Similarity Measures of T-Spherical Fuzzy Sets Based on the Cosine Function and Their Applications in Pattern Recognition

In this manuscript, nine similarity measures of T-spherical fuzzy set (TSFS) considering the membership degree, the hesitancy degree, the non-membership degree and the refusal degree are developed according to the cosine function. Besides, the generalizations of existing similarity measures are the similarity measures of TSFS proposed in this paper, which indicates the breadth and novelty of the proposed similarity measures. More importantly, the nine similarity measures of TSFSs are applied to pattern recognition. Then, we make a comparative study, that is, we apply the nine similarity measures of TSFSs developed in this manuscript to picture fuzzy environment, and the results obtained are consistent with the previous results. This application make the problem of building material recognition better solved in the real world. Finally, two numerical examples show the validity of the proposed similarity measure between TSFSs.


I. INTRODUCTION
The similarity measures are significant and useful measuring tools for determining the degree of similarity between two objects. Similarity measures between fuzzy sets have attracted the attention of researchers because of its wide application in various fields such as image processing [1], pattern recognition [2] and decision-making [3], [4]. In recent years [5]- [8], many related researchers have proposed and discussed various similarity measures between fuzzy sets. With the continuous development of fuzzy sets, fuzzy sets have become a very practical method to process uncertain information and multi-attribute decision-making (MADM) problems. Zadeh introduced the fuzzy set theory [9] in 1965, and the fuzzy set theory is one of the most widely used applications in the practical application of uncertainty modeling. The characteristic function on the unit interval [0, 1] defined the membership degree of the set element s of the fuzzy set. By subtracting membership degree from 1, the non-membership degree of fuzzy set is obtained.
The associate editor coordinating the review of this manuscript and approving it for publication was Hualong Yu .
The concept of zadeh's fuzzy set is extended by Atanassov [10]- [12] to intuitionistic fuzzy set (IFS), and Atanassov [10]- [12] independently defined IFS' membership degree and non-membership degree, namely s and d. But, the sum of the membership degree and the non-membership degree of IFSs must belong to the interval [0,1], namely Sum (s, d) ∈ [0,1]. What's more, the hesitancy degree is 1 − Sum (s, d). The reason why IFS is widely used in various fields [13] is that it is more capable of handling and expressing uncertain information. A good similarity measure between IFSs was developed by Li and Cheng [14], and this similarity measure was used to pattern recognition. More importantly, the similarity measure of Li and Cheng [14] was improved by Mitchell [15]. With the extension of the hamming distance on the fuzzy set as the background, a similarity measure between IFSs was proposed by Szmidt and Kacprzyk [16] according to the hamming distance. According to the Hausdorff distance, the distance between IFSs was successfully calculated by Hung and Yang [17], and some similarity measures were produced between IFSs. A few novel similarity measures between elements and IFSs were proposed by Liu [18]. According to VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ some aggregation operators, a few IFSs' similarity measures were developed by Xia and Xu [19], and they were applied to group decision making problems. According to the operational principle of fuzzy numbers, the Hamy Mean (HM) operator was improved by Liu and Liu [20] to linguistic intuitionistic fuzzy numbers (LIFNs), and it was used to multiple-attribute group decision making. The cosine similarity measure between IFSs was developed by Ye [21]. Then, the IFSs' cosine similarity measures were improved by Shi and Ye [22]. Besides, the cotangent similarity measure between IFSs was developed by Tian [23] based on cotangent function, and it was used to medical diagnosis. Furthermore, the cotangent similarity measure among IFSs considering membership, non-membership and hesitancy degree was proposed by Rajarajeswari and Uma [24]. With the help of the cosine function, two novel cosine similarity measures and weighted cosine similarity measures that consider membership, non-membership and hesitancy degree were developed by Ye [25]. The intuitionistic vector similarity measures were proposed by Son and Phong [26], and they were applied to medical diagnosis. In some cases, the Sum (s, d) exceeds the interval [0,1]. At this time, the value cannot be assigned to the characteristic function, so Atanassov's IFS model is limited. Therefore, the structure of the Pythagorean fuzzy set (PyFS) was developed by Yager [27], Yager and Abbasov [28]. Then, this extended the scope of IFS because the values' range of the membership degree of PyFS is Sum s 2 , d 2 ∈ [0,1]. Wei and Wei [29] developed ten similarity measures of PyFS, including cosine similarity measures, weighted cosine similarity measures, cotangent similarity measures and weighted cotangent similarity measures. And these similarity measures were applied to pattern recognition and medical diagnosis. Peng and Yang [30] developed a Pythagorean advantage and disadvantage ranking model, and applied it to the uncertainty multi-attribute group decision making problem. Garg [31] proposed a new improved precision function of internal valued PyFSs and applied it to the decision making process. With the help of Pythagorean fuzzy power aggregation operators, the Pythagorean fuzzy multiple attribute decision-making problems were handled by Wei and Lu [32]. Similarly, a symmetric Pythagorean fuzzy weighted geometric operator which applied to multiple criteria decision problem was developed by Ma and Xu [33].
