Fuzzy Bags Research Articles

Location of medical warehouse applying BBTOPSIS based multi-criteria decision making with basic uncertain information

The aim of this paper is to introduce a combination of Basic Uncertain Information (BUI) and a Bag Based Technique for Order Preference by Similarity to Ideal Solution (BBTOPSIS), which is further applied to multi-attribute decision making (MADM) with BUI. To realize the decision process, a novel comparison law is developed to derive the superiority, inferiority and noninferiority multi-attribute canonical fuzzy bags. Mathematical properties of the developed comparison law is discussed. Besides, to extend traditional TOPSIS method in BUI, a novel distance measure between BUI is also introduced, which is composed by distance between transformed intervals and similarity between BUI. Superiority of the developed distance measure is illustrated. Finally, a decision algorithm is presented to solve MADM with BUI by using the developed BBTOPSIS under BUI. A numerical example on location of medical warehouse is presented to illustrate the feasibility and validity of the developed decision method.

Parameters of Fuzzy Bags

A revised definition for fuzzy bags is reviewed, developing the concept of bags given by Delgado et al. 2009 from which each bag has two parts, function and summary information. Then, the definitions of fuzzy bag expected value, bag entropy and bag similarity are introduced. By some examples, the new concepts are illustrated.

On Algebraic Structure of L-Fuzzy Bags

This study introduces a revised definition for fuzzy bags. It is based on the definition of bags given by Delgado et al. (Int J Intell Syst 2009;24:706–721) in which each bag has two parts: function and summary information. The new definition is given as a special case of L-fuzzy bags, where L is a complete lattice. By some examples, the new concept is illustrated. Furthermore, the algebraic structure of L-fuzzy bags is studied and the concept of α-cuts, L-fuzzy bag relations, and related theorems are given.

IF-Bags and Knowledge Representation in Soft Decision Analysis

The concept of IF-Bags was introduced by the author as a generalization of the notion of fuzzy bags. In case of IF-Bags, each element is associated with a crisp bag drawn from the Cartesian product I×I of the unit interval I = [0, 1]. This paper introduces a method for quantitatively measuring the similarity between two IF-Bags. As a consequence, the notions of a measure of coherence and a measure of hesitancy between two IF-Bags are also introduced. It is observed that the measure of coherence and the measure of hesitancy between the IF-Bags can be regarded as crucial factors in case of scenario evaluation as well as grading that relates to knowledge representation in soft decision analysis problems.

Fuzzy bags, Polyakov loop and gauge/string duality

Confinement in SU($N$) gauge theory is due to the linear potential between colored objects. At short distances, the linear contribution could be considered as the quadratic correction to the leading Coulomb term. Recent lattice data show that such quadratic corrections also appear in the deconfined phase, in both the thermal quantities and the Polyakov loop. These contributions are studied systematically employing the gauge/string duality. "Confinement" in ${\mathcal N}=4$ SU($N$) Super Yang-Mills (SYM) theory could be achieved kinematically when the theory is defined on a compact space manifold. In the large-$N$ limit, deconfinement of ${\mathcal N}=4$ SYM on $\mathbb{S}^3$ at strong coupling is dual to the Hawking-Page phase transition in the global Anti-de Sitter spacetime. Meantime, all the thermal quantities and the Polyakov loop achieve significant quadratic contributions. Similar results can also be obtained at weak coupling. However, when confinement is induced dynamically through the local dilaton field in the gravity-dilaton system, these contributions can not be generated consistently. This is in accordance with the fact that there is no dimension-2 gauge-invariant operator in the boundary gauge theory. Based on these results, we suspect that quadratic corrections, and also confinement, should be due to global or non-local effects in the bulk spacetime.

The notion of intuitionistic fuzzy IC-bags

Abstract. This paper presents an overview of the existing notions of Bags, Fuzzy Bags, IC-Bags, IF-Bags and Fuzzy IC-Bags. Based on these notions, the concept of Intuitionistic Fuzzy Bags with Interval Counts (Intuitionistic fuzzy IC-Bags) is proposed. Further, some characteristics of Intuitionistic fuzzy IC-Bags are studied, and some examples are furnished in this context.

