A novel difference and derivative of linearly correlated fuzzy number-valued functions

2022 ◽  
pp. 1-17
Author(s):  
Yonghong Shen
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Hukuhara Difference ◽  
Interval Numbers ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Generalized Hukuhara Difference ◽  
Interval Valued

In the present paper, the notion of the linearly correlated difference for linearly correlated fuzzy numbers is introduced. Especially, the linearly correlated difference and the generalized Hukuhara difference are coincident for interval numbers or even symmetric fuzzy numbers. Accordingly, an appropriate metric is induced by using the norm and the linearly correlated difference in the set of linearly correlated fuzzy numbers. Based on the symmetry of the basic fuzzy number, the linearly correlated derivative is proposed by the linearly correlated difference of linearly correlated fuzzy number-valued functions. In both non-symmetric and symmetric cases, the equivalent characterizations of the linearly correlated differentiability of a linearly correlated fuzzy number-valued function are established, respectively. Moreover, it is shown that the linearly correlated derivative is consistent with the generalized Hukuhara derivative for interval-valued functions.

scholarly journals A Heterogeneous MCDM Framework for Sustainable Supplier Evaluation and Selection Based on the IVIF-TODIM Method

2019 ◽  
Vol 11 (18) ◽  
pp. 5057 ◽  
Author(s):  
Ren-Jie Mao ◽  
Jian-Xin You ◽  
Chun-Yan Duan ◽  
Lu-Ning Shao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Third Party ◽  
Multi Criteria Decision Making ◽  
Interval Numbers ◽  
Intuitionistic Fuzzy Numbers ◽  
Sustainability Performance ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Interval Valued

The third-party platform named ECO system is used by many transnational companies to monitor the sustainability performance of their global suppliers because of its easiness and shareability. Nonetheless, methods used in this platform for evaluating and calculating the sustainability performance of the alternative suppliers are criticized for their lack of accuracy. In response to these problems, this paper presents a heterogeneous multi-criteria decision-making (MCDM) method based on interval-valued intuitionistic fuzzy--an acronym in Portuguese for interactive multi-criteria decision making (IVIF--TODIM) to improve the efficiency of the evaluation model. Considering the varying features of evaluation criteria, i.e., either quantitative or qualitative, the evaluation values under different criteria are expressed in their appropriate information types. In this paper, a general method based on the relative closeness to the technique for order preference by similarity to ideal solution (TOPSIS) method is applied for aggregating the heterogeneous assessment information, including crisp numbers, interval numbers, and triangular fuzzy numbers (TFNs), into interval-valued intuitionistic fuzzy numbers (IVIFNs). Then, the TODIM (an acronym in Portuguese for interactive multi-criteria decision making) is extended and employed to prioritize the alternative suppliers. Finally, the applicability and effectiveness of the proposed method is verified by a practical example of polymer manufacturing company and a comparison analysis with existing methods.

A QUANTITY PROPERTY-BASED FUZZY NUMBER RANKING METHOD FOR DECISION MAKING WITH UNCERTAINTY

2012 ◽  
Vol 20 (supp01) ◽  
pp. 133-145 ◽  
Author(s):  
FACHAO LI ◽  
FEI GUAN ◽  
CHENXIA JIN
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Ranking Method ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Interval Numbers ◽  
Interval Representation ◽  
Ranking Model ◽  
Key Issues

One of the key issues for support fuzzy decision-making is fuzzy number ranking. The existing ranking methods either do not provide a total ordering or cannot be effectively applied to decision-making processes. In this paper, we first give five basic principles that interval number ranking must satisfy, and construct a quantitative ranking model of interval numbers based on the synthesis effects of each index. We then propose a new constructions method of synthesis effect function systematically. Third, we also develop a new fuzzy numbers ranking model based on numerical characteristics, combining with the interval representation theorem of fuzzy numbers, and analyze the performance and characteristics of this ranking method by a case-based example. The results indicate that this proposed ranking method has good operability and interpretability, which can integrate the decision consciousness into decision process effectively and serve as a guideline for constructing different fuzzy decision methods.

