Eigen Fuzzy Sets and their Application to Evaluate the Effectiveness of Actions in Decision Problems

Ferdinando Di Martino; Salvatore Sessa

doi:10.3390/math8111999

Eigen Fuzzy Sets and their Application to Evaluate the Effectiveness of Actions in Decision Problems

Mathematics ◽

10.3390/math8111999 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1999

Author(s):

Ferdinando Di Martino ◽

Salvatore Sessa

Keyword(s):

Fuzzy Sets ◽

Fuzzy Set ◽

Fuzzy Relation ◽

New Method ◽

Decision Problems ◽

Fuzzy Relations ◽

Italian City ◽

Historical Center

We propose a new method based on the greatest (resp., smallest) eigen fuzzy set (GEFS, resp., SEFS) of a fuzzy relation R with respect to the max–min (resp., min–max) composition in order to implement the actions of a decisor. Using information derived from judgments of the evaluators on how much a characteristic is improved with respect to others, we construct the fuzzy relations, RMAX (resp., RMIN), where any entry RMAXijj (resp., RMINij) expresses how much the efficacy produced on the ith characteristic is equal to or greater (resp., lesser) than that one produced by the jth characteristic. The GEFS of RMAX (resp., SEFS of RMIN) are calculated in order to improve the performances of each characteristic. In the wake of previous applications based on GEFS and SEFS, we propose a method to evaluate the tourism enhancement policies in the historical center of an important Italian city. This method is new and different from those known in the literature so far. It is applied to evaluate benefits brought about by locals in order to enhance tourism in a historical center Comparison tests show that the results obtained are consistent with those expressed by the tourists interviewed

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Generating Fuzzy Sets and Fuzzy Relations Based on Information

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2021.20.19 ◽

2021 ◽

Vol 20 ◽

pp. 178-185

Author(s):

Radwan Abu- Gdairi ◽

Ibrahim Noaman

Keyword(s):

Fuzzy Sets ◽

Knowledge Discovery ◽

Set Theory ◽

Membership Function ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Fuzzy Relation ◽

Knowledge Discovery In Databases ◽

Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced

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Implementation of Equilibrium Optimizer Algorithm for MPPT in a wind turbine with PMSG

WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL ◽

10.37394/23203.2021.16.18 ◽

2021 ◽

Vol 16 ◽

Author(s):

Radwan Abu- Gdairi ◽

Ibrahim Noaman

Keyword(s):

Wind Turbine ◽

Fuzzy Sets ◽

Knowledge Discovery ◽

Set Theory ◽

Membership Function ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Fuzzy Relation ◽

Knowledge Discovery In Databases ◽

Fuzzy Relations

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Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201557 ◽

2021 ◽

pp. 1-17

Author(s):

Changlin Xu ◽

Juhong Shen

Keyword(s):

Decision Making ◽

Pattern Recognition ◽

Fuzzy Sets ◽

Fuzzy Set ◽

Medical Diagnosis ◽

Intuitionistic Fuzzy Set ◽

Similarity Measures ◽

New Method ◽

Fuzzy Decision Making ◽

Multi Criteria Decision Making

Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

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PERTURBATION OF INTUITIONISTIC FUZZY RELATIONS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488501000648 ◽

2001 ◽

Vol 09 (01) ◽

pp. 81-103 ◽

Cited By ~ 11

Author(s):

H. BUSTINCE ◽

P. BURILLO

Keyword(s):

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Fuzzy Relation ◽

Fuzzy Relations ◽

Intuitionistic Fuzzy ◽

Do So

In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations afterward obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another also intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the conditions there must be for the new intuitionistic fuzzy relation to maintain the original properties.

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Energy and Entropy Measures of Fuzzy Relations for Data Analysis

10.20944/preprints201804.0246.v1 ◽

2018 ◽

Author(s):

Ferdinando Di Martino ◽

Salvatore Sessa

Keyword(s):

Fuzzy Set ◽

Fuzzy Rule ◽

Threshold Value ◽

Fuzzy Relation ◽

Fuzzy Rules ◽

Fuzzy Relations ◽

Input Output ◽

Input And Output ◽

Entropy Measures ◽

The Relationship

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation) in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the relationship input-output. We consider a new index of the fuzziness of the input-output based over R1 and R2. In our method this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set for choosing the most relevant fuzzy rules with respect to the data.

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RELASI FUZZY PADA GRUP FAKTOR FUZZY

JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON ◽

10.20527/epsilon.v14i1.2394 ◽

2020 ◽

Vol 14 (1) ◽

pp. 33

Author(s):

Ahmad Madani ◽

Saman Abdurrahman ◽

Na'imah Hijriati

Keyword(s):

Group Theory ◽

Fuzzy Set ◽

Fuzzy Relation ◽

Factor Group ◽

Fuzzy Relations ◽

Fuzzy Group ◽

Congruence Relations ◽

Fuzzy Congruence ◽

Fuzzy Subgroups ◽

Fuzzy Subsets

Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation if and if is a fuzzy congruence relations on fuzzy group and a fuzzy relation defined of is a fuzzy congruence relations on fuzzy factor group.

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Image Thresholding Computation Using Atanassov’s Intuitionistic Fuzzy Sets

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2007.p0187 ◽

2007 ◽

Vol 11 (2) ◽

pp. 187-194 ◽

Cited By ~ 10

Author(s):

H. Bustince ◽

◽

E. Barrenechea ◽

M. Pagola ◽

R. Orduna

Keyword(s):

Fuzzy Sets ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Intuitionistic Fuzzy Sets ◽

New Method ◽

Threshold Selection ◽

Uniform Illumination ◽

Intuitionistic Fuzzy ◽

Atanassov’S Intuitionistic Fuzzy Sets

In this paper, a new thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs) and restricted dissimilarity functions is introduced. In recent years, various thresholding techniques ([18, 24]) based on fuzzy set theory have been introduced to overcome the problem of non-uniform illumination and inherent image vagueness. In this paper we analyze this task and propose a new method for handling the grayness ambiguity and vagueness during the process of threshold selection.

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SOME FORMULAE TO CALCULATE THE ENTROPIES OF THE IMAGE FUZZY SETS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488503002363 ◽

2003 ◽

Vol 11 (05) ◽

pp. 615-626 ◽

Cited By ~ 4

Author(s):

DUG HUN HONG ◽

JANG HAN KIM

Keyword(s):

Fuzzy Sets ◽

Membership Function ◽

Fuzzy Set ◽

New Method ◽

Extension Principle

In this paper, we introduce a simple new method on calculating the entropy of the image fuzzy set gotten by the extension principle without calculating its membership function.

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