Fuzzy Geometric Research Articles

NeuFG: Neural Fuzzy Geometric Representation for 3-D Reconstruction

NeuFG: Neural Fuzzy Geometric Representation for 3-D Reconstruction

Revolutionizing Multi-Criteria Decision Making with the Triangular Fuzzy Geometry Bonferroni Mean Operator (TFGBM)

This study investigates the Multi-Criteria Decision Making (MCDM) topic to address the complexities of decision processes involving ambiguous information. We introduce the Triangular Fuzzy Geometric Bonferroni Mean (TFGBM) operator, a novel aggregation technique inspired by the Geometric Bonferroni Mean (GBM) concept. This operator is intended to aggregate triangular fuzzy numbers within MCDM problems effectively. We thoroughly investigate the properties of TFGBM and its distinct forms to ensure its practical utility. We introduce the Triangular Fuzzy Geometric Weighted Bonferroni Mean (TFGWBM) operator to accommodate situations where input factors have variable degrees of significance. Based on this foundation, we present a comprehensive framework for decision-making involving multiple attributes in ambiguous triangular fuzzy environments. A relevant case study regarding selecting an optimal location for a Halal center demonstrates the efficacy and applicability of our methodology. We emphasize the tangibility and efficiency of the suggested methodology in improving decision-making processes by emphasizing this real-world application.

Retracted: Some Generalized T-Spherical and Group-Generalized Fuzzy Geometric Aggregation Operators with Application in MADM Problems

Retracted: Some Generalized T-Spherical and Group-Generalized Fuzzy Geometric Aggregation Operators with Application in MADM Problems

Identifying and analyzing the barriers of Internet-of-Things in sustainable supply chain through newly proposed spherical fuzzy geometric mean

Many industrial firms have gained strategic benefits from the use of IoT in supply chain (SC) and operations, but still, several firms are reluctant in applying this technology in their firm. Therefore, this study is going to identify and analyze the most influential barriers faced by firms during the adoption of IoT in attaining sustainable SC. The novelty of the current research work is the use of Analytical Hierarchy Process (AHP) under spherical fuzzy set to assess those identified barriers which are linked with IoT implementation in the context of sustainable SC. Compared to previously developed extension of fuzzy sets such as Intuitionistic and Pythagorean fuzzy sets, Spherical fuzzy set uses three dimensional membership functions capable of handling more uncertainty and ambiguity of preference given by the decision makers. The barriers are analyzed by segregating them into four major categories i.e. economic, organisational, environmental, and technological barriers. In terms of computational complexity the proposed spherical fuzzy AHP is much simpler to the previously developed spherical fuzzy AHP, as it utilizes the newly proposed Spherical Fuzzy Geometric Mean to compute the final score of the barriers. It is found that economic factor is the most influential factor among organizational, environmental and technological barriers. Overall operational cost and financial constraints/insufficient budget are the two most influential factors or major cause which acts as a hurdle in implementing IoT in the context of sustainable SC. The analysis on the crucial barriers in the adoption of IoT in sustainable SC suggest that financial rewards and compensations should be provided to the firms who adopted green material and green devices in IoT technologies.

Fuzzy Geometric Spaces and Transitivity of β-Relation on Fuzzy Hypergroups

In this paper, the notion of a fuzzy geometric space is introduced. Some structures related to it are studied and connections of them are investigated. By using fuzzy blocks of a fuzzy geometric space, the concept of strongly transitivity of fuzzy geometric spaces is defined and studied. Finally, it is proved that the relation [Formula: see text] is transitive on fuzzy hypergroups, by associating strongly transitivity fuzzy geometric spaces to fuzzy hypergroups.

Some Generalized T-Spherical and Group-Generalized Fuzzy Geometric Aggregation Operators with Application in MADM Problems

In this article, the generalized parameter is involved in T-spherical fuzzy set (TSFS), and with the help of this generalized parameter, some generalized geometric aggregation operators for TSFSs are proposed. Then these operators are extended for group-generalized parameter. By using proposed operators, an algorithm is developed for the MADM problem. To check the validity of proposed operators, a numerical example is also investigated. In a comparative analysis, it is discussed that, under some conditions, the proposed work can be reduced to other fuzzy structures. An example is also solved in which it is shown that our proposed technique is superior to the existing technique.

Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

Q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management

The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in which degree of truthness and degree of falsity meet the condition 0≤Θ˘2(x)+K2(x)≤1. Another extension of PFS is a q´-rung orthopair fuzzy set (q´-ROFS), in which truthness degree and falsity degree meet the condition 0≤Θ˘q´(x)+Kq´(x)≤1,(q´≥1), so they can characterize the scope of imprecise information in more comprehensive way. q´-ROFS theory is superior to FS, IFS, and PFS theory with distinguished characteristics. This study develops a few aggregation operators (AOs) for the fusion of q´-ROF information and introduces a new approach to decision-making based on the proposed operators. In the framework of this investigation, the idea of a generalized parameter is integrated into the q´-ROFS theory and different generalized q´-ROF geometric aggregation operators are presented. Subsequently, the AOs are extended to a “group-based generalized parameter”, with the perception of different specialists/decision makers. We developed q´-ROF geometric aggregation operator under generalized parameter and q´-ROF geometric aggregation operator under group-based generalized parameter. Increased water requirements, in parallel with water scarcity, force water utilities in developing countries to follow complex operating techniques for the distribution of the available amounts of water. Reducing water losses from water supply systems can help to bridge the gap between supply and demand. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the q´-ROF environment. An illustrative example related to water loss management has been given to show the validity of the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the liability and dominance of proposed techniques to the existing one is also considered.

