Vague Correlation Coefficient of Interval Vague Sets

Robinson, Philip J.; Amirtharaj, E. C. Henry

doi:10.4018/ijfsa.2012010102

Cited by 21 publications

(17 citation statements)

References 24 publications

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“…Thus, with the development of GrC, multi-granularity knowledge discovery has become an important direction in the research of artificial intelligence. The uncertainty of the decision information systems is an important parameter for obtaining a good decision-making [9], [20], [38], [40], [50], [61]. In a great deal of literatures [15], [22], [29], [31], [32], [39], many researchers came into conclusion that how to describe a vague concept with an approximation set in rough knowledge space is the priority.…”

Section: Introductionmentioning

confidence: 99%

“…Bonikowski and Wybraniec-Skardowska [4] proposed a new formal approach to vagueness, and many important conditions concerning the membership relation for vague sets were established as well. John and Amirtharaj [20] proposed a novel similarity measure based on statistical confidence intervals and discussed its rules in multi-granularity spaces.…”

Section: Introductionmentioning

confidence: 99%

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The Uncertainty Analysis of Vague Sets in Rough Approximation Spaces

2019

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Vague sets, as well as intuitionistic fuzzy sets, are extensions of fuzzy sets. Based on fuzzy sets, vague sets generalize the membership degree from a single value to an interval value. Vague sets have a more powerful ability to process fuzzy information than fuzzy sets to some degree. In addition as we all know, human cognition is usually a gradual process. As a result, in a given multi-granularity space, how to characterize a vague concept and further measure its uncertainty, become a hot issue worth studying. However, the uncertainty of vague sets in rough approximation spaces is still lacking relative studies. Therefore, in order to more effectively excavate knowledge from vague sets, this paper focuses on the uncertainty of vague sets and reveals its hidden rules. First, change rules of the average fuzziness of the vague value with changing its truth membership degree and false membership degree are discussed. Second, in rough approximation spaces, the uncertainty of vague sets, i.e., the uncertainty of average-stepvague sets are analyzed. Then, its change rules with changing granularity are analyzed and discussed. Next, to better approximate a vague concept, change rules of uncertainty for approximation sets of vague sets with changing knowledge granularity are discussed. Finally, several illustration examples are listed to verify the obtained conclusions. These rules are in accordance with human cognitive mechanisms in multi-granularity knowledge spaces.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Uncertainty Analysis of Vague Sets in Rough Approximation Spaces

2019

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“…Park et al [22] proposed the correlation coefficient of interval valued intuitionistic fuzzy sets. Robinson and Amirtharaj [23][24][25][26] proposed correlation coefficient for vague sets, interval vague sets, triangular and trapezoidal IFSs, and a revised correlation coefficient for triangular and trapezoidal IFSs using graded mean integration representation. In this paper, a novel method of correlation coefficient of trapezoidal fuzzy intuitionistic fuzzy sets (TzFIFSs) is proposed and developed by taking into account the membership, nonmembership, and the hesitation degrees of TzFIFSs.…”

Section: Introductionmentioning

confidence: 99%

MADM Problems with Correlation Coefficient of Trapezoidal Fuzzy Intuitionistic Fuzzy Sets

Robinson¹,

Amirtharaj²

2014

Advances in Decision Sciences

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This paper discusses on the notion of trapezoidal fuzzy intuitionistic fuzzy sets (TzFIFSs) and some of the arithmetic operations of the same. Correlation coefficient of TzFIFS is proposed based on the membership, nonmembership, and hesitation degrees. The weighted averaging (WA) operator and the weighted geometric (WG) operator are proposed for TzFIFSs. Based on these operators and the correlation coefficient defined for the TzFIFS, new multiattribute decision making (MADM) models are proposed and numerical illustration is given.

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“…Correlation coefficient is used as a tool to rank alternatives since it preserves the linear relationship between the variables. Robinson & Amirtharaj [11][12][13][14][15] defined correlation coefficient for Interval vague sets and triangular and trapezoidal intuitionistic fuzzy sets and proposed different MAGDM algorithms. Wei et al [21] and Park et al [9] have also adopted correlation coefficient as a ranking tool for deciding the best alternatives.…”

Section: Introductionmentioning

confidence: 99%

Interval Valued Intuitionistic Fuzzy MAGDM Problems with OWA Entropy Weights

Solairaju¹,

Robinson²,

Rethinakumar³

2014

IJMTT

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In this paper, the Multiple Attribute Group Decision Making (MAGDM) problems is based on the Renyi's, Daroczy's and R-norm entropy weights especially when the attribute weights are completely unknown. The interval-valued intuitionistic fuzzy ordered weighted averaging (IIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid averaging (IIFHA) operator are utilized to aggregate the interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers. Correlation coefficient of Interval Valued Intuitionistic Fuzzy Sets (IVIFS) is utilized to rank the alternatives and select the most desirable one. A numerical illustration is presented to demonstrate the proposed approach.

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Vague Correlation Coefficient of Interval Vague Sets

Cited by 21 publications

References 24 publications

The Uncertainty Analysis of Vague Sets in Rough Approximation Spaces

The Uncertainty Analysis of Vague Sets in Rough Approximation Spaces

MADM Problems with Correlation Coefficient of Trapezoidal Fuzzy Intuitionistic Fuzzy Sets

Interval Valued Intuitionistic Fuzzy MAGDM Problems with OWA Entropy Weights

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