| Multi-attribute decision making theory was one of the important theoretical basis to solve many problems on management science, the common multi-attribute decision making methods included interval number theory, fuzzy set theory, gray system theory, probability theory, rough set theory and set pair analysis,etc.. However, with the development of the society, many problems background was more and more complex, used the above decision making method has been unable to get a satisfactory solution. Therefore, Molodtsov proposed the soft set theory, soft set mainly took attribute parameters as the research objects, effectively overcame the disadvantage of inflexible in other decision making methods. Because the parameter setting had the advantage of unconstrained, since the soft set was proposed, its expansion study had been widely concerned, proposed fuzzy soft set, intuitionistic fuzzy soft set, interval fuzzy soft set and triangle fuzzy soft set in succession, and had been widely concerned on economy, management, military and environment. But there were still exist some problems, such as the corresponding expansion study of soft set was not perfect enough, at the same time the application on mining engineering and other fields was less.The paper took the planned construction coal mine of Junjin raw coal limited liability company as engineering background, fully considered in mine construction process will involve many influencing factors, and the data generally had fuzziness, concealment and complexity, at the same time there were maybe exist situations like deletion information,etc.. Therefore, after collected and arranged the related construction data of Junjin coal mine, used MATLAB7.0 software to data processing and mapping comparative analysis, and used fuzzy soft set, mixed soft set, intuitionistic fuzzy soft set entropy and its expansion study results systematic studied the decision making problems like investment risk, project investment scheme, coal mining equipment supply enterprise optimization, etc.. Mainly completed the following several aspects.1. Arrangementanalyzed the construction background data of Junjin coal mine(1) By collecting, finishing and analyzing the construction data of Junjin coal mine, obtained mine construction scale and the main technical scheme, investment capital source and the make sure conditions. And analyzed the influencing factors of mine project construction respectively from two aspects such as coal mine resource conditions and coal mine construction conditions, indicated the mining area coal seam which was divided into five layers storage conditions are complex, and the coal mining could be used as steam coal, power generation coal, refining and gasification to coal. The mining area belonged to mid temperate zone continental monsoon climate, the mine belonged to low gas mine and its general water inflow was 30m3/h, relative gas emission rate was 4.14m3/t, and the absolute emission amount was 0.2331 m3/min. At the same time, the mine had better external transportation conditions with traffic convenience around, and resources integration mine construction was also conform to the national working opinions on promote coal mine enterprise merger and recombination.(2) Analyzed Junjin coal mine financial situation from the aspects such as project estimation and financing, raw coal production cost, profitability and uncertainty, etc.. The results showed that the calculation for engineering construction investment was reliable. The construction funds all came from operating profit in the past of enterprise, the unit production cost of raw coal was 201.05 yuan, the average annual profit could reach 32.0395 million. Although there were some uncertainty, anti-risk property was strong.2. Group decision making method of intuitionistic fuzzy soft set and its application on the coal mine investment risk(1) System introduced the conceptions of soft set, fuzzy soft set and intuitionistic fuzzy soft set, analyzed the score value function, accuracy function, addition, numerical multiplication operation and weighted average operator formula of the intuitionistic fuzzy number. Proposed the conception of intuitionistic fuzzy soft matrix on the basis of the existing fuzzy soft matrix, and gave the addition, numerical multiplication, distance and integrated operational formula of intuitionistic fuzzy soft matrix, at the same time stipulated the order.(2) By analyzed the existing decision making method, pointed out the lack of the soft set decision making method of average weight method for possible choice values and simple probability method with incomplete information, namely the computational complexity was heavy of the average method for all possible choice values, and must be recalculate all possible choice values when added or reduced parameters and objects. Though the simple probability method avoided the above defect, and made full use of the existing calculation results, the imputed value only made use of the corresponding partial data message where the probability value was 1, at the same time was not consider the accuracy of the imputed value.