and, on the contrary to the classical one, it also detects and locates parametric faults. Moreover, it allows identification of these faults, such that sign of the faulty parameter deviation is designated. The method has deterministic character as well as it can be applied on the verification and production stage.
EN
The paper proposes a methodology for fuzzy multi-criteria analysis of decisions in a raster-based geographical information system (GIS) to determine the optimal locations for territorial objects. Recommendations about the stages of choosing alternatives for spatial and non-spatial constraints are given. It is shown that the fuzzyfication of criteria, that is, the conversion of their attribute values into a fuzzy set, based on expert evaluation of a fuzzy membership function, allows screening alternatives by determining thresholds of alpha-cut of fuzzy sets for each criterion, followed by combining criteria attributes using aggregation operators: minimum, maximum, weighted sum, OWA operator Jager. Adding to the procedure of multicriteria analysis of the additional stage of filtration of alternatives gives the opportunity to reduce the number of alternatives, and in the future and the processing time of the criteria layers by aggregator operators. The proposed algorithm for screening alternatives can be performed in a GIS environment using Fuzzy Membership, Overlay and raster calculators tools.
PL
Wykorzystano teorię zbiorów rozmytych do prognozowania zapotrzebowania na energię elektryczną na terenach wiejskich opracowując dwa rozmyte modele liniowe. Posłużono się przy tym danymi dotyczącymi sprzedaży energii elektrycznej odbiorcom wiejskim w latach 1985-2000 przez wybraną spółkę dystrybucyjną.
EN
The fuzzy set theory was applied for the purposes of forecasting power demand in rural areas, through development of two fuzzy linear models. When doing this, the researchers used data regarding sale of electric power to rural consumers between 1985 and 2000, by selected distributing company.
14
Content available remote Intuitionistic Fuzzy Transportation Problem by Zero Point Method
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EN
The transportation problems (TPs) support the optimal management of the transport deliveries. In classical TPs the decision maker has information about the crisp values of the transportation costs, availability and demand of the products. Sometimes in the parameters of TPs in real life there is ambiguity and vagueness caused by uncontrollable market factors. Uncertain values can be represented by fuzzy sets (FSs) of Zadeh. The FSs have the degrees of membership and nonmembership. The concept of intuitionistic fuzzy sets (IFSs) originated in 1983 as an extension of FSs. Atanasov’s IFSs also have a degree of hesitansy to representing the obscure environment. In this paper we formulate the TP, in which the transportation costs, supply and demand values are intuitionistic fuzzy pairs (IFPs), depending on the diesel prices, road condition, weather and other factors. Additional constraints are included in the problem: limits for the transportation costs. Its main objective is to determine the quantities of delivery from producers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The aim of the paper is to extend the fuzzy zero point method (FZPM [35]) to the intuitionistic FZPM (IFZPM) to find an optimal solution of the intuitionistic fuzzy TP (IFTP) using the IFSs and index matrix (IM) concepts, proposed by Atanassov. The solution algorithm is demonstrated by a numerical example. Its optimal solution is compared with that obtained by the intuitionistic fuzzy zero suffix method (IFZSM).
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Content available remote An evaluation of project completion with application of fuzzy set theory
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EN
The project management contains such elements as management of time, cost, communications, procurement, quality, risk or scope of project. Each of these fields can be considered as a set of constraints, and then there is a possibility to verify their fulfillment in sense of an enterprise's constraints and its environment. These constraints determine a completion of project activities and its success or failure, finally. The paper aims to present a problem of project management in terms of fuzzy constraints satisfaction problem, and then the using of constraint programming techniques to the evaluation of project completion. A fuzzy constraints satisfaction problem enables a description of data in distinct, as well as imprecise form, in a unified framework. It seems especially important in case of unique activities of project, when their estimation is based on linguistic information from experts.
PL
W ramach zarządzania przedsięwzięciem wymienia się najczęściej takie elementy jak zarządzanie czasem, kosztami, komunikacją, dostawami, jakością, ryzykiem czy zakresem projektu. Każdy z tych obszarów zarządzania projektem można rozpatrywać w postaci zbioru ograniczeń, a następnie sprawdzać ich spełnienie w aspekcie ograniczeń wynikających z charakteru przedsiębiorstwa wdrażającego przedsięwzięcie oraz jego otoczenia. Ograniczenia te determinują realizację poszczególnych czynności projektu i ostatecznie to czy zakończy się on sukcesem, czy niepowodzeniem. Celem pracy jest przedstawienie problemu zarządzania przedsięwzięciem w postaci rozmytego problemu spełniania ograniczeń, a następnie wykorzystanie technik programowania z ograniczeniami do oceny realizacji przedsięwzięcia. Rozmyty problem spełniania ograniczeń umożliwia wyrażenie danych tak w postaci precyzyjnej, jak i nieprecyzyjnej w ramach jednego podejścia. Wydaje się to szczególnie istotne w przypadku planowania realizacji czynności unikalnych projektu, gdy ich szacowanie jest dokonywane przede wszystkim w oparciu o opinie ekspertów.
