Generalized dice similarity measures for complex q-Rung Orthopair fuzzy sets and its application

Garg, Harish; Ali, Zeeshan; Mahmood, Tahir

doi:10.1007/s40747-020-00203-x

Cited by 33 publications

(14 citation statements)

References 49 publications

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“…, and the infimum and supremum are taken in (I(R), ⩽) (Of course, the infimal and supremal in (2) and (3) can also be taken in (I(R), ≤ )). e last two are WIVP-metrics on Y 3 (but the first is not in general); all of them can be used to measure the difference between any two q-rung orthopair fuzzy sets (q ≥ 1) [35][36][37][38][39][40] or 3-polar fuzzy sets [34] Φ, Ψ ∈ Y 3 .…”

Section: Definition and Examples Of Wivp-metricmentioning

confidence: 99%

An Easy-to-Understand Method to Construct Desired Distance-Like Measures

Garg

et al. 2021

Complexity

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Metrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain (or easy to be coined by practitioners) pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators (easy to be coined by practitioners). The simple reason to do this is that data for a real world problem are sometimes from multiagents. A distance-like notion, called weak interval-valued pseudo-metrics (briefly, WIVP-metrics), is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate (including using what “material”) an expected or demanded WIVP-metric (even interval-valued metric) in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly.

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Section: Definition and Examples Of Wivp-metricmentioning

confidence: 99%

An Easy-to-Understand Method to Construct Desired Distance-Like Measures

Garg

et al. 2021

Complexity

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“…e fuzzy modeling comprises knowledge base, fuzzification process, inference engine, and defuzzification procedure. Specifics could be concisely illustrated in the literature [58][59][60]. Firstly, the fuzzification process utilizes membership functions (MFs) to fuzzify the S/N proportions.…”

Section: Phase (Ii): Fuzzy Modelingmentioning

confidence: 99%

Optimization for a Flexure Hinge Using an Effective Hybrid Approach of Fuzzy Logic and Moth-Flame Optimization Algorithm

Dang

Chau

et al. 2021

Mathematical Problems in Engineering

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Flexure hinge is a critical element in a positioner of a nanoindentation tester. To effectively work, a suitable flexure hinge should simultaneously meet multiple objectives, including rotation axis shift, safety factor, and angular deflection. The main aim of this article was to illustrate a hybrid method of the Taguchi method, fuzzy logic, response surface method, and Moth-flame optimization algorithm to solve the design optimization of a flexure hinge in order to enhance the three quality characteristics of the flexure hinge. Firstly, four common flexure hinges are compared together to seek the best suitable one. Secondly, numerical experiments are gathered via the Taguchi-based detasFlex software. Thirdly, three objective functions are transferred into signal to noises in order to eliminate the unit differences. Later on, fuzzy modeling is proposed to interpolate these three objective functions into one integrated objective function. An integrated regression equation is built using the response surface method. Finally, the flexure hinge is optimized by the Moth-flame optimization algorithm. The results found that the rotation axis shift is 10.944∗10−5 mm, the high safety factor is 2.993, and the angular deflection is 52.0058∗10−3 rad. The verifications are in a suitable agreement with the forecasted results. An analysis of variance and sensitivity analysis are also performed to identify the effects and meaningful contributions of input variables on the integrated objective function. In addition, employing the Wilcoxon signed rank test and the Friedman test, the results find that the proficiency of the proposed method has more benefits than the ASO algorithm and the GA. The results of this research provide a beneficial approach for conducting complicated multiobjective optimal problems.

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“…Garg [24] proposed applications of Einstein operations under PFS environment. Garg et al [25] derived new generalized dice similarity measures for complex q-rung orthopair fuzzy sets and established certain properties of suggested information measures. Garg and Arora [26] studied Archimedean t-norm of the intuitionistic fuzzy soft set (IFSS) and developed new generalized Maclaurin symmetric mean aggregation operators for information aggregation.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems

Iampan

Santos‐García

Riaz

et al. 2021

Journal of Mathematics

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The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed novel aggregation operators (AOs) under linear Diophantine fuzzy set (LDFS). A q -Rung orthopair fuzzy set ( q -ROFS), Pythagorean fuzzy set (PFS), and intuitionistic fuzzy set (IFS) are rudimentary concepts in computational intelligence, which have diverse applications in modeling uncertainty and MCDM. Unfortunately, these theories have their own limitations related to the membership and nonmembership grades. The linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty which has the ability to relax the strict constraints of IFS, PFS, and q –ROFS by considering reference/control parameters. LDFS provides an appropriate way to the decision experts (DEs) in order to deal with vague and uncertain information in a comprehensive way. Under these environments, we introduce several AOs named as linear Diophantine fuzzy Einstein weighted averaging (LDFEWA) operator, linear Diophantine fuzzy Einstein ordered weighted averaging (LDFEOWA) operator, linear Diophantine fuzzy Einstein weighted geometric (LDFEWG) operator, and linear Diophantine fuzzy Einstein ordered weighted geometric (LDFEOWG) operator. We investigate certain characteristics and operational laws with some illustrations. Ultimately, an innovative approach for MCDM under the linear Diophantine fuzzy information is examined by implementing suggested aggregation operators. A useful example related to a country’s national health administration (NHA) to create a fully developed postacute care (PAC) model network for the health recovery of patients suffering from cerebrovascular diseases (CVDs) is exhibited to specify the practicability and efficacy of the intended approach.

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Generalized dice similarity measures for complex q-Rung Orthopair fuzzy sets and its application

Cited by 33 publications

References 49 publications

An Easy-to-Understand Method to Construct Desired Distance-Like Measures

An Easy-to-Understand Method to Construct Desired Distance-Like Measures

Optimization for a Flexure Hinge Using an Effective Hybrid Approach of Fuzzy Logic and Moth-Flame Optimization Algorithm

Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems

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