Here, the structures of the FSs have been successfully improved by the structures of the IFSs. However, in the case of voting (vote in favor, hesitation, vote against, and refusal) with more than two characteristic functions, the model of Atanassov's IFS cannot explain this. Therefore, Cuong [34] developed a structure that uses s, i and d to represent three characteristic functions, called picture fuzzy set (PFS). Then, the sum of the three characteristic functions of PFS must belong to [0,1], that is, Sum (s, i, d) ∈ [0,1]. Besides, the refusal degree of PFS is 1−Sum (s, i, d). A new decentralized picture fuzzy clustering method was proposed by Son [35] and applied to various practical problems. A new hybrid method among intuitionistic fuzzy recommender system and picture fuzzy clustering was gave by Thong and Son [36], and this new method was used to medical diagnosis. A picture fuzzy cross-entropy model was developed by Wei [37] and applied to multi-attribute decision making (MADM). Wei [38] developed eight similarity measures of PFS, including cosine similarity measures, weighted cosine similarity measures, cotangent similarity measures and weighted cotangent similarity measures. And these similarity measures were applied to strategic decision making. Based on picture fuzzy information, Wei and Gao [39] developed a generalized dice similarity measure model and applied it to the field of building material recognition.
Although the structures of PFSs have successfully improved the structures of FSs and IFSs, the structure of PFSs still has certain limitations in some cases. In other words, PFSs cannot independently assign membership degrees of characteristic functions. Based on the Reference [10], [27], [34], a new model of spherical fuzzy set (SFS) was developed by Mahmood et al. [40]. Since this new model extended the range of PFSs, it became a generalization of PFSs. Here, three characteristic functions of SFSs are represented by s, i and d. Although sometimes the sum of s, i and d may exceeded [0,1] interval, their sum of squares must be in the interval [0,1], that is, 1]. This made the range of SFSs larger than PFSs. In the case of s = 0.8, i = 0.6 and d = 0.7, then Sum 0.8 2 , 0.6 2 , 0.7 2 = 1.49 is greater than 1, so the range of SFSs is limited. To solve this situation, a model called T-spherical fuzzy set (TSFS) was firstly developed by Smarandache [41] who called it n-hyperspherical fuzzy set (and it is a particular case of the neutrosophic set) and then by Mahmood et al. [40]. Here, the reason why the structure of TSFS is completely unrestricted is that the three characteristic functions of TSFS are represented by s, i and d, and they satisfy Sum (s n , i n , d n ) ∈ [0, 1], n ∈ Z . Considering this new condition, for a triplet (0.8,0.6,0.7) and n = 4, Sum 0.8 4 , 0.6 4 , 0.7 4 = 0.7793 ∈ [0, 1]. Then, the view of Mahmood et al. [40] is strengthened, that is, TSFS is the generalization structure of IFS, PFS and SFS. Rafiq et al. [42] developed ten similarity measures of SFS, including cosine similarity measures, weighted cosine similarity measures, cotangent similarity measures and weighted cotangent similarity measures. And these similarity measures were applied to building material recognition. With the help of linguistic spherical fuzzy sets, Liu et al. [43] developed an approach based on linguistic fuzzy for public evaluation of shared bicycles in China. Ullah et al. [44] developed a note on geometric aggregation operators in Spherical fuzzy environment and applied it to multi-attribute decision making. Ullah et al. [45] developed some correlation coefficients for T-spherical fuzzy sets and applied them to clustering and multi-attribute decision making. According to T-spherical fuzzy graphs' notion, two algorithms for solving supply chain management and service center evaluation problems were developed by Guleria and Bajaj [46]. Quek et al. [47] proposed a novel method based on generalized T-spherical fuzzy weighted aggregation operators on neutrosophic sets and applied it to multi-attribute decision making problem. Ullah et al. [48] developed a multi-attribute decision making method based on the interval-valued T-spherical fuzzy set (IVTSFS) and applied it to policy evaluation. With the help of the improved interactive aggregation operators, a new algorithm of T-spherical fuzzy multi-attribute decision making for multi-attribute group decision making problems was developed by Garg et al. [49]. With the help of novel operational laws, Liu et al. [50] developed a T-spherical fuzzy power muirhead mean operator and applied it to multi-attribute group decision-making problems.
