Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making

Dutta, Palash; Saikia, Bornali

doi:10.1007/s41066-019-00175-5

Cited by 38 publications

(7 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, its limitations were discussed in the same as it fails to rank the images consistently in some situations. Proportionally, Dutta and Saikia 24 built up a strategy for ordering IFNs, in light of the idea of convex combination of "value" multiplied with "mean" of the membership and the nonmembership function following Chutia and Saikia. 23 Be that as it may, the images of the IFNs were not incorporated in their investigation.…”

Section: The Literature Reviewmentioning

confidence: 99%

Ordering intuitionistic fuzzy numbers by a convex combination of values and multiple of ambiguity inclusion functions with ambiguities of membership and nonmembership functions

Chutia

2021

Int J Intell Syst

View full text Add to dashboard Cite

Ranking methods of intuitionistic fuzzy numbers are abundant in literature. However, an adequately accepted approach of ordering intuitionistic fuzzy numbers is not apparent. This motivates to develop a new method of ordering intuitionistic fuzzy numbers. In many cases, studies of ranking intuitionistic fuzzy numbers do not investigate the reasonable properties that a ranking method should follow. Furthermore, the majority of existing methods do not meet the reasonable properties. Furthermore, investigating the consistency in image ordering was never a concern in previous studies of ranking intuitionistic fuzzy numbers. Hence, in this paper, an innovative method of ranking intuitionistic fuzzy numbers has been developed. The method is based on the index of optimism, that is, a convex combination of value and multiple of ambiguity inclusion function with ambiguity of membership function and value and multiple of ambiguity inclusion function with ambiguity of nonmembership function. The present method exclusively complies with the reasonable properties as it satisfies all the reasonable properties of a ranking method. Further, newer properties that depicts the consistency in ranking the intuitionistic fuzzy numbers with their corresponding images are also being developed in this study. It is worth mentioning that the present method consistently ranks the intuitionistic fuzzy numbers and their corresponding images.

show abstract

Section: The Literature Reviewmentioning

confidence: 99%

Ordering intuitionistic fuzzy numbers by a convex combination of values and multiple of ambiguity inclusion functions with ambiguities of membership and nonmembership functions

Chutia

2021

Int J Intell Syst

View full text Add to dashboard Cite

show abstract

“…In this section, basic operations on SEFVs are reviewed and adopted from [41]. Suppose A = S E (a, h) and B = S E (b, k) are two SEFVs defined on a universe of discourse X.…”

Section: Arithmetic On Sefvsmentioning

confidence: 99%

Mathematics of uncertainty: an exploration on semi-elliptic fuzzy variable and its properties

Dutta

2019

SN Appl. Sci.

Self Cite

View full text Add to dashboard Cite

Uncertainty is more or less encountered in industrial and medical systems as well. Uncertainty theory is an upgraded theory which comprises of possibility measure, necessity measure and credibility measure plays significant role in modelling uncertainty. In connection with uncertainty modeling, a special and intricate fuzzy variable viz., semi-elliptic fuzzy variable (SEFV) is thrashed out here. Subsequently, an attempt has been made to derive possibility, necessity and credibility measure of the SEFV first. Later, some other properties such as expected value, variance, rational upper bound etc are presented and based on that mean and variance ranking of SEFVs are proposed. Afterwards reliability analysis and medical diagnosis cases are carried out which exhibit the efficiency and novelty of the derived SEFV. In this work done, it is observed that the present work has the capability to resolve problems under uncertain complex situations. better to treat uncertainty and further studied by acolyte researchers such as Dubois and Prade [26], Klir [27], Yager [28] etc. Furthermore, Dubois and Prade [29] studied mean value of fuzzy numbers, Ban [30] discussed fuzzy valued measure and conditional expectations of fuzzy numbers, Heilpern [31]studied expected value of fuzzy numbers, Carlsson and Fuller [32] developed possiblistic mean and variance of fuzzy numbers, Chen and Tan [33] further developed mean value and variance of multiplication of fuzzy numbers. Nevertheless in the absence of self duality measure the earlier studies lead to the exaggeration of the reality. keeping this in mind, Liu and Liu [34] initiated a concept termed as credibility theory. Li and Liu [35] presented a sufficient and necessary condition for credibility measures. Further Liu and Liu [36] systematically studied and developed credibility theory. After that some extended studies on credibility theory can be observed in Liu [37], Zhou et al. [38], Yi et al. [39], Garai et al. [40].Although various types of fuzzy variables are encountered, however, an exceptional and intricate fuzzy variable SEFV in terms of credibility theory is not deliberated yet. This paper presents an approach to derive possibility, necessity and credibility measure of the SEFV. Furthermore, expected value, variance, rational upper bound etc of SEFV are presented. Then ranking of SEFNs through expected value and variance is proposed. Finally, novelty and applicability has been exhibited by performing reliability analysis and medical diagnosis cases.

show abstract

“…Considering the high complexity of decision making, the evaluation information provided by the public and experts is usually given in the form of fuzzy numbers. At present, the common forms of fuzzy numbers include interval numbers [31], triangular fuzzy numbers [32], intuitionistic fuzzy numbers [33], linguistic variables [34], and so on. For the decision problems studied in this article, the public and experts are more likely to express their opinions in subjective ways.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Agent Linguistic-Style Large Group Decision-Making Method Considering Public Expectations

Zhu

Cai

Pan

et al. 2021

Int J Comput Intell Syst

View full text Add to dashboard Cite

Focusing on the characteristics of public participation and large group decision making of major livelihood projects, this paper proposes a multi-agent linguistic-style large group decision-making method with the consideration of public expectations. Firstly, based on the discrimination degree of evaluating information, the comprehensive weight of each attribute is calculated with the principle of maximum entropy. Secondly, the expert preference information for different alternatives is clustered and several aggregations are formed. Thirdly, the preference conflict level of experts' group for each alternative is calculated, and a conflict-oriented experts' aggregation weight optimization model is constructed to ensure the effectiveness of conflict resolution. Fourthly, the public group's satisfaction is determined with the expectation distribution of public’s and the expert group's preference, so as to obtain the sorting result of the decision alternatives. Finally, the effectiveness and applicability of the proposed method are verified by method comparison.

show abstract

Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making

Cited by 38 publications

References 13 publications

Ordering intuitionistic fuzzy numbers by a convex combination of values and multiple of ambiguity inclusion functions with ambiguities of membership and nonmembership functions

Ordering intuitionistic fuzzy numbers by a convex combination of values and multiple of ambiguity inclusion functions with ambiguities of membership and nonmembership functions

Mathematics of uncertainty: an exploration on semi-elliptic fuzzy variable and its properties

A Multi-Agent Linguistic-Style Large Group Decision-Making Method Considering Public Expectations

Contact Info

Product

Resources

About