Hydrogen Production Technologies Evaluation Based on Interval-Valued Intuitionistic Fuzzy Multiattribute Decision Making Method

. We establish a decision making model for evaluating hydrogen production technologies in China, based on interval-valued intuitionisticfuzzysettheory.Firstofall,weproposeaseriesofinteractioninterval-valuedintuitionisticfuzzyaggregationoperators comparingthemwithsomewidelyusedandcitedaggregationoperators.Inparticular,wefocusonthekeyissueoftherelationships betweentheproposedoperatorsandexistingoperatorsforclearunderstandingofthemotivationforproposingtheseinteraction operators.Thisresearchthenstudiesagroupdecisionmakingmethodfordeterminingthebesthydrogenproductiontechnologies usinginterval-valuedintuitionisticfuzzyapproach.Theresearchresultsofthispaperaremorescientificfortworeasons.First,the interval-valuedintuitionisticfuzzyapproachappliedinthispaperismoresuitablethanotherapproachesregardingtheexpression ofthedecisionmaker’spreferenceinformation.Second,theresultsareobtainedbytheinteractionbetweenthemembership degreeintervalandthenonmembershipdegreeinterval.Additionally,weapplythisapproachtoevaluatethehydrogenproduction technologiesinChinaandcompareitwithothermethods.


Introduction
One of the important parts of multicriteria decision making is intuitionistic fuzzy multiattribute decision making, and it is an important branch of operations research and management sciences.Intuitionistic fuzzy set (IFS) is a useful technique to describe the fuzziness of the world and it was characterized by membership degree and nonmembership degree [1].Three years later, Atanassov and Gargov [2] extended the IFS to a more generalized form and introduced the interval-valued intuitionistic fuzzy set (IIFS).IIFS is characterized by the membership degree range and nonmembership degree range.Therefore, IIFS is more powerful to depict the fuzziness of the world and has been utilized in many fields, especially in decision making [3][4][5][6][7][8].
During the interval-valued intuitionistic fuzzy multicriteria decision making process, the experts often provide their evaluation information which should be aggregated by using the proper aggregation methods.Intervalvalued intuitionistic fuzzy aggregation operators play an important role in multicriteria decision making.Up to now, there are many aggregation operators for IIFNs; the most basic interval-valued intuitionistic fuzzy aggregation operators are interval-valued intuitionistic fuzzy weighted average (IIFWA) operator and interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator proposed by Xu [9], based on which, a lot of extended operators are proposed by researchers, such as generalized intervalvalued intuitionistic fuzzy geometric operator [10], intervalvalued intuitionistic fuzzy Einstein ordered weighted geometric (I-IVIFEOWG) operator proposed by Yang and Yuan [11], induced interval-valued intuitionistic fuzzy Hamacher ordered weighted geometric (I-IVIFHOWG) operator [12], the interval-valued intuitionistic fuzzy Einstein weighted geometric operator, interval-valued intuitionistic fuzzy Einstein ordered weighted geometric operator and intervalvalued intuitionistic fuzzy Einstein hybrid weighted geometric operator [13], and induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging (IG-IVIFHSA) operator [14].

Some Basic Concepts
Intuitionistic fuzzy set (IFS) proposed by Atanassov [1] is characterized by the ability of defining the membership degree   () and nonmembership degree V  () of an element to a set simultaneously, and the   () and V  () are the real numbers belonging to a set [0, 1].Interval-valued intuitionistic fuzzy set (IIFS), proposed by Atanassov and Gargov [2], can express the experts' preference information more effectively since it uses the interval number instead of real number to express the membership degree and nonmembership degree.The definition of the IIFS is shown as follows.

Interval-Valued Intuitionistic Fuzzy
Interactive Aggregation Operators Example 3 shows that the nonmembership degrees range of the sum of the two IIFNs is totally decided by the nonmembership degree range of α1 without any consideration of other IIFNs, which is not reasonable in reality.(5) Example 4 shows that the membership degrees range of the product of the two IIFNs is totally decided by the membership degree range of α1 without any consideration of other IIFNs, which is not workable.
The above analysis indicates that the definition of IIFNs introduced by Xu [9] could be improved to some extent, and we defined some new operations for IIFNs motivated by the idea of He et al. [15,16].

Interval-Valued Intuitionistic Fuzzy
Interactive Aggregation Operators.In Section 3.1, we have introduced the new operations for IIFNs based on the analysis of the imperfections of the existing operations.The main advantage of the new operations is that it can handle the extreme cases better such as the nonmembership degree range or the membership degree range reduced to the [0, 0].Furthermore, the new aggregation operators for IIFNs also need to be addressed.Therefore, we proposed a series of interaction interval-valued intuitionistic fuzzy aggregation operators for aggregating the IIFNs.The comparisons with the existing operators are also presented.
Proof.The mathematical induction method is applied to prove (9).
Like Example 11, here we illustrate Example 14 to show the application of IIFIWG operator in aggregating the IIFNs.[9] to aggregate the four IIFNs; the result can be obtained as follows: From Example 14, we can find out that the aggregated result based on the IIFWG operator is ⟨[0, 0], [0.2526, 0.4894]⟩ and the membership degree range is [0, 0] which is totally determined by the membership degree of IIFN α1 .This was obviously an unreasonable calculated result.

Journal of Applied Mathematics
Based on the IIFIWG operator (Definition 12 and Theorem 13), the aggregated result is as follows: Obviously, the membership degree range is [0.1390, 0.3659] rather than [0, 0] and was more reasonable than the result obtained by IIFWG operator.
Based on the IIFIOWA operator proposed in this paper, we can get Obviously, this result seems more reasonable.
Based on the IIFOWG operator proposed by Xu [9], we can get This aggregation result indicates that the membership degree range of the α * is determined by the IIFN α1 .
Based on the IIFIOWG operator proposed in this paper, we can get Obviously, this result seems more reasonable.

Application of the Proposed Operators to Evaluate the Hydrogen Production Technologies
With China's sustained and rapid economic and social development, energy resources, and increasing pressure on the environment, developing light pollution and renewable energy is of great significance to China's sustainable development.Hydrogen is recognized as clean energy, low carbon, and zero carbon energy source which has attracted wide attention in various countries [45][46][47].Hydrogen technologies evaluation involves multiattribute decision making and many attribute should be evaluated, such as environment, economic, and social [48].
One high-tech development company in Zhejiang Province, China, intends to invest in the hydrogen energy production.Three kinds of hydrogen production technologies have been identified according to their own business situation and the famous energy expert's suggestions, such as nuclear based high temperature electrolysis technology (NHTET), electrolysis of water technology by hydropower, and coal gasification technology, expressed by  1 ,  2 , and  3 .The company wants to find out the most suitable technique from the three alternatives mainly according to environment performance  1 , economic performance  2 , social performance  3 , and the support degree of government policies  4 .Meanwhile, the four attributes have different importance weight and could be determined by many effective methods, such as AHP.Here we suppose the weight of the four attributes is (0.14, 0.36, 0.32, 0.18)  .The performance of the three alternatives on the four attributes is expressed by IIFNs and is shown in Table 1.
First, we use the IIFIWA operator to aggregate the performance of the four attributes for three kinds of hydrogen production technologies, respectively, Since  (α 2 ) >  (α 3 ) >  (α 1 ) , then Therefore, the most suitable hydrogen production technology is  2 .