A T-spherical divergence measure based on Jensen-Shannon divergence measure was proposed by Wu et al. [51], and it was applied in the field of building material recognition. Ullah et al. [52] developed the concepts of T-spherical fuzzy Hamacher-weighted averaging and T-spherical fuzzy Hamacher-weighted geometric aggregation operators and applied they to multi-attribute group decision-making problems. Khan et al. [53] developed some interval-neutrosophic Dombi PBM operator and applied they to multi-attribute group decision-making problems. Some T-spherical fuzzy einstein hybrid aggregation operators were developed by Munir et al. [54], and they were applied to multi-attribute decision-making problems.
Developing some similarity measures for TSFS is the purpose of this article. The limitations of some existing similarity measures [14], [17], [29], [38], [42], [55] and the problem that these similarity measures can not be used to information which provided in TSFS environment are discussed in this manuscript. In order to solve this problem, we propose some new TSFS's similarity measures. Moreover, the generalizations of existing similarity measures [14], [17], [29], [38], [42], [55] are the similarity measures of TSFS proposed in this paper. Therefore, it is worth noting that the special cases of the similarity measures proposed in this paper are the similarity measures of the References [14], [17], [29], [38], [42], [55], which indicates the breadth and novelty of the proposed similarity measures. The new similarity measures are applied to solve the problem of pattern recognition. Then we discussed the results.
The subsequent parts of this manuscript are arranged as follows. The Part 2 describes the preconditions of the work in detail. In Part 3, nine novel similarity measures of TSFS are developed. Two numerical examples in Part 4, 5 illustrate the rationality of the proposed similarity measures. Finally, the conclusions are given in Part 6.

II. PRELIMINARIES
In this section, some basic concepts and similarity measures related to IFS, PyFS, PFS, and SFS are reviewed.
Definition 1 [10], [12]: Let X is a finite domain. Then the form I = { x, s(x), d(x) } is an IFS in X , and the membership degree and the non-membership degree of x ∈ X in the interval [0, 1] are represented by s and d, respectively.
The sum of s and d is in the range of 0 ≤ Sum(s, d) ≤ 1. And r(x) = 1 − Sum (s, d) is the hesitancy degree. Furthermore, the intuitionistic fuzzy number (IFN) is the duplet (s, d).
Place I 1 = x, s I 1 (x), d I 1 (x) and I 2 = x, s I 2 (x), d I 2 (x) be two IFSs in the X . The cosine similarity measure of IFSs I 1 and I 2 was developed by Ye [21] as follows: In considering the membership degree, non-membership degree and hesitancy degree, the cosine similarity measure of IFSs was further developed by Shi and Ye [22] as (2), shown at the bottom of the next page.
According to the cosine function, two cosine similarity measures of IFSs I 1 and I 2 were developed by Ye [25]: where the symbol ∨ is the maximum operation. Besides, a cotangent similarity measure of IFSs I 1 and I 2 was developed by Tian [23] as follows: In considering the membership degree, hesitancy degree and non-membership degree, the cotangent similarity measure of IFSs was developed by Rajarajeswari and Uma [24] as follows: where the symbol ∨ is the maximum operation. Definition 2 [27]: Let X is a finite domain. Then the form P y = { x, s(x), d(x) } is a PyFS in X , and the membership degree and the non-membership degree of x ∈ X in the interval [0, 1] are represented by s and d, respectively. The sum of squares of s and d is in the range of 0 ≤ Sum(s 2 , d 2 ) ≤ 1. And r(x) = 1−Sum s 2 , d 2 is the hesitancy degree. Furthermore, the Pythagorean fuzzy number (PyFN) is the duplet (s, d).