(3) Promoted the imputation method of missing data in soft set decision making under fuzzy soft set. Firstly, divided the information of different parameters set into complete information set and incomplete information set, and proposed the probability solution formula of existing data which appeared under the different parameters. By the research obtained the choice value weighted sum method and simple mathematical expectation method, and took mathematical induction to prove the decision making results of this two methods were equivalent. At the same time the research showed that the simple mathematical expectation method was better than the choice value weighted sum method. When made decisions, could fill in the incomplete information by simple mathematical expectation method to make the decision making system completion. Then further researched the rationality and validity of imputed values. Proposed using the trust discount thought in evidence theory to build correction model of imputed values to effectively reduce the deviation of decision making system in the filled process. Finally built the fuzzy soft set decision making model with incomplete information which used fuzzy soft set entropy theory to determine the weights of different decision makers and parameters, and proposed the integration operation formula. At last gave the group decision making steps.(4) About the group decision making of intuitionistic fuzzy soft set with incomplete information problem, firstly discussed the determination method of incomplete information, divided the information set of different parameters into complete information set and incomplete information set, and gave the probability solution formula of the corresponding membership degree and non-membership degree for missing data which appeared in the different parameters, then obtained the missing data imputation method which was similar to the simple mathematical expectation method. Considered the imputed value just made system completion, but without analyzed the influence of its value to good or bad system, so used the evidence theory and utility theory to modified the imputed value, proposed the basic probability distribution value solution formula of which took intuitionistic fuzzy numbers as fill type values, used the trust discount thought to complete the effective measure of the imputed value of uncertainty, to achieve the purpose of the imputed value correction and reduce system decision making deviation. In decision making model, the weight of decision makers was determined by the principle of the distance which between the above weight and the average preference intuitionistic fuzzy soft set decision making matrix was smaller, the weight was greater, the weight of parameters was determined by intuitionistic fuzzy soft set entropy measure which was proposed in the paper. Obtained the intuitionistic fuzzy number of each object according to the intuitionistic fuzzy soft set integrated operational, and made a sorting decision making according to the principle of the score value was larger, the decision making was more optimal.(5) Made risk analysis for Junjin coal mine project investment. Discussed the project respectively from the internal conditions and external conditions of the mine. Finally built Junjin coal mine investment risk evaluation index system which took three factors such as natural conditions and technical risk, production management and financial risk, market and policy risk as first grade indexes, and ten factors such as reserves and engineering conditions, natural environment risk, resource risk, external cooperation conditions, engineering risk, production management risk, financial risk, international coal market, domestic coal market and policy risk as second index.(6) Practical analyzed Junjin coal mine investment risk by the group decision making method of intuitionistic fuzzy soft set with incomplete information,according to the actual situation of Junjin coal mine, assumed that there are four risk assessment results such as risk was low, risk was moderate, risk was higher and risk was the highest. Three experts respectively evaluated from three aspects such as natural conditions and technical risk, production management and financial risk, and market and policy risk. The decision making results showed that the risk of Junjin coal mine investment risk assessment was low. The research showed that bring in the intuitionistic fuzzy number was more conform to the actual engineering background, and improved the reliability of decision making results by using the evidence theory and integrated operational.3. Mixed soft set decision making model and its application in Junjin coal mine project investment scheme optimization(1) Introduced the conceptions of interval intuitionistic fuzzy set and the weighted average operator, and on the basis of this proposed comprehensive considerate the distance formula and expected value formula of membership degree interval, non-membership degree interval and hesitate degree interval.(2) By consulting a large amount of references, classification studied on the mixed decision making problem of which contained interval intuitionistic fuzzy number, pointed out the shortage of the existing decision making method was data transform information lose problem and the decision making process mainly gave priority to static. Aimed at these shortages, researched the mixed decision making model which constituted by interval value, language type and interval intuitionistic fuzzy number in the paper, proposed the thought of unified transform mixed evaluation soft matrix into interval intuitionistic fuzzy soft matrix, and gave the concrete conversion formula. Defined the distance between interval intuitionistic fuzzy number and similarity formula, and determined decision makers weights by the distance and similarity between the preference information and entirety preference information of decision makers. Aimed at the condition of the attribute weight was language type, proposed firstly translated it into interval intuitionistic fuzzy number and then determined weight by the method of seeking expectation.