Klir-Yuan Fuzzy Implication in Fuzzy Relations

2019 ◽  
Author(s):  
Sanela Nesimovic ◽  
Dzenan Gusic
Keyword(s):  
Fuzzy Relations ◽  
Fuzzy Implication

scholarly journals Interval Information Content of Fuzzy Relation and the Application in the Fuzzy Implication Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yiying Shi
Keyword(s):  
Information Content ◽  
Similarity Measure ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fuzzy Implication ◽  
Solid Foundation ◽  
Rule Optimization ◽  
Interval Comparison

In rule optimization, some rule characteristics were extracted to describe the uncertainty correlations of fuzzy relations, but the concrete numbers cannot express correlations with uncertainty, such as “at least 0.1 and up to 0.5.” To solve this problem, a novel definition concerning interval information content of fuzzy relation has been proposed in this manuscript to realize the fuzziness measurement of the fuzzy relation. Also, its definition and expressions have also been constructed. Meanwhile based on the interval information content, the issues of fuzzy implication ranking and clustering were analyzed. Finally, utilizing the combination of possibility’s interval comparison equations and interval value’s similarity measure, the classifications of implication operators were proved to be realizable. The achievements in the presented work will provide a reasonable index to measure the fuzzy implication operators and lay a solid foundation for further research.

Pattern Recognition Based on Fuzzy Set and Genetic Algorithm

2014 ◽  
Vol 14 (03) ◽  
pp. 1450009
Author(s):  
Kumar S. Ray
Keyword(s):  
Genetic Algorithm ◽  
Soft Computing ◽  
Pattern Classification ◽  
Support Vector ◽  
Fuzzy Relations ◽  
Pima Indians ◽  
Fuzzy Implication ◽  
Pattern Space ◽  
New Interpretation ◽  
Pattern Classifier

In this paper, we consider a soft computing approach to pattern classification. Our basic tools for soft computing are fuzzy relational calculus (FRC) and genetic algorithm (GA). We introduce a new interpretation of multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. We also consider the notion of a fuzzy pattern vector to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space. The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one-dimensional fuzzy implication. For the estimation of Ri we use floating point representation of GA. Thus a set of fuzzy relations is formed from the new interpretation of MFI. This set of fuzzy relations is termed as the core of the pattern classifier. Once the classifier is constructed the non-fuzzy features of a test pattern can be classified. The performance of the proposed scheme is tested on synthetic data. Subsequently, we use the proposed scheme for the vowel classification problem of an Indian language. Finally, a benchmark of performance is established by considering multiplayer perception (MLP), support vector machine (SVM) and the present method. The Abalone, Hosse Colic and Pima Indians data sets, obtained from UCL database repository are used for the said benchmark study. This new tool for pattern classification is very effective for classification of patterns under vegue and imprecise environment. It can provide multiple classification under overlapped classes.

scholarly journals Fuzzy Functional and Multivalued Dependencies for Frank’s Class of Additive Generators

2021 ◽  
Vol 15 ◽  
pp. 8-22
Author(s):  
Sanela Nesimovic ◽  
Dzenan Gusic
Keyword(s):  
Fuzzy Relation ◽  
Inference Rules ◽  
Fuzzy Relations ◽  
Fuzzy Implication ◽  
Resolution Principle ◽  
Multivalued Dependency

In this paper we consider all possible dependencies that can be built upon similarity-based fuzzy relations, that is, fuzzy functional and fuzzy multivalued dependencies. Motivated by the fact that the classical obtaining of new dependencies via inference rules may be tedious and uncertain, we replace it by the automated one, where the key role is played by the resolution principle techniques and the fuzzy formulas in place of fuzzy dependencies. We prove that some fuzzy multivalued dependency is actively correct with respect to given fuzzy relation instance if and only if the corresponding fuzzy formula is in line with the attached interpretation. Additionally, we require the tuples of the instance to be conformant (up to some extent) on the leading set of attributes. The equivalence as well as the conclusion are generalized to sets of attributes. The research is conducted by representing the attributes and fuzzy dependencies in the form of fuzzy formulas, and the application of fuzzy implication operators derived from carefully selected Frank’s classes of additive generators

Identifying lake longer-term dynamics via fuzzy relations and non-linear Kalman filters

1999 ◽  
Author(s):  
Tatjana D. Kolemishevska-Gugulovska ◽  
Georgi M. Dimirovski ◽  
A. Talha Dinibutun ◽  
Norman E. Gough
Keyword(s):  
Kalman Filters ◽  
Fuzzy Relations ◽  
Non Linear

Pythagorean fuzzy full implication multiple I method and corresponding applications

2021 ◽  
pp. 1-15
Author(s):  
TaiBen Nan ◽  
Haidong Zhang ◽  
Yanping He
Keyword(s):  
Decision Making ◽  
Modus Ponens ◽  
Pythagorean Fuzzy Set ◽  
Implication Operator ◽  
Continuity Properties ◽  
Fuzzy Implication ◽  
Decision Making Problem ◽  
Fuzzy Implication Operator ◽  
Degree Of Similarity ◽  
Fuzzy Modus Ponens

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

scholarly journals Third Zadeh’s Intuitionistic Fuzzy Implication

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 619
Author(s):  
Krassimir Atanassov
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

George Klir and Bo Yuan named after Lotfi Zadeh the implication p→q=max(1−p,min(p,q)) (also Early Zadeh implication). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and studied their basic properties. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is proposed and some of its properties are studied.

scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

scholarly journals Study of Two Families of Generalized Yager’s Implications for Describing the Structure of Generalized (h,e)-Implications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1490
Author(s):  
Raquel Fernandez-Peralta ◽  
Sebastia Massanet ◽  
Arnau Mir
Keyword(s):  
Representation Theorem ◽  
Internal Factors ◽  
Fuzzy Implication ◽  
The Family

In this study, we analyze the family of generalized (h,e)-implications. We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized (h,e)-implication in terms of two families of fuzzy implication functions. These two families can be interpreted as particular cases of the (f,g) and (g,f)-implications, which are two families of fuzzy implication functions that generalize the well-known f and g-generated implications proposed by Yager through a generalization of the internal factors x and 1x, respectively. The behavior and additional properties of these two families are also studied in detail.

MEDUSA: A Fuzzy Expert System for Medical Diagnosis of Acute Abdominal Pain

1994 ◽  
Vol 33 (05) ◽  
pp. 522-529 ◽  
Author(s):  
M. Fathi-Torbaghan ◽  
D. Meyer
Keyword(s):  
Fuzzy Logic ◽  
Abdominal Pain ◽  
Expert System ◽  
Acute Abdominal Pain ◽  
Medical Knowledge ◽  
Clinical Problem ◽  
Fuzzy Relations ◽  
Diagnostic Decision ◽  
Special Cases ◽  
Hybrid Concept

Abstract:Even today, the diagnosis of acute abdominal pain represents a serious clinical problem. The medical knowledge in this field is characterized by uncertainty, imprecision and vagueness. This situation lends itself especially to be solved by the application of fuzzy logic. A fuzzy logic-based expert system for diagnostic decision support is presented (MEDUSA). The representation and application of uncertain and imprecise knowledge is realized by fuzzy sets and fuzzy relations. The hybrid concept of the system enables the integration of rulebased, heuristic and casebased reasoning on the basis of imprecise information. The central idea of the integration is to use casebased reasoning for the management of special cases, and rulebased reasoning for the representation of normal cases. The heuristic principle is ideally suited for making uncertain, hypothetical inferences on the basis of fuzzy data and fuzzy relations.

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