scholarly journals Application of a Similarity Measure Using Fuzzy Sets to Select the Optimal Plan for an Air-Assisted Rice Seeder

2021 ◽  
Vol 11 (15) ◽  
pp. 6715
Author(s):  
Nguyen Thanh Hai ◽  
Tadashi Chosa ◽  
Seishu Tojo ◽  
Ngo Thi-Hien
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Similarity Measure ◽  
Correlation Coefficients ◽  
Topsis Method ◽  
Optimal Plan ◽  
Technical Parameters ◽  
Decision Variables ◽  
Order Preference ◽  
Technical Factors

Air-assisted rice seeders were designed to perform sowing while ensuring the alignment and depth of seeds within the allowable standard range of 5–10 mm. Their performance varies on the basis of different specifications; thus, it is necessary to evaluate them to select the best one. Fuzzy set theory allows us to flexibly handle practical problems, especially applied problems in engineering. In this paper, a new similarity measure using fuzzy sets is proposed, and its advantages were tested using the technique for order preference by similarity to ideal solution (TOPSIS) method to select technical parameters for the sowing machines. The experiments allowed identifying the best results. The correlations between input attributes and decision variables were determined on the basis of their correlation coefficients with technical factors. The influence of technical factors on output results was also examined to determine the technical factors providing superior product quality.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

scholarly journals Improved cosine and cotangent function-based similarity measures for q-rung orthopair fuzzy sets and TOPSIS method

2021 ◽  
Author(s):  
Muhammad Jabir Khan ◽  
Poom Kumam ◽  
Nasser Aedh Alreshidi ◽  
Wiyada Kumam
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
Topsis Method ◽  
Inclusion Relation ◽  
Strict Inclusion ◽  
Numerical Examples ◽  
Ideal Solutions ◽  
Relative Ideal

AbstractDespite the importance of cosine and cotangent function- based similarity measures, the literature has not provided a satisfactory formulation for the case of q-rung orthopair fuzzy set (qROFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a similarity measure and strict inclusion relation. In addition, the maximum operator-based similarity measures are criticized. Then, new improved, axiomatically supported cosine and cotangent function-based similarity measures for qROFSs are proposed. Additional properties of the new similarity measures are discussed to guarantee their good performance. Two algorithmic procedures of TOPSIS method that based on fixed and relative ideal solutions are discussed. The numerical examples are provided to support the findings

Program Evaluation Model of Bridge Blasting of Engineer Corps Based on Intuitionist Fuzzy Sets and TOPSIS Method

2012 ◽  
Vol 246-247 ◽  
pp. 466-471
Author(s):  
Cheng Xiang Tian ◽  
Cheng Qun Fu ◽  
Lei Zhou ◽  
Jie Guo
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Evaluation Model ◽  
Optimal Solution ◽  
Evaluation Index System ◽  
Evaluation Index ◽  
Impact Factors ◽  
Topsis Method ◽  
Concept Building

The implementation of bridge blasting process for ground burst unit of Corps Engineers is complex with lots of impact factors, and it is difficult to determine the blasting program. In order to better solve the problem, the author in this paper proposes a new assessing approach of bridge blasting program based on combination of intuitionist fuzzy set theory and TPOSIS, and defines the optimal solution as well as worst solution of intuitionist fuzzy concept, building the evaluation index system of bridge blasting program majors in blasting target, the implementation staff for blasting, blasting tools and equipments. In this way, the author establishes the model of corps engineers of bridge blasting program based on intuitionist fuzzy sets and TOPSIS method, and verifies the model through the use of instances to prove the feasibility and effectiveness of the model with this method.

Novel similarity measures and multi-expert TOPSIS method using picture m-polar fuzzy sets

2021 ◽  
pp. 1-16
Author(s):  
Dliouah Ahmed ◽  
Binxiang Dai
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Alternative Solution ◽  
Topsis Method ◽  
Numerical Example ◽  
Picture Fuzzy Sets

In this paper, we give a new notion of the picture m-polar fuzzy sets (Pm-PFSs) (i.e, combination between the picture fuzzy sets (PFSs) and the m-polar fuzzy sets (m-PFSs)) and study several of the structure operations including subset, equal, union, intersection, and complement. After that, the basic definitions, theorems, and examples on Pm-PFSs are explained. Also, the certain distance between two Pm-PFSs and a novel similarity measure for Pm-PFSs based on distances are defined. MCDM is animated for Pm-PFS data that take into account the distances for the best alternative (solution) by proposed an application of similarity measure for Pm-PFSs in decision-making. Finally, we construct a new methodology to extend the TOPSIS to Pm-PFS in which capable of different objects recognizing belonging to the same family and illustrate its applicability via a numerical example.

scholarly journals A New Method for MAGDM Based on Improved TOPSIS and a Novel Pythagorean Fuzzy Soft Entropy

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 905 ◽  
Author(s):  
Han ◽  
Li ◽  
Song ◽  
Zhang ◽  
Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Topsis Method ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Order Preference

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the real world and possess good symmetry. The entropy measure is the most widespread form of uncertainty measure. In this paper, we improve the technique for order preference by similarity to an ideal solution (TOPSIS) method to better deal with multiple-attribute group decision making (MAGDM) problems based on Pythagorean fuzzy soft sets (PFSSs). To better determine the weights of attributes, we firstly define a novel Pythagorean fuzzy soft entropy which is more reasonable and valid. Meanwhile the entropy has good symmetry. Entropy for PFSSs which is used to determine the subjective weights of attributes is also defined. Then we introduce a measure to calculate integrated weights by combining objective weights and subjective weights. Based on the integrated weights, the TOPSIS method is generalized and improved to solve the MAGDM problem. A distance measure taking into account the characteristics of Pythagorean fuzzy numbers (PFNs) is used to calculate distance between alternatives and ideal solutions. Finally, the proposed MAGDM method is applied in the case of selecting a missile position. Compared with other methods, it is shown that the proposed method can rank alternatives more reasonably and have higher distinguishability.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

Transforming Family Resemblance Concepts into Fuzzy Sets

2021 ◽  
pp. 004912412098619
Author(s):  
Francesco Veri
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Concept Formation ◽  
Family Resemblance ◽  
Prototype Theory ◽  
Power Mean

This article aims to clarify fundamental aspects of the process of assigning fuzzy scores to conditions based on family resemblance (FR) structures by considering prototype and set theories. Prototype theory and set theory consider FR structures from two different angles. Specifically, set theory links the conceptualization of FR to the idea of sufficient and INUS (Insufficient but Necessary part of a condition, which is itself Unnecessary but Sufficient for the result) sets. In contrast, concept membership in prototype theory is strictly linked to the notion of similarity (or resemblance) in relation to the prototype, which is the anchor of the ideational content of the concept. After an introductive section where I elucidate set-theoretic and prototypical aspects of concept formation, I individuate the axiomatic properties that identify the principles of transforming FR structures into fuzzy sets. Finally, I propose an algorithm based on the power mean that is able to operationalize FR structures considering both set-theoretic and prototype theory perspectives.

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