Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.

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ERP selection using picture fuzzy CODAS method

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202564 ◽

2021 ◽

pp. 1-11

Author(s):

Hacer Yumurtacı Aydoğmuş ◽

Eren Kamber ◽

Cengiz Kahraman

Keyword(s):

Decision Analysis ◽

Fuzzy Sets ◽

Fuzzy Numbers ◽

Ideal Solution ◽

Application Area ◽

Erp System ◽

Mcdm Method ◽

Negative Ideal Solution ◽

Picture Fuzzy Sets ◽

System Selection

The purpose of this study is to develop an extension of CODAS method using picture fuzzy sets. In this respect, a new methodology is introduced to figure out how picture fuzzy numbers can be applied to CODAS method. COmbinative Distance-based Assessment (CODAS) is a new MCDM method proposed by Ghorabaee et al. Picture fuzzy sets (PFSs) are a new extension of ordinary fuzzy sets for representing human’s judgments having possibility more than two answers such as yes, no, refusal and neutral. Compared with other studies, the proposed method integrates multi-criteria decision analysis with picture fuzzy uncertainty based on Euclidean and Taxicab distances and negative ideal solution. ERP system selection problem is handled as the application area of the developed method, picture fuzzy CODAS. Results indicate that the new proposed method finds meaningful rankings through picture fuzzy sets. Comparative analyzes show that the presented method gives successful and robust results for the solutions of MCDM problems under fuzziness.

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Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras

Mathematics ◽

10.3390/math7111036 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1036

Author(s):

Young Bae Jun ◽

Seok-Zun Song

Keyword(s):

Information Processing ◽

Fuzzy Sets ◽

Fuzzy Set ◽

Negative Information ◽

Positive Information ◽

Fuzzy Ideal ◽

Recent Trends ◽

Modern Information ◽

Bipolar Fuzzy Sets

Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negative information. Positive information, for example, already observed or experienced, indicates what is guaranteed to be possible, and negative information indicates that it is impossible, prohibited, or certainly false. The purpose of this paper is to apply the bipolar fuzzy set to BCK/BCI-algebras. The notion of (translated) k-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of k-fold bipolar fuzzy subalgebra/ideal are considered, and relations between k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are displayed. Extension of k-fold bipolar fuzzy subalgebra is discussed.

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Fuzzy Sets and Fuzzy Logic-Based Methods in Multicriteria Decision Analysis

International Series in Operations Research & Management Science - Trends in Multiple Criteria Decision Analysis ◽

10.1007/978-1-4419-5904-1_6 ◽

2010 ◽

pp. 157-175

Author(s):

Radko Mesiar ◽

Lucia Vavríková

Keyword(s):

Fuzzy Logic ◽

Decision Analysis ◽

Fuzzy Sets ◽

Multicriteria Decision Analysis ◽

Multicriteria Decision

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AN INCLUSION COMPARISON APPROACH FOR MULTIPLE CRITERIA DECISION ANALYSIS BASED ON INTERVAL-VALUED INTUITIONISTIC FUZZY SETS

Technological and Economic Development of Economy ◽

10.3846/20294913.2014.989930 ◽

2015 ◽

Vol 22 (3) ◽

pp. 357-392 ◽

Cited By ~ 3

Author(s):

Ting-Yu CHEN

Keyword(s):

Decision Analysis ◽

Fuzzy Sets ◽

Programming Model ◽

Intuitionistic Fuzzy Sets ◽

Multiple Criteria ◽

Multiple Criteria Decision Analysis ◽

Intuitionistic Fuzzy ◽

Nonlinear Programming Model ◽

Ranking Order ◽

Interval Valued

The theory of interval-valued intuitionistic fuzzy sets provides an intuitive and feasible way of addressing uncertain and ambiguous properties. Many useful models and methods have been developed for multiple criteria decision analysis within the interval-valued intuitionistic fuzzy environment. In contrast to the elaborate existing methods, this paper establishes a simple and effective method for managing the sophisticated data expressed by interval-valued intuitionistic fuzzy sets. An inclusion comparison possibility defined on interval-valued intuitionistic fuzzy sets is proposed, and some important properties are investigated. Then, an inclusion-based index that considers positive and negative ideals is offered. Considering the maximal comprehensive inclusion-based indices, this paper constructs a linear programming model (for consistent information) and an integrated, nonlinear programming model (for inconsistent information) to estimate the criterion weights and the optimal ranking order of the alternatives under an incomplete preference structure. The feasibility of the proposed method is illustrated by a practical example of selecting a suitable bridge construction method, and a comparative analysis with other relevant methods is conducted to validate the effectiveness and applicability of the proposed methodology.

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