A multiparameter group decision making method based on the interval-valued intuitionistic fuzzy soft set

Gong, Zengtai; Xie, Ting; Shi, Zhanhong; Pan, Wenqing

doi:10.1109/icmlc.2011.6016727

Cited by 6 publications

(3 citation statements)

References 31 publications

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“…Here, we will do this for the IVIFS case. Partially, the idea was generated with regards to the definition of a soft set and some of its modifications [1,2,[8][9][10][11][12][13][14]. But in the present research, we will keep only the IFS-and IVIFS-forms of the sets without adding any soft-set component.…”

Section: Resultsmentioning

confidence: 99%

Interval-valued intuitionistic fuzzy sets over universes with special forms

Atanassov¹,

Vassilev²

2019

NIFS

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Section: Resultsmentioning

confidence: 99%

Interval-valued intuitionistic fuzzy sets over universes with special forms

Atanassov¹,

Vassilev²

2019

NIFS

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“…If we take x 1 , 0.6, 0.3 as an element of intuitionistic fuzzy set A of voting, then we can interpret it as "the voting for the candidate x 1 is 0.6 for 0.3 against and 0.1 abstentions". IFS theory has been widely applied in various fields such as decision analysis, pattern recognition, machine learning, image processing, and so on [12][13][14]. In this paper, we further discuss the generalized variational inequalities with intuitionistic fuzzy relations.…”

Section: Introductionmentioning

confidence: 99%

Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems

Xie

2022

J Inequal Appl

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The fuzzy set theory enables us to represent our knowledge under multiple interpretations and axiomatic foundations from linguistic to computational representations. While the intuitionistic fuzzy set, as a generalization of the fuzzy set, cannot only represent the tolerance levels, but also the intolerance levels which a decision maker can tolerate and cannot tolerate in the accomplishment of a linguistic interpretation, in this paper, we introduce the generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations. It is shown that such problems can be transformed into the classical (nonfuzzy) generalized variational inequalities by means of level sets of the intuitionistic fuzzy relation. Furthermore, the equivalence between the generalized variational inequalities with intuitionistic fuzzy relations and the fuzzy fixed point problems is established. Finally, based on the projection method, we propose an iterative algorithm and a projected neural network model for the generalized variational inequalities with intuitionistic fuzzy relations, and the stability of the proposed projected dynamical system is also investigated.

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“…Yang et al [33] introduced the concept of interval-valued fuzzy soft set and a decision making problem is analyzed by the interval-valued fuzzy soft set. In 2011, Gong et al [8] introduced the interval-valued intuitionistic fuzzy soft set and described its application to multi-parameter group decision-making problems. In 2014, Wang et al [30] introduced the hesitant fuzzy soft set (HFSS) by combining the notion of hesitancy with Molodtsov's soft set.…”

Section: Introductionmentioning

confidence: 99%

A Hesitant Soft Fuzzy Rough Set and its Applications

Xie

Gong

2019

IEEE Access

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The difficulty of establishing a common membership degree is not because there is a margin of error or some possibility distribution values, but because there is a set of possible values. Based on hesitant fuzzy sets and soft sets, a hesitant soft fuzzy rough set model is proposed in this paper. Basic properties of hesitant soft fuzzy rough sets are investigated in detail. We obtain a decomposition theorem for a hesitant fuzzy binary relation, which states that every typical hesitant fuzzy binary relation on a set can be represented by a well-structured family of fuzzy binary relations on that set. Indeed, a hesitant fuzzy soft set can induce a hesitant fuzzy binary relation. Then we give the relationship between hesitant fuzzy rough sets and hesitant soft fuzzy rough sets. In addition, we prove a characterization theorem for the hesitant soft fuzzy rough set model, which shows that the lower and upper hesitant soft fuzzy rough approximations can be equivalently defined by using level sets of the hesitant fuzzy soft set. Finally, by analyzing the limitations and advantages in the existing literatures, we establish an approach to decision making problem based on the hesitant soft fuzzy rough set model proposed in this paper and give a practical example to illustrate the validity of the novel method.

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A multiparameter group decision making method based on the interval-valued intuitionistic fuzzy soft set

Cited by 6 publications

References 31 publications

Interval-valued intuitionistic fuzzy sets over universes with special forms

Interval-valued intuitionistic fuzzy sets over universes with special forms

Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems

A Hesitant Soft Fuzzy Rough Set and its Applications

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