EN
Marine navigation consists in continuous observation of the situation at sea, determination the anti-collision manoeuvre. So it necessary to determine ship safe trajectory as a sequence of ship course changing manoeuvres. Each manoeuvre is undertaken on the basis of information obtained from the anti-collision system ARPA. This paper describes a method of safe ship control in the collision situation in a fuzzy environment based on a branch and bound method and a genetic algorithm. The optimal safe ship trajectory in a collision situation is presented as multistage decision-making process.
17
Content available remote Ant Colony Optimization Algorithm for Fuzzy Transport Modelling
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EN
Public transport plays an important role in our live. The good service is very important. Up to 1000 km, trains and buses play the main role in the public transport. The number of the people and which kind of transport they prefer is important information for transport operators. In this paper is proposed algorithm for transport modelling and passenger flow, based on Ant Colony Optimization method. The problem is described as multi-objective optimization problem. There are two optimization purposes: minimal transportation time and minimal price. Some fuzzy element is included. When the price is in a predefined interval it is considered the same. Similar for the starting traveling time. The aim is to show how many passengers will prefer train and how many will prefer buses according their preferences, the price or the time.
PL
Badania przeprowadzone przez autorów dotyczące zagadnienia, jaki jest optymalny zestaw elementów modelu rozmytego doprowadziły do wniosku, że jest to taki zestaw, który powoduje, że model rozmyty wytwarza pomiędzy punktami wiedzy eksperckiej oszczędną powierzchnie wielomianową określoną wzorami (9), (11), etc. Charakterystyka ta posiada najmniejszą powierzchnię względem wszystkich innych możliwych modeli interpolacyjnych, a sam model jest bardzo prosty i spełnia postulat „brzytwy Occam’a”. Potwierdziły to badania eksperymentalne przeprowadzone przez autorów. Określono elementy (funkcje przynależności i operatory) modelu rozmytego, które umożliwiają uzyskanie minimalnej powierzchni interpolacyjnej a przez to optymalnego, bezpiecznego modelu rozmytego. Ze względu na konieczne ograniczenia objętości artykułu problem został przedstawiony bardzo skrótowo.
EN
In expert fuzzy models various membership functions, various operators for AND and OR operations, for implication in single rules and aggregation of activated conclusions of single rules in one resultant conclusion, and various defuzzification methods can be chosen by a modeler. Is there, in the universal case, possible to answer the question, which set of the above elements of the fuzzy model is optimal? The authors try to give the answer to this difficult, but very interesting question in this paper.
PL
W pracy przedstawiono koncepcję metody zintegrowanego zarządzania wartością i ryzykiem przedsięwzięć inwestycyjnych w ujęciu ilościowym przy zastosowaniu teorii zbiorów rozmytych. Ocena wartości przedsięwzięcia budowlanego jest rozumiana jako korzyści, które odnosi inwestor przedsięwzięcia w okresie całego cyklu życia projektu inwestycyjnego oraz na ocenie wielkości ryzyka, jakimi obarczone są te korzyści, gdzie ryzyko jest rozumiane jako odchylenie tych korzyści od wielkości oczekiwanych. Główną ideą omawianej metody zarządzania wartością i ryzykiem w podejmowaniu przedsięwzięcia inwestycyjnego jest określenie takich rozwiązań technologiczno-organizacyjnych i projektowych, które pozwalają uzyskać inwestorowi maksymalną wartość (korzyść) przedsięwzięcia przy minimalnej wielkości ryzyka. Metody zarządzania wartością i ryzykiem (Value end Risk Managament - V-RM) są nadrzędne w stosunku do inżynierii wartości (Value Engineering - VE) koncentrującej się na optymalizacji rozwiązań konstrukcyjnych bez uwzględnienia ryzyka. W pracy, po analizie dotychczasowych osiągnięć w zakresie zarządzania wartością i ryzykiem przy podejmowaniu przedsięwzięć inwestycyjnych, zaproponowano autorskie podejście w ujęciu ilościowym do metody zarządzanie wartością i ryzykiem. Podejście ilościowe w zaproponowanej metodzie opiera się na modelu oceny przedsięwzięcia inwestycyjnego za pomocą metody bieżącej netto (Net Present Yalue - NPV) oraz współczynnika zmienności wartości netto C(NPV], przy założeniu równych wartości nakładów na porównywane przedsięwzięcia lub podobnych wartościach współczynnika wartości bieżącej netto (Net Present Value Rano - NPVR}. Do omawianej metody zaproponowano również procedurę wyboru przedsięwzięcia inwestycyjnego w zależności od preferencji do podejmowania ryzyka przez inwestora. W procedurze tej zastosowano teorię zbiorów rozmytych, która według autora jest w niewielkim stopniu wykorzystywana do analiz ryzyka w budownictwie w naszym kraju. Przedstawiono również procedury odnoszące się do zaproponowanej metody zarządzania wartością i ryzykiem, a mianowicie do oceny efektywności inwestycyjnych przedsięwzięć budowlanych w postaci liczby rozmytej, oceny strumieni pieniężnych i wynikowych wartości NPV. do