Place P y 1 = x, s P y 1 (x), d P y 1 (x) and P y 2 = x, s P y 2 (x), d P y 2 (x) be two PyFSs in the X . The cosine similarity measure of PyFSs P y 1 and P y 2 was developed by Wei and Wei [29] as (7), shown at the bottom of the next page. VOLUME 8, 2020 In considering the membership degree, hesitancy degree and non-membership degree, the cosine similarity measure of PyFSs P y 1 and P y 2 was developed by Wei and Wei [29] as (8), shown at the bottom of the this page.
If consider the weights of ω i = 1, Wei and Wei [29] developed the weighted cosine similarity measures of PyFSs P y 1 and P y 2 as (9) and (10), shown at the bottom of the this page.
According to the cosine function, Wei and Wei [29] developed the cosine similarity measures of PyFSs P y 1 and P y 2 as follows: where the symbol ∨ is the maximum operation. Definition 3 [34]: Let X is a finite domain. Then the form Place be two PFSs in the X .
According to the cosine function, the cosine similarity measures of PFSs P 1 and P 2 were developed by Wei [38] as follows: where the symbol ∨ is the maximum operation. Definition 4 [40]: Let X is a finite domain. Then the form is the refusal degree. Furthermore, the spherical fuzzy number (SFN) is the triplet (s, i, d).

III. SOME SIMILARITY MEASURES BASED ON THE COSINE FUNCTION FOR T-SPHERICAL FUZZY SETS
Definition 5 [40]: Let X is a finite domain. Then the 98184 VOLUME 8, 2020

A. COSINE SIMILARITY MEASURE FOR TSFSS
Definition 6 [56]: Place T 1 = x, s T 1 (x), i T 1 (x), d T 1 (x) and T 2 = x, s T 2 (x), i T 2 (x), d T 2 (x) be two TSFSs in the X , a cosine similarity measure of TSFSs T 1 and T 2 is developed as (15), shown at the bottom of the next page.
In the case of t = 1, this cosine similarity measure becomes the correlation coefficient between TSFSs T 1 and T 2 . In other words, So, the following properties are also suitable for the cosine similarity measure of TSFSs D, G and M : Property 1: Let D, G and M be three TSFNs, then . Proof is shown in Reference [56].
Definition 7 [56]: The distance measure of the angle between two TSFNs T 1 and T 2 is developed as follows: Here, the following properties are suitable for the distance measure of the angle of three TSFNs D, G and M : Place In considering the membership degree, hesitancy degree, non-membership degree and refusal degree of TSFS, we develop the cosine similarity measure between TSFSs as (16), shown at the bottom of the next page.
In the case of t = 1, this cosine similarity measure becomes the correlation coefficient between TSFSs T 1 and T 2 . In other words, So, the following properties are also suitable for the cosine similarity measure of TSFSs D and G: Property 3: Let D and G be two TSFNs, then S TSFS (D, G) = 1 if D = G and i = 1, 2, · · · , t. Proof: x Obviously, this property is correct according to the cosine value.
y Obviously, this property is correct.
If ω i is the weight, we develop the weighted cosine similarity measures of TSFSs T 1 and T 2 as (17) and (18), shown at the bottom of the next page.
Here, the weight vector is ω i = (ω 1 , ω 2 , · · · , ω t ) T . And In the case of ω = (1/t, 1/t, · · · , 1/t) T , then the weighted cosine similarity measure degenerates to cosine similarity measure. In other words, when ω i = 1/t, i = 1, 2, · · · , t, then is obtained. Similarly, the following properties are also suitable for the weighted cosine similarity measure of TSFSs D and G: Property 4: Let D and G be two TSFNs, then S TSFS (D, G) = 1 if D = G and i = 1, 2, · · · , t. According to the previous proof method, we can get a similar proof.

B. SIMILARITY MEASURES OF TSFSS BASED ON THE COSINE FUNCTION
With the help of the cosine function, the four cosine similarity measures of TSFSs are developed in this part, and their properties are analyzed.
