On Pythagorean fuzzy soft matrices, operations and their applications in decision making and medical diagnosis

Guleria, Abhishek; Bajaj, Rakesh Kumar

doi:10.1007/s00500-018-3419-z

Cited by 73 publications

(29 citation statements)

References 14 publications

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“…Thus, it is only necessary to prove that (T1.1) and (T1.3) are satisfied. D G,β (p 1 , p 2 ) ≥ 0 according to the definition in (19). From ( 7), one obtains:…”

Section: Proposed Pf Distance Measuresmentioning

confidence: 99%

“…Pythagorean membership grades are characterized by the membership degree, the non-membership degree, the indeterminacy degree, the strength of commitment, and the direction of commitment [11], [13], [17], [18]. PF sets with Pythagorean membership grades satisfy the relaxed condition that the square sum of the membership degree and the non-membership degree is equal to or less than one [10]- [13], [19], [20]. This relaxed condition provides an obvious advantage to PF sets, namely, a wider coverage of the information span [19].…”

Section: Introductionmentioning

confidence: 99%

“…PF sets with Pythagorean membership grades satisfy the relaxed condition that the square sum of the membership degree and the non-membership degree is equal to or less than one [10]- [13], [19], [20]. This relaxed condition provides an obvious advantage to PF sets, namely, a wider coverage of the information span [19]. Due to various information insufficiency issues in practical decision situations, PF sets have become an important tool because they can effectively model higher-order fuzziness and uncertainty in MCDA problems [16], [19], [21]- [24].…”

Section: Introductionmentioning

confidence: 99%

“…This relaxed condition provides an obvious advantage to PF sets, namely, a wider coverage of the information span [19]. Due to various information insufficiency issues in practical decision situations, PF sets have become an important tool because they can effectively model higher-order fuzziness and uncertainty in MCDA problems [16], [19], [21]- [24].…”

Section: Introductionmentioning

confidence: 99%

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Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty

Chen

2019

IEEE Access

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This paper aims at developing a novel generalized distance measure of Pythagorean fuzzy (PF) sets and constructing a distance-based compromise approach for multiple criteria decision analysis (MCDA) within PF environments. The theory of Pythagorean fuzziness provides a representative model of nonstandard fuzzy sets; it is valuable for representing complex vague or imprecise information in many practical applications. The distance measure for Pythagorean membership grades is important because it can effectively quantify the separation between PF information. Based on the essential characteristics of PF sets (membership, non-membership, strength, and direction), this paper proposes several distance measures, namely, new Hamming and Euclidean distances and a generalized distance measure that is based on them for Pythagorean membership grades and for PF sets. Moreover, the useful and desirable properties of the proposed PF distance measures are investigated to evaluate their advantages and form a solid theoretical basis. In addition, to evaluate the performance of the proposed distance measures in practice, this paper establishes a PF-distance-based compromise approach for addressing MCDA problems that involve PF information. The effectiveness and practicability of the developed approach are further evaluated through a case study on bridge-superstructure construction methods. According to the application results and comparative analysis, the proposed PF distance measures are accurate and outperform other methods in handling the inherent uncertainties of evaluation information. Furthermore, the PF-distance-based compromise approach can accommodate the much higher degrees of uncertainty in real-life decision scenarios and effectively determine the priority ranking among candidate alternatives for managing complicated MCDA problems.

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“…Thus, it is only necessary to prove that (T1.1) and (T1.3) are satisfied. D G,β (p 1 , p 2 ) ≥ 0 according to the definition in (19). From ( 7), one obtains:…”

Section: Proposed Pf Distance Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty

Chen

2019

IEEE Access

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“…The concept of Pythagorean fuzzy (PF) sets, originally developed by Yager [16]- [18] and Yager and Abbasov [19], is useful to represent ambiguous and uncertain decision information [20], [21]. As a valuable extension of intuitionistic fuzzy sets, Pythagorean membership grades involved in a PF set relax the condition that the sum of membership and non-membership degrees is less than or equal to one with the square sum is less than or equal to one [15], [22]- [24]. Accordingly, PF sets have been widely popular in handling complex uncertainty involved in practical decision-making problems, and they have attracted numerous scholars' research interests in recent years.…”

Section: Introductionmentioning

confidence: 99%

Multiple Criteria Group Decision Making Using a Parametric Linear Programming Technique for Multidimensional Analysis of Preference Under Uncertainty of Pythagorean Fuzziness

Chen

2019

IEEE Access

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This paper aims to utilize the core structure of linear programming technique for multidimensional analysis of preference (LINMAP) to propose a parametric LINMAP methodology for addressing multiple criteria group decision-making problems based on Pythagorean fuzzy sets. To compare Pythagorean membership grades, this paper presents a Hamming distance-based approach for identifying closeness-based order relations based on Pythagorean fuzzy closeness indices. The concept of comprehensive closeness measures is introduced to measure individual order consistency and inconsistency between subjective preference relations and objective order relations. In the spirit of LINMAP, this paper determines individual goodness of fit and poorness of fit and further constructs a novel parametric LINMAP model. The applicability of the developed approach is explored by a practical application of railway project investment. Some comparative analyses are conducted to demonstrate the usefulness and advantages of the proposed methodology.INDEX TERMS Multiple criteria group decision making, Pythagorean fuzzy set, Pythagorean membership grade, closeness-based order relation.

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Fuzzy Logic-Based Software Systems

Chrysafiadi

2023

Learning and Analytics in Intelligent Systems

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On Pythagorean fuzzy soft matrices, operations and their applications in decision making and medical diagnosis

Cited by 73 publications

References 14 publications

Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty

Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty

Multiple Criteria Group Decision Making Using a Parametric Linear Programming Technique for Multidimensional Analysis of Preference Under Uncertainty of Pythagorean Fuzziness

Fuzzy Logic-Based Software Systems

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