Extensions of Intuitionistic Fuzzy Geometric Interaction Operators and Their Application to Cognitive Microcredit Origination

The intuitionistic fuzzy set (IFS), a popular tool to present decision makers’ cognitive information, has received considerable attention from researchers. To extend the interaction operational laws in the computation of cognitive information, this paper focuses on investigating extensions of geometric interaction aggregation operators by means of the t-norm and the corresponding t-conorm under an intuitionistic fuzzy environment. We develop the extending intuitionistic fuzzy-weighted geometric interaction averaging (EIFWGIA) operator, the extending intuitionistic fuzzy-ordered weighted geometric interaction averaging (EIFOWGIA) operator, the intuitionistic fuzzy weighted geometric interaction quasi-arithmetic mean (IFWGIQAM), and the intuitionistic fuzzy-ordered weighted geometric interaction quasi-arithmetic mean (IFOWGIQAM). We investigate the properties of the proposed extensions and apply the extensions to the cognitive microcredit origination problem. For different generator functions h and ϕ, the proposed IFWGIQAM and IFOWGIQAM degenerate into existing intuitionistic fuzzy aggregation operators or extensions, some of which consider situations that in which no interactions exist between membership and non-membership functions, which can be used in more decision situations. The methods developed in this paper can be used to account for several decision situations. The numerical example demonstrates the validity of the proposed approaches by means of comparisons.

Determining Fuzzy Distance between Sets by Application of Fixed Point Technique Using Weak Contractions and Fuzzy Geometric Notions

In the present paper, we solve the problem of determining the fuzzy distance between two subsets of a fuzzy metric space. We address the problem by reducing it to the problem of finding an optimal approximate solution of a fixed point equation. This approach is well studied for the corresponding problem in metric spaces and is known as proximity point problem. We employ fuzzy weak contractions for that purpose. Fuzzy weak contraction is a recently introduced concept intermediate to a fuzzy contraction and a fuzzy non-expansive mapping. Fuzzy versions of some geometric properties essentially belonging to Hilbert spaces are considered in the main theorem. We include an illustrative example and two corollaries, one of which comes from a well-known fixed point theorem. The illustrative example shows that the main theorem properly includes its corollaries. The work is in the domain of fuzzy global optimization by use of fixed point methods.

A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems

Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n-dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.

The Origin and Development of Fuzzy Geometric Programming

ABSTRACT Fuzzy Geometric Programming has been in discussion for 32 years since 1987. According to Cao, the author, he in the paper introduces its development process, aiming to promote this new branch, attracting scholars home and abroad to join in ranks of the research, and helping to solve the three conjectures of Fuzzy Geometric Programming proposed by Cao [Three guess of fuzzy geometric programming. Vol. 147. Springer; 2012. p. 591–594. (Advances in intelligent and soft computing)]. At present, many books and teaching materials of it have been translated into Persian with some published.

Application of Dual Hesitant Fuzzy Geometric Bonferroni Mean Operators in Deciding an Energy Policy for the Society

Dual hesitant fuzzy geometric Bonferroni mean is defined for dual hesitant fuzzy sets. Different properties of dual hesitant fuzzy geometric Bonferroni mean are discussed. Some special cases are studied in detail for dual hesitant fuzzy geometric Bonferroni mean. In addition, dual hesitant fuzzy weighted geometric Bonferroni mean and dual hesitant fuzzy Choquet geometric Bonferroni mean are proposed. A multicriteria decision-making method is discussed to find the best alternative among different alternatives by using proposed aggregated operators and an illustrated example is also given to understand our proposal.

Generalized Scaled Prioritized Intuitionistic Fuzzy Geometric Interaction Aggregation Operators and Their Applications to the Selection of Cold Chain Logistics Enterprises

Generalized Scaled Prioritized Intuitionistic Fuzzy Geometric Interaction Aggregation Operators and Their Applications to the Selection of Cold Chain Logistics Enterprises

A Generalized Triangular Intuitionistic Fuzzy Geometric Averaging Operator for Decision-Making in Engineering and Management

Triangular intuitionistic fuzzy number (TIFN) is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multi-criteria decision-making problems, as well as for expressing and reflecting the evaluation information in several dimensions. In this paper, the TIFN has been applied for solving multi-criteria decision-making (MCDM) problems, first, by defining some existing triangular intuitionistic fuzzy geometric aggregation operators, and then developing a new triangular intuitionistic fuzzy geometric aggregation operator, which is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed is proposed. Finally, a numerical example is provided to show the applicability and rationality of the presented method, followed by a comparative analysis using similar existing computational approaches.

A Method for Group Decision Making Based on Interval-Valued Intuitionistic Fuzzy Geometric Distance Measures

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

OPTIMIZATION OF AN ECONOMIC GREEN MANUFACTURING INVENTORY MODEL USING FUZZY GEOMETRIC PROGRAMMING.

27Jul 2016 OPTIMIZATION OF AN ECONOMIC GREEN MANUFACTURING INVENTORY MODEL USING FUZZY GEOMETRIC PROGRAMMING Nivetha Martin and P. Pandiammal Assistant Professor, Department of Mathematics, Arul Anandar College(Autonomous),Madurai Tamil Nadu. Assistant Professor, Department of Mathematics, GTN Arts College, Dindigul, Tamil Nadu.

Optimization of Structural Design by Fuzzy Geometric Programming Technique

Optimization of Structural Design by Fuzzy Geometric Programming Technique

Derivation and Comparative Study on Centroid Ranking Value of TrIFN and Apply on Fuzzy Geometric Programming

Derivation and Comparative Study on Centroid Ranking Value of TrIFN and Apply on Fuzzy Geometric Programming

Fuzzy Geometric Programming Approach in Multi-objective Multivariate Stratified Sample Surveys in Presence of Non-Response

Fuzzy Geometric Programming Approach in Multi-objective Multivariate Stratified Sample Surveys in Presence of Non-Response