Definition 8: Place X = {x 1 , x 2 , · · · , x t } is a finite domain, and T 1 = x, s T 1 (x), i T 1 (x), d T 1 (x) and T 2 = x, s T 2 (x), i T 2 (x), d T 2 (x) in X be two TSFSs. We develop the cosine similarity measures of TSFSs as follows: where the symbol ∨ is the maximum operation.
The following properties are also suitable for the cosine similarity measures TSFCS k (T 1 , Proof: x Obviously, this property is correct according to the cosine value. VOLUME 8, 2020 y Obviously, this property is correct.
When the cosine function is on the interval [0, π /2], it is a decreasing function. So, for k = 1, 2 is obtained.
So we have completed the above proofs.
Similarly, the following properties are also suitable for the weighted cosine similarity measure WTSFCS k (T 1 , T 2 ), (k = 1, 2, 3, 4): Property 6: Let D and G be two TSFNs, then . By using previous proof, we can finish the proofs.

C. SIMILARITY MEASURES OF TSFSS BASED ON THE COTANGENT FUNCTION
The four cotangent similarity measures of TSFSs are developed in this part.
Definition 9: Place X = {x 1 , x 2 , · · · , x t } is a finite domain, and T 1 = x, s T 1 (x), i T 1 (x), d T 1 (x) and T 2 = x, s T 2 (x), i T 2 (x), d T 2 (x) in X be two TSFSs. We develop VOLUME 8, 2020 the cotangent similarity measures of TSFSs as follows: where the symbol ∨ is the maximum operation. Place T 1 = x, s T 1 (x), i T 1 (x), d T 1 (x) and T 2 = x, s T 2 (x), i T 2 (x), d T 2 (x) be two TSFSs in the domain of X = {x 1 , x 2 , · · · , x t } . What's more, in considering the membership degree, hesitancy degree, non-membership degree and refusal degree of TSFS, we develop two cotangent similarity measure between TSFSs as follows: where the symbol ∨ is the maximum operation. The weight of the elements x i ∈ X is considered by the researchers in many cases. For example, in multiple attribute decision making, since different attributes have different importance, different weights are usually assigned to Here, the weight vector is ω i = (ω 1 , ω 2 , · · · , ω t ) T , and the symbol ∨ is the maximum operation. And there is ω i ∈ [0, 1] , i = 1, 2, · · · , t, t i=1 ω i = 1. In the case of ω = (1/t, 1/t, · · · , 1/t) T , then the weighted cotangent similarity measure degenerates to cotangent similarity measure. In other words, when ω i = 1/t, i = 1, 2, · · · , t, then WTSFCT k (T 1 , T 2 ) = TSFCT k (T 1 , T 2 ) , k = 1, 2, 3, 4 is obtained.

IV. APPLICATION IN BUILDING MATERIAL RECOGNITION
The tools of similarity measures have been widely used in multi-attribute decision making. Therefore, we apply the similarity measures proposed in this paper to a building material recognition problem [56] that requires evaluating for unknown building materials.
Example 1: Place TSFNs T i (i = 1, 2, 3, 4) on X = {x i : i = 1, 2, 3, . . . , 7} represent four building materials. And the weight is ω = (0.16, 0.12, 0.09, 0.18, 0.20, 0.10, 0.15) T in this example. Besides, the data of Table 1 is applied to the similarity measures of TSFS proposed in this paper. Then the values of the similarity measures of TSFSs are used to evaluate the unknown building material T .
The data of TSFNs at n = 4 in Table 1 cannot be processed by the similarity measures of IFSs and PFSs. Since there is only n = 2 in the SFSs, even the similarity measures of SFSs cannot process the data of Table 1. This illustrates the power and diversity of similarity measures for TSFSs. Therefore, we apply the similarity measures of the TSFSs developed in this paper to the data in Table 1. And the results are shown in Table 2.
According to the numerical results shown in Table 2, except for WTSFCS 2 (T i , T ) and WTSFCT 2 (T i , T ) , i = 1, 2, 3, 4, it can be concluded that the degree of similarity of T 2 and T is the largest of nine similarity measures of TSFSs. In other words, based on the principle of maximum degree of the similarity measure of TSFSs, the seven similarity measures of TSFSs recognize the unknown building material T as the known building material T 2 . With reference to the similarity measures proposed by Ullah [56], we obtain consistent results that the seven similarity measures of TSFSs recognize the unknown building material T as the known building material T 2 . This shows that the proposed method of similarity measures of TSFSs is completely feasible.