RL-bags: A conceptual, level-based approach to fuzzy bags

In this paper we claim that, though algebraically well-defined, bags are not well suited for representing and reasoning with real-world information, and we propose suitable alternatives. We extend the same discussion to the fuzzy case, in which membership of elements to bags is gradual, extending the proposed alternatives. There are two main ideas behind our approach. The first is that in general the elements of a bag can be identified and are distinguishable in the real world and, when this is not the case, we are facing a problem of representation of partial knowledge, i.e., we have a lack of information. Under this consideration, we discuss and criticize the usual operations for bags. The second is to manage the fuzziness by levels using a recent level-based representation approach that extends that of fuzzy sets and keeps all the properties of the crisp case. The classical notion of bag can be seen in our approach as a bag summary. We propose a new model that generalizes the existing approach, defining new operations from this new perspective. We also propose how to deal with fuzziness and incompleteness following our approach, doing a review of the existing approaches and applications concerning bags.

Different generalizations of bags

We consider four different generalizations of bags (alias multisets). We first discuss Yager’s fuzzy bags having different sets of operations. It is shown that one is not a generalization of fuzzy sets but a mapping of them into fuzzy bags, since operations are inconsistent between the two, while the other includes fuzzy sets as particular cases. Third type is called real-valued bags which is simpler than the former two and is a kind of the reduction of fuzzy bags. Finally, the fourth generalization called G-bags includes all three except the first type. It is a minimal extension of the second and the third generalizations. Bag relations are defined for the third type of real-valued bags, which can further be generalized for G-bags.

Crisp bags, one-dimensional fuzzy bags, multidimensional fuzzy bags: Comparing successful and unsuccessful user's Web behavior

In all studies of user's behavior on searching the Web, researchers found that their search strategy or traversal process showed a pattern of moving back and forth between searching and browsing. These activities of searching and browsing are inclusive activities to complete a goal-oriented task to find the answer for the query. The moving back and forth, including backtracking to a former Web page, constitutes the measurable or physical states or actions that a user takes while searching the Web. How do we account for the repeated searching and browsing and shifting between different Web pages to better understand the behavior of users? Is there a mathematical model that can help model actions of users to distinguish between two users while their repeated actions are accounted for since it is a part of their behavior or inherent essence to arrive at the goal of answering the questions regardless whether they are successful or unsuccessful? The idea of a set does not help account for repeated actions since in a set repeated objects are ignored. In some situations, we want a structure in which a collections of objects in the same sense as a set but a redundancy counts. The structure of a bag as a framework can help study the behavior of users and uncover some intrinsic properties about users. Also would bags help distinguish between two sets of users based on their syntactic properties without a priori knowledge of their semantic properties? This study constitutes a premier in applying bags to user's mining of the Web. The research will consider queries that depend on one variable or “univariable.” An example of “univariable” queries is “Find the number of Web pages of users whose searching is less than the average.” Crisp bags failed to answer such a query. Fuzzy operators were used successfully in comparing the “fuzzy bag” of the successful users to the “fuzzy bag” of unsuccessful users to answer such a query. A distance between two fuzzy bags was also established. The research also considered queries that depend on more than one variable or multivariable. An example of a “multivariable” query is “Find the number of Web pages of users whose number of searches is less than average and hyperlink navigation is less than the average.” One-dimensional fuzzy bags were extended to two-dimensional fuzzy bags and two-dimensional fuzzy bag operators were used to answer such a query. © 2009 Wiley Periodicals, Inc.

The set of fuzzy relative integers and fuzzy bags

A characterization of fuzzy bags with conjunctive fuzzy integers (f) provides a general framework in which sets, bags, fuzzy sets, and fuzzy bags are treated in a uniform way. In this context, the ...

International journal of intelligent systems: Special issue on “fuzzy bags, cardinality, and quantification”

International Journal of Intelligent SystemsVolume 24, Issue 6 p. 569-571 Introduction International journal of intelligent systems: Special issue on “fuzzy bags, cardinality, and quantification” Miguel Delgado, Miguel Delgado mdelgado@ugr.es Department of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainSearch for more papers by this authorDaniel Sánchez, Corresponding Author Daniel Sánchez daniel@decsai.ugr.es Department of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainDepartment of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainSearch for more papers by this authorMaría-Amparo Vila, María-Amparo Vila vila@decsai.urg.es Department of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainSearch for more papers by this author Miguel Delgado, Miguel Delgado mdelgado@ugr.es Department of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainSearch for more papers by this authorDaniel Sánchez, Corresponding Author Daniel Sánchez daniel@decsai.ugr.es Department of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainDepartment of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainSearch for more papers by this authorMaría-Amparo Vila, María-Amparo Vila vila@decsai.urg.es Department of Computer Science and Artificial Intelligence of the University of Granada, E.T.S.I.I.T., C/ Periodista Daniel Saucedo Aranda s/n, 18071 Granada, SpainSearch for more papers by this author First published: 13 April 2009 https://doi.org/10.1002/int.20356AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume24, Issue6Special Issue: Fuzzy Bags, Cardinality, and QuantificationJune 2009Pages 569-571 RelatedInformation