określenia rozmycia tych parametrów, oraz procedury umożliwiającej podejmowanie decyzji w zakresie odpowiedniej struktury inwestycji, bazującej na zastosowaniu liczb rozmytych w rozmytej analizie regresji. Autor ma świadomość możliwości zastosowań innych metod ilościowych do omawianej metody zarządzania wartością ryzykiem, ale zastosowanie teorii zbiorów rozmytych do analizy efektywności wydaje się najbardziej naturalne, gdyż w budownictwie eksperci często używają określeń jakościowych. Zaproponowane w pracy autorskie podejście do wymienionych procedur oraz zastosowanie teorii zbiorów rozmytych oraz zmiennych lingwistycznych umożliwia przejście w oszacowaniu zjawisk ze sposobów jakościowych na ilościowe, co pozwala na bardziej precyzyjny wybór wariantu planowanego budowlanego przedsięwzięcia inwestycyjnego. Badania i analizy przedstawione w pracy oraz zaproponowana metoda V-RM w ujęciu ilościowym, może przyczynić się do zwrócenia uwagi na lepsze wykorzystanie środków finansowych przeznaczonych na realizację przedsięwzięć i uzyskanie z nich większych korzyści, a także zapewnić odpowiedni standard realizacji obiektów budowlanych. Jest to szczególnie istotne w zmieniających się uwarunkowaniach techniczno-finansowyeh, które będą miały wpływ na środowisko funkcjonowania przemysłu budowlanego, gdzie w przyszłości będzie się liczyć zrównoważone wykorzystanie zasobów, jakość produktu budowlanego oraz efektywność wykorzystania środków finansowych.
EN
The thesis presents the concepts of the value and risk management method in investment projects according to the quantitative approach using the fuzzy set theory. The paper is based on assessment of value of a construction project, which is understood as benefits gained hy the project investor throughout the entire investment project life cycle and on assessment of risk associated with these benefits, with risk understood as a deviation ol these benefits from the expected values. The main concept of the discussed value and risk management method in an investment project is to specify the technological, organizational and project solutions, which would allow the investor to obtain the maximum value (benefit) from the project while maintaining the minimum risk level. The Value and Risk Management (V-RM) methods are superior to Value Engineering (VII), focused on optimization of construction solutions without taking risk into account. The author, upon analysis of achievements in the field of risk and value management in investment projects, proposes a unique quantitative approach to the value and risk manage ment method. The quantitative approach in the proposed method is based on the investment project asscx sment method using the net present value (NPV) and the net present value changeability ratio, assuming equal values of expenditure for the compared project or similar values ol the net present value ratio (NPVR). For the examined method, a procedure of selection of the investment project was proposed depending on the preferences of the investor with regard to risk The procedure employs the fuzzy set theory, which, according to the author, is used rarely in our country in construction issues. Subsequent procedures referring to the proposed value and risk management method \\cic also presented, pertaining to assessment of effectiveness of construction investment projects in the form of a fuzzy number, assessment of cash flow stream expenditures and the resulting NPV values for specification of fuzzincss of these parameters, as well as a procedure allowing to make decisions with regard to the appropriate investment structure, basing on application of fuzzy numbers in fuzzy regression analysis. The author is aware of the possibility of application of other quantitative methods to (he discussed risk and value management method, but application of the fuzzy set theorv to analy sis of effectiveness seem to be the most natural choice, since construction experts often refer to qualitative terms. The approach to the above-mentioned procedures and application of the full set theory and linguistic variables in the thesis allows us to shift from qualitative to quantitative assessment of phenomena, which results in a more precise selection of a variant for the planned investment project. Application of the fuzzy set theory to the proposed value and risk management method using a quantitative approach is due to the nature of these sets, used for a formal and qualita tive presentation of terms, which are not precise and unambiguous. Research and analysis performed within the framework of the study and me proposed V-RM method from the quantitative perspective may be conducive to better use of financial means for implementation of projects and obtaining greater benefits, as well as to assure the appropriate standard of performance of construction facilities. This is particularly important under the changing technical and financial conditions, which will influence the construction industry, as in the future it will attach great importance to sustainable use of resources, quality of construction products and effective use of financial means.
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