Multi-criteria decision making method based on improved cosine similarity measure with interval neutrosophic sets

Abstract

Purpose The fuzziness and complexity of evaluation information are common phenomenon in practical decision-making problem, interval neutrosophic sets (INSs) is a power tool to deal with ambiguous information. Similarity measure plays an important role in judging the degree between ideal and each alternative in decision-making process, the purpose of this paper is to establish a multi-criteria decision-making method based on similarity measure under INSs. Design/methodology/approach Based on an extension of existing cosine similarity, this paper first introduces an improved cosine similarity measure between interval neutosophic numbers, which considers the degrees of the truth membership, the indeterminacy membership and the falsity membership of the evaluation values. And then a multi-criteria decision-making method is established based on the improved cosine similarity measure, in which the ordered weighted averaging (OWA) is adopted to aggregate the neutrosophic information related to each alternative. Finally, an example on supplier selection is given to illustrate the feasibility and practicality of the presented decision-making method. Findings In the whole process of research and practice, it was realized that the application field of the proposed similarity measure theory still should be expanded, and the development of interval number theory is one of further research direction. Originality/value The main contributions of this paper are as follows: this study presents an improved cosine similarity measure under INSs, in which the weights of the three independent components of an interval number are taken into account; OWA are adopted to aggregate the neutrosophic information related to each alternative; and a multi-criteria decision-making method using the proposed similarity is developed under INSs.

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

“…Hence, Equations (25), (31), and (35) are used in comparison to determine their relationship with α j of Equation (26). By the same observation, it is found that Equations (27), (32), and (36) are related to β j of Equation (28).…”

“…In Equations (25) and (27), the most natural approach f ðxÞ = x is applied by us. Meanwhile, in Equations (31) and (32), Ye and Fu [7] used f ðxÞ = tan ðπx/4Þ, and in Equations (35) and (36) For a similarity measure, say Sim, Simð0Þ = 1, and Simð1Þ = 0 are ideal, such as in Equations (25), (27), (31), and (32) and then abstractly expressed in Equations (33) and (34), researchers use 1 − ∑ m j=1 w j f ðα j Þ or 1 − ∑ m j=1 w j f ðβ j Þ.…”

“…Ninety-three papers have cited Ye [6] in their references. We list them in the following: Peng and Dai [8], Ye [9], Biswas et al [10], Broumi et al [11], Chatterjee et al [12,13], Cui and Ye [14], Fan [15], Fan et al [16], Fu et al [17], Gou and Wang [18], Jha et al [19,20], Li et al [21][22][23], Liu and Luo [24], Luo et al [25], Nancy and Garg [26], Nguyen et al [27], Peng [28], Peng and Dai [29], Rajangam and Annamalai [30], Şahin [31], Shao et al [32], Shi and Yuan [33], Tian et al [34], Wang et al [35], Wei and Zhang [36], Xie et al [37], Ye [38], Zhai et al [39], Zhang et al [40], Zhao et al [41], Akram et al [42], Ali et al [43], Cai and Yang [44], Fan et al [45], Garg and Nancy [46], Guan et al [47], Karaaslan and Hayat [48], Khanet al [49], Küçük and Şahin [50], Liu [51], Liu et al…”

Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

“…The decision making refers to the human activities that rank the alternatives and select the optimal ones [26,38,39,55]. It is extremely common in our daily life and national industrial development [10,13,23].…”

Modeling Multi-Criteria Decision-Making in Dynamic Neutrosophic Environments Bases on Choquet Integral

“…Choquet integral-based aggregation operator has been applied [8,9], and it has improved the weakness of simple weighted sum method. For example, if we consider a set of four alternatives {x 1 , x 2 , x 3 , x 4 } where each alternative x i is evaluated with three criteria to maximize: x 1 = (18; 10; 10), x 2 = (10,18,10), x 3 = (10,10,18), x 4 = (14,11,12), in truth, the alternative x 4 is not a selected solution with a weighted sum operator, however this alternative is the most balanced alternative and it would likely be a good option. This shortcoming has been overcome by defining a new operator using Choquet integral to make fuzzy measurement [6].…”