An extended characterization of fuzzy bags

The algebraic structures known as bags were introduced by R. Yager as set-like algebraic structures where elements are allowed to be repeated. Since the original papers by Yager, different definiti...

Some thermodynamic aspects of pure glue, fuzzy bags, and gauge/string duality

The thermodynamic properties of an $SU(3)$ gauge theory without quarks are calculated using a string formulation for $1.2{T}_{c}\ensuremath{\le}T\ensuremath{\le}3{T}_{c}$. The results are in good agreement with the lattice data. We also comment on $SU(N)$ gauge theories.

Fuzzy Bags and Wilson Lines

I start with an elementary observation about the pressure in the deconfined phase of a SU(3) gauge theory without quarks. This suggests a ``fuzzy'' bag model for the analogous pressure in QCD, with dynamical quarks. I then sketch how the deconfined phase might be described using an effective theory of Wilson lines. To leading order in weak coupling, the effective electric field appears in a form familiar from the lattice theory of Banks and Ukawa.

The set of fuzzy rational numbers and flexible querying

A fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership. This notion can be viewed as a generalization of the concepts of set, fuzzy set and bag. The set of fuzzy integers ( N f ) provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed. In the field of databases, the use of fuzzy bags is motivated by their ability to manage both quantities and preferences. However, N f becomes too restricted a framework when dealing with queries based on difference or division operations. So, a more general structure based on the set of fuzzy relative integers ( Z f ) in which exact differences can be performed, has been first developed. In this paper, we carry on with this approach and we extend Z f to the set of fuzzy rational numbers ( Q f ). This context leads to define a closed system of multiplicative operations and allows to perform exact divisions. Applied to flexible querying of databases, Q f and the notion of division on fuzzy numbers allow to generalize the relational division. They define a sound basis for queries involving ratios between quantities.

NOTION OF FUZZY IC-BAGS

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

On fuzzy bags and their application to flexible querying

An issue in extending database management functionalities is to increase the expressiveness of query languages. Flexible querying enables users to express preferences inside requirements and priorities inside compound queries. The answers are then qualified and sorted out. The fuzzy sets theory offers a general framework for dealing with flexible queries. Moreover the bag type plays an important role in databases. Systems taking into account both flexible queries and bags define fuzzy bags. A new approach of this concept, based on the notion of fuzzy cardinalities, is presented in this paper. Fuzzy cardinalities provide a general framework in which different collection types: set, fuzzy set, bag and fuzzy bag are treated in a uniform way and can then be composed. We show how they can be used to build up flexible queries and to manipulate both quantitative and qualitative information on the elements of collections.

An application of Yager's bag theory in multicriteria based decision making problems

We consider a problem of selecting most suitable action out of n alternatives on the basis of k factors or criteria where m judges supply information on all of these k factors/criteria. Our observation is that in many situations the criteria values are not crisp, but rather fuzzy bags. The method is based on the concept of a measure of similarity between two fuzzy bags, which is defined in this paper. An algorithm for the method is presented, and a hypothetical application-oriented example is demonstrated. ©1999 John Wiley & Sons, Inc.

Fuzzy shadows

In the present paper, we consider the concept of shadows introduced by Blizard and the theory of fuzzy bags developed by Yager. Then we define fuzzy shadows and develop some properties of them with examples. Some propositions on fuzzy shadows are also studied.

Canonical fuzzy bags and bag fuzzy measures as a basis for MADM with mixed non cardinal data

This contribution introduces what will be called ‘SINE analysis’, a new approach to multiple attribute decision making (MADM) with mixed noncardinal data. This approach is based upon the notion of canonical fuzzy bags and their scalar evaluations by bag fuzzy measures.