Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in r...Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.展开更多
This paper aims to introduce the novel concept of the bipolar picture fuzzy set(BPFS)as a hybrid structure of bipolar fuzzy set(BFS)and picture fuzzy set(PFS).BPFS is a new kind of fuzzy sets to deal with bipolarity(b...This paper aims to introduce the novel concept of the bipolar picture fuzzy set(BPFS)as a hybrid structure of bipolar fuzzy set(BFS)and picture fuzzy set(PFS).BPFS is a new kind of fuzzy sets to deal with bipolarity(both positive and negative aspects)to each membership degree(belonging-ness),neutral membership(not decided),and non-membership degree(refusal).In this article,some basic properties of bipolar picture fuzzy sets(BPFSs)and their fundamental operations are introduced.The score function,accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy numbers(BPFNs).Additionally,the concept of new distance measures of BPFSs is presented to discuss geometrical properties of BPFSs.In the context of BPFSs,certain aggregation operators(AOs)named as“bipolar picture fuzzy weighted geometric(BPFWG)operator,bipolar picture fuzzy ordered weighted geometric(BPFOWG)operator and bipolar picture fuzzy hybrid geometric(BPFHG)operator”are defined for information aggregation of BPFNs.Based on the proposed AOs,a new multicriteria decision-making(MCDM)approach is proposed to address uncertain real-life situations.Finally,a practical application of proposed methodology is also illustrated to discuss its feasibility and applicability.展开更多
基金supported by“Algebra and Applications Research Unit,Division of Computational Science,Faculty of Science,Prince of Songkla University”.
文摘Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.
文摘This paper aims to introduce the novel concept of the bipolar picture fuzzy set(BPFS)as a hybrid structure of bipolar fuzzy set(BFS)and picture fuzzy set(PFS).BPFS is a new kind of fuzzy sets to deal with bipolarity(both positive and negative aspects)to each membership degree(belonging-ness),neutral membership(not decided),and non-membership degree(refusal).In this article,some basic properties of bipolar picture fuzzy sets(BPFSs)and their fundamental operations are introduced.The score function,accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy numbers(BPFNs).Additionally,the concept of new distance measures of BPFSs is presented to discuss geometrical properties of BPFSs.In the context of BPFSs,certain aggregation operators(AOs)named as“bipolar picture fuzzy weighted geometric(BPFWG)operator,bipolar picture fuzzy ordered weighted geometric(BPFOWG)operator and bipolar picture fuzzy hybrid geometric(BPFHG)operator”are defined for information aggregation of BPFNs.Based on the proposed AOs,a new multicriteria decision-making(MCDM)approach is proposed to address uncertain real-life situations.Finally,a practical application of proposed methodology is also illustrated to discuss its feasibility and applicability.