V. COMPARATIVE STUDY AND ADVANTAGES
Now, we use the similarity measures of TSFS for n = 1 proposed in this manuscript to solve the problem of building material recognition in the Reference [57].
Example 2: For the problem from the Reference [57], 1, 2, 3, 4) represents four building materials. And the weight is ω = (0.12, 0.15, 0.09, 0.16, 0.20, 0.10, 0.18) T in this example. And the data of Table 3 is applied to the similarity measures of TSFS proposed in this manuscript. Then the values of the similarity measures of TSFSs are used to evaluate the unknown building material T .
The purpose of this building material recognition problem is to identify pattern T as one of the categories T i (i = 1, 2, 3, 4) . Table 3 provides the data in the picture fuzzy environment. Therefore, when we use the similarity measures of TSFS proposed in this manuscript for table 3, place n = 1. And the results obtained are shown in Table 4.
According to the numerical results shown in Table 4, it can be concluded that the degree of similarity of T 4 and T is the largest of nine similarity measures of TSFSs. In other words, based on the principle of maximum degree of the similarity measure of TSFSs, all nine similarity measures of TSFSs recognize the unknown building material T as the known building material T 4 . With reference to the similarity measures proposed by Wei [57], we obtain consistent results. This further strengthens the feasibility and superiority of the proposed method of similarity measures of TSFSs. Similarly, respectively let i T 1 (x) = i T 2 (x) = 0, n = 2 and n = 2, then the similarity measures developed in this manuscript can also handle the information in the PyFSs and SFSs environment. In contrast, the similarity measures of PyFSs, PFSs and SFSs cannot handle the information in the TSFSs environment.
Although the structures of SFSs have successfully improved the structures of FSs, IFSs, PyFSs and PFSs, the structure of SFSs still has certain limitations in some cases. Extensions to FSs, IFSs, PyFSs, PFSs, and SFSs are TSFSs. TSFSs have the membership function, hesitancy function and non-membership function. And the condition is that the sum of the three characteristic functions is less than or equal to 1. In some cases, TSFSs can handle information that SFSs and PyFSs cannot process. For instance, in the case of s = 0.6, i = 0.7 and d = 0.8, then Sum 0.6 2 , 0.7 2 , 0.8 2 = 1.49 is greater than 1, so the range of SFSs is limited. Nevertheless, for the triplet (0.6,0.7,0.8) in TSFSs, let n = 4, then Sum 0.6 4 , 0.7 4 , 0.8 4 = 0.7793 is less than 1. That is to say, the special part of the T-spherical fuzzy degrees is all the Pythagorean fuzzy degrees and spherical fuzzy degrees, which indicates that TSFS is more powerful in dealing with uncertainty information. Therefore, the similarity measure of TSFS is more suitable to solve the problem of multi-attribute decision making in practice.

VI. CONCLUSION
The background of IFSs, PyFSs, PFSs and SFSs and the limitations of their structures were discussed in detail in this manuscript. With the help of some numerical examples, how to use the structure of TSFS to improve the existing structure is discussed. In this manuscript, nine similarity measures of TSFSs considering the membership degree, hesitancy degree, non-membership degree and refusal degree were developed according to the cosine function. Besides, the generalizations of existing similarity measures are the similarity measures of TSFS proposed in this paper. In other words, it is worth noting that the special cases of the similarity measures proposed in this paper are the existing similarity measures, which indicates the breadth and novelty of the proposed similarity measures. More importantly, the nine similarity measures of TSFSs were applied to pattern recognition. This application made the problem of pattern recognition better solved in the real world. Then, we made a comparative study, that is, we applied the nine similarity measures of TSFSs developed in this manuscript to picture fuzzy environment, and the results obtained are consistent with the previous results. Finally, two numerical examples showed the validity of the proposed similarity measure between TSFSs. On the other hand, since the range of interval-valued T-spherical fuzzy sets is wider, we will further study the interval-valued T-spherical fuzzy sets in the future. In addition, we will develop some divergence measures and distances of intervalvalued T-spherical fuzzy sets, and apply these extended researches of interval-valued T-spherical fuzzy sets to clustering, pattern recognition, medical diagnosis and multiattribute decision making.