Uncertainty and ambiguity are pervasive in real-world intelligent systems,necessitating advanced mathematical frameworks for effective modeling and analysis.Fermatean fuzzy sets(FFSs),as a recent extension of classica...Uncertainty and ambiguity are pervasive in real-world intelligent systems,necessitating advanced mathematical frameworks for effective modeling and analysis.Fermatean fuzzy sets(FFSs),as a recent extension of classical fuzzy theory,provide enhanced flexibility for representing complex uncertainty.In this paper,we propose a unified parametric divergence operator for FFSs,which comprehensively captures the interplay among membership,nonmembership,and hesitation degrees.The proposed operator is rigorously analyzed with respect to key mathematical properties,including non-negativity,non-degeneracy,and symmetry.Notably,several well-known divergence operators,such as Jensen-Shannon divergence,Hellinger distance,andχ2-divergence,are shown to be special cases within our unified framework.Extensive experiments on pattern classification,hierarchical clustering,and multiattribute decision-making tasks demonstrate the competitive performance and stability of the proposed operator.These results confirm both the theoretical significance and practical value of our method for advanced fuzzy information processing in machine learning and intelligent decision-making.展开更多
In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle...In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.展开更多
文摘Uncertainty and ambiguity are pervasive in real-world intelligent systems,necessitating advanced mathematical frameworks for effective modeling and analysis.Fermatean fuzzy sets(FFSs),as a recent extension of classical fuzzy theory,provide enhanced flexibility for representing complex uncertainty.In this paper,we propose a unified parametric divergence operator for FFSs,which comprehensively captures the interplay among membership,nonmembership,and hesitation degrees.The proposed operator is rigorously analyzed with respect to key mathematical properties,including non-negativity,non-degeneracy,and symmetry.Notably,several well-known divergence operators,such as Jensen-Shannon divergence,Hellinger distance,andχ2-divergence,are shown to be special cases within our unified framework.Extensive experiments on pattern classification,hierarchical clustering,and multiattribute decision-making tasks demonstrate the competitive performance and stability of the proposed operator.These results confirm both the theoretical significance and practical value of our method for advanced fuzzy information processing in machine learning and intelligent decision-making.
文摘In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.