Application of interval-valued triangular fuzzy numbers and their functional to the healthcare problems

Dependability ◽  
2021 ◽  
Vol 21 (1) ◽  
pp. 23-33
Author(s):  
Kapil Naithani ◽  
Rajesh Dangwal
Keyword(s):  
Failure Probability ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fault Tree Analysis ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
Index Method ◽  
Estimate Reliability ◽  
Failure Tree ◽  
Interval Valued

Aim. In healthcare field there exist different types of uncertainty due to medical error generated by human and technologies. In general the crisp value generate loss of precision and inaccuracy about result and therefore the available data is not sufficient to assessed clinical process up to desired degree of accuracy. Therefore fuzzy set theory play as an important and advance role in accuracy of results in healthcare related problems. Methods. Here for more accuracy of result, we use functional fuzzy numbers in this paper. This study uses a new fuzzy fault tree analysis for patient safety risk modelling in healthcare. In this paper we will use level (λ, ρ) interval-valued triangular fuzzy number, their functional, t-norm operation and centre of gravity defuzzification method to evaluate fuzzy failure probability and estimate reliability of system. The effectiveness of these methods is illustrated by an example related to healthcare problems and then we analyse the result obtained with the other existing techniques. Tanaka et al.’s approach has been used to give the rank of basic events of the considered problems. Also, we use functional of fuzzy numbers to analyse the change in fuzzy failure probability. Results. The paper examines the application of the failure tree, t-norm and functional fuzzy numbers in the context of interval-valued triangular fuzzy numbers. The research examined two types of healthcare-specific problems and the corresponding defuzzification techniques for the purpose of reliability analysis using the existing methods. The authors concluded that t-norm is not associated with significant accumulation and identified how a functional fuzzy number affects reliability. Similarly, using the V index method, the least critical events were found for each system.

Newton’s divided gH-difference interpolation formula with unequal spacing for interval-valued function using Hukuhara difference

2021 ◽  
pp. 2250093
Author(s):  
Bapin Mondal ◽  
Md Sadikur Rahman
Keyword(s):  
Significant Role ◽  
Unknown Function ◽  
Interpolation Formula ◽  
Interval Uncertainty ◽  
Hukuhara Difference ◽  
Numerical Examples ◽  
Generalized Hukuhara Difference ◽  
Interval Valued Function ◽  
Definition Of ◽  
Interval Valued

Interval interpolation formulae play a significant role to find the value of an unknown function at some points under interval uncertainty. The objective of this paper is to establish Newton’s divided interpolation formula for interval-valued functions using generalized Hukuhara difference of intervals. For this purpose, arithmetic of intervals, Hukuhara difference and its some properties and concept of interval-valued function have been discussed briefly. Using Hukuhara difference of intervals, the definition of Newton’s divided gH-difference for interval-valued function has been introduced. Then Newton’s divided gH-differences interpolation formula has been derived. Finally, with the help of some numerical examples, the proposed interpolation formula has been illustrated.

DECISION MAKING BASED ON STATISTICAL DATA, SIGNED DISTANCE AND COMPOSITIONAL RULE OF INFERENCE

2004 ◽  
Vol 12 (02) ◽  
pp. 161-190 ◽  
Author(s):  
JING-SHING YAO ◽  
MING-MIIN YU
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Statistical Data ◽  
Fuzzy Decision Making ◽  
Seamless Integration ◽  
Transit System ◽  
Signed Distance ◽  
Decision Making Problem ◽  
Interval Valued

An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.

Calculus for interval-valued functions using generalized Hukuhara derivative and applications

2013 ◽  
Vol 219 ◽  
pp. 49-67 ◽  
Author(s):  
Y. Chalco-Cano ◽  
A. Rufián-Lizana ◽  
H. Román-Flores ◽  
M.D. Jiménez-Gamero
Keyword(s):  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Interval Valued

scholarly journals The Interval-Valued Trapezoidal Approximation of Interval-Valued Fuzzy Numbers and Its Application in Fuzzy Risk Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Zengtai Gong ◽  
Shexiang Hai
Keyword(s):  
Risk Analysis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Approximation Operator ◽  
Weighted Distance ◽  
Trapezoidal Fuzzy Number ◽  
The Core ◽  
Fuzzy Risk Analysis ◽  
The Given ◽  
Interval Valued

Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods.

scholarly journals Metric Properties between Trapezoidal Intuitionistic Fuzzy Numbers

2019 ◽  
Vol 8 (3) ◽  
pp. 3951-3954
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Interval Numbers ◽  
New Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy ◽  
Metric Distance ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Generally ranking of fuzzy number is more essential for convertion of fuzzy number to crisp one. In this manuscript, a new approach to rank the trapezoidal intuitionistic fuzzy numbers using cuts is established. The metric distance of the interval numbers is extended to trapezoidal intuitionistic fuzzy numbers. By using both the ranking of trapezoidal intuitionistic fuzzy numbers and cuts there is abundant scope of investigating the numerical problems in optimization.

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