Hausdorffness on generalized intuitionistic fuzzy filters

Park, Jin Han; Park, Jin Keun

doi:10.1016/j.ins.2004.02.002

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…Therefore, the minimum operator appears to be a natural choice as a t-norm, and it is thoroughly studied [16]. Furthermore, GIFS-MSs are applied for fuzzy filtering [40], multiple criteria decision-making [41], and similarity measuring and pattern recognition [21]. The generalized IF index represents the degree of uncertainty of GIFS-MS, and it is given as follows:…”

Section: Definition 3 ([16]mentioning

confidence: 99%

A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

2021

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One of the main issues in IFS theory are generalizations of intuitionistic fuzzy set (IFS) definition as well as IFS operations. In this paper, we present the LBIFS-IBA approach by applying operations based on interpolative Boolean algebra (IBA) on generalized IFS. Namely, LBIFS are defined as a special case of Liu’s generalized IFS with the maximal interpretational surface. By extending the interpretational surface, the descriptive power of the approach is enhanced, and therefore the problematic situations when μA+νA>1 can be modeled. In addition, IBA-based algebra secures Boolean properties of the proposed approach. Considerable attention is given to comprehension of uncertainty within LBIFS-IBA, i.e., we propose a novel manner of uncertainty interpretation by treating values from [−1,1] interval. In order to prove its importance, we compare LBIFS-IBA with several well-known IFS generalizations, showing that only our approach offers meaningful uncertainty interpretation is all selected cases. Additionally, we illustrate the practical benefits of LBIFS-IBA by applying it to an example of modeling Japanese candlesticks for price charting and paying special attention to uncertainty interpretation.

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Section: Definition 3 ([16]mentioning

confidence: 99%

A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

2021

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“…Park [18] defined the notion of intuitionistic fuzzy metric spaces. Park and Park [19] introduced the notion of generalized intuitionistic fuzzy filters based on the notion of generalized intuitionistic fuzzy sets given by Mondal and Samanta [20], and defined the notion of Hausdorffness on generalized intuitionistic fuzzy filters. Deschrijver and Kerre [21] introduced the notion of uninorm in interval-valued fuzzy set theory.…”

Section: Introductionmentioning

confidence: 99%

A Method for Estimating Criteria Weights from Intuitionistic Preference Relations

2009

Fuzzy Information and Engineering

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An intuitionistic preference relation is a powerful means to express decision makers'information of intuitionistic preference over criteria in the process of multi-criteria decision making. In this paper, we first define the concept of its consistence and give the equivalent interval fuzzy preference relation of it. Then we develop a method for estimating criteria weights from it, and then extend the method to accommodate group decision making based on them And finally, we use some numerical examples to illustrate the feasibility and validity of the developed method.

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A Method for Estimating Criteria Weights from Intuitionistic Preference Relations

Advances in Soft Computing

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Hausdorffness on generalized intuitionistic fuzzy filters

Cited by 5 publications

References 11 publications

A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

A Method for Estimating Criteria Weights from Intuitionistic Preference Relations

A Method for Estimating Criteria Weights from Intuitionistic Preference Relations

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