(3) Aimed at the score function in the existing decision making model was generally not considered the influence of hesitancy degree, introduced two parameters which were hesitancy degree conversion and support degree conversion, proposed a new two-parameter score function, and proved the score function meet some excellent properties. By introducing two-parameter was not only realize dynamic decision making, but also made the decision making process become more flexible and the accuracy of decision making results become much higher. Meanwhile, space mapping analysis by MATLAB7.0 software, intuitive saw the influence of two parameters changing to the decision making results.(4) According to the characteristics of Junjin coal mine project investment, based on fully considered the influences of investment recovery period, investment profit rate, investment reward rate and net present value of coal mine project investment scheme, the influences of geological reserves of new build mine, annual production capacity of coal mine and mine area, the influences of the economic traction situation of different investment construction schemes to the city where it is and the related industries and environment, and the influences of whether it could be obtain the national policy and the strong support of local government. Constructed the coal mine project investment decision making index system which was composed of six aspects such as resource factors, economic factors, political factors, social factors, ecological factors and risk factors.(5) Applied mixed soft set decision making method in Junjin coal mine project investment scheme optimization. Example analysis showed that the mixed soft set decision making model was more confirm to the actual requirement of group decision making with complex engineering background. The introduction of aggregation operation and two-parameter score function ensured the dynamic of mixed group decision making method and the reliability of decision making results. At the same time the model had advantages of the evaluation mode was flexible and the programming was easy.4. Interval triangle fuzzy soft set theory and its application in coal mine coal mining equipment supply enterprise selection(1) After detailed introduced the definitions of interval fuzzy soft set and triangle fuzzy soft set, proposed the conception of interval triangle fuzzy soft set. And on the basis of give the definition of standard interval triangle fuzzy number, discussed the operation properties of intersection,union, addition and scalar-multiplication in succession, determined the specific formula. The research showed that all this operation properties can ensure the sealing of standard interval triangle fuzzy number operation.(2) Based on the conception of interval triangle fuzzy soft set, further gave the definitions of soft subset, soft superset, equality, “AND”, “OR”, complement, discussed the operation properties of associative law, distribution rate and dual law, and gave the proof procedure.(3) To enrich the operation property of interval triangle fuzzy soft set, proposed the definitions of intersection, union and complement which was similar to the classical set, and more conform to the actual needs, easier to understand and more facilitate popularization and application. On the basis of the above intersection, union and complement, further discussed the related properties of associative law, distribution rate and dual law, obtained some theorems and gave the proof procedure.(4) The research showed that interval triangle fuzzy soft set was equivalent to interval triangle fuzzy soft matrix. Proposed the conception of interval triangle fuzzy soft matrix to improve the maneuverability of fuzzy soft set in practical application. The soft set operation property could become more flexible and its application scope become more extensive by using the relevant knowledge of matrix theory. Aimed at interval triangle fuzzy soft matrix, discussed the integrated operational to obtain comprehensive decision making message, gave interval triangle fuzzy soft matrix count weighted average operator formula of which the weight was know, and used mathematical induction to strict proof.(5) Considered the value of the decision making information was different in different moments and the importance of time variable was greater when it was more and more close to the last moment, determined time weight by the method of build exponential decay model. Then aggregated the interval triangle fuzzy soft matrix in different moments according to the integrated operational formula, obtained comprehensive decision making soft matrix.Based on the selective values and decision making value solving formula of interval triangle fuzzy soft set gave different schemes. Comprehensive the above method, built dynamic interval triangle fuzzy soft set decision making model of which comprehensive considered the temporal variation and gave the decision making steps.(6) Junjin coal mine needed to purchase different various of equipment which contained shearer, flexible flight conveyor, single hydraulic prop, emulsion pump station, heading equipment and ventilation equipment in the construction process in succession, its value was 37.2484 million. How to choose coal mining equipment supply enterprise was a task worthy to research, now investigated the alternative enterprises respectively from three aspects such as equipment quality and performance price ratio, enterprise technology sustainable innovation ability and after service year by year, the investigation stage was set to three years, the attenuation coefficient was ?(28)5.0, then brought initial evaluation value into the model to decision making analysis. The research showed that because of considering the dynamic influence of temporal variation, the model was more conform to the actual, the flexibility was stronger, and the integrated operational was further improve the reliability of decision making results. Meanwhile, the model also could solve the related mining problems which were similar to the coal mine coal mining equipment supply enterprise optimization.5. Intuitionistic fuzzy entropy and the improvement of intuitionistic fuzzy soft set entropy and its application research(1) Firstly introduced the related knowledge of fuzzy entropy and intuitionistic fuzzy entropy, then aimed at intuitionistic fuzzy entropy measure should comprehensively consider the influences of two aspects such as intuitiveness and fuzziness, where intuitiveness was decided by hesitancy degree, and fuzziness was decided by the difference degree between membership degree and non-membership degree. Finally, respectively from three aspects such as only describe intuitiveness, only describe fuzziness and at the same time to describe intuitiveness and fuzziness to classified study the entropy measure of intuitionistic fuzzy set and pointed out the insufficient by example comparison analysis.(2) To intuitive describe the properties which the intuitionistic fuzzy entropy should be have, mapped triangle plane with point A)0,0,1(,point B)0,1,0( and point C)1,0,0( in three-dimensional space by MATLAB7.0 software, was intuitionistic fuzzy entropy plane. Any point in triangle(35)ABC all corresponded to an intuitionistic fuzzy number. It could be seen by graphical analysis that the new entropy should meet when intuitiveness, namely hesitancy degree was equal, the entropy value would increase with the increase of fuzziness. That was to say, any mapped a linear which was parallel to AB in triangle(35)ABC, points on the linear were more close to mid point, the entropy was larger. While when fuzziness, namely the absolute value of poor between membership degree and non-membership degree was equal, the entropy value would increase with the increase of intuitiveness. That was to say, any mapped a linear which was parallel to CD in triangle(35)ABC, D was the mid point of AB,points on the linear were more close to the point C, the entropy was larger. So the entropy value obtained the maximum value only at the point of C)1,0,0(.(3) Further research showed that the function between fuzziness and intuitiveness in intuitionistic fuzzy entropy could cancel each other out. Based on this, proposed the conception of isentropic arc, and constructed the intuitionistic fuzzy entropy measure formula which was more conform to the objective reality, at the same time proved all conditions of the new entropy meet axiomatic definition. Example comparative analysis showed that the operation result of two new entropy measure which proposed in the paper was more reasonable and effective than the existing entropy measure.(4) Aimed at the existing intuitionistic fuzzy soft set entropy only considered the intuitiveness problem, proposed new intuitionistic fuzzy soft set entropy axiomatic definition. This definition comprehensively considered the influences of intuitiveness and fuzziness to soft set entropy. At the same time introduced a new soft set entropy measure formula, and proved this formula meet all conditions of new axiomatic definition. Discussed the parameter entropy problem on the basis of soft set entropy measure and gave the specific solving arithmetic expression.(5) Based on entropy weight theory, proposed TOPSIS group decision making model on the basis of intuitionistic fuzzy set. Expert weights in the model were determined according to the principle of the evaluation information was more far away from group, the average evaluation value weight was smaller, parameter index weight was solved by the new intuitionistic fuzzy entropy measure. After determined the experts weights, obtained comprehensive information matrix by compound each expert information using aggregation operator. Determined positive and negative ideal solution according to TOPSIS method in comprehensive matrix, brought parameter index weight into closeness degree formula, as the principle of the value was larger, the result was more optimal to realize the decision making. Finally gave the decision making steps.(6) According to Junjin coal mine actual background, preliminary determined take central side-by-side ventilation system and mechanical extraction ventilation method, mine air quantity computation basis and distribution condition were introduced in detail. By consulting the related data, finally determined the influencing factors of Junjin coal mine ventilation system were six indexes such as fan combined operation station number, external air leakage amount, fan total power, mining area supply air volume, fan wind pressure and mine ventilation equivalent orifice. Applied the TOPSIS group decision making method in Junjin coal mine ventilation system scheme optimization which was based on the entropy weight theory, and choose the optimal scheme in four mine ventilation system construction beforehand cases. Example research showed that the computational complexity of the decision making model was relative smaller, easier to understand and was easy to master for mine technicians. At the same time decision making results could provide theoretical reference and suggestions for relevant decision making departments. |
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