基于直觉模糊推理的态势与威胁评估研究
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摘要
未来作战环境的信息是海量的、复杂的、高度分布和冗余的。作战单元需要访问战场的融合信息,形成正确的战场感知,及时准确地理解战场态势,评估敌方威胁,了解敌方企图和能力,并迅速进行决策。因此,高层信息融合的态势与威胁评估研究必须面向军事决策。对此,直觉模糊集(IFS)理论提供了新的求解途径和方法。在此背景下,本文运用IFS这一崭新的数学工具,对态势和威胁评估问题进行深入研究。
首先,针对Zadeh模糊集(ZFS)的各种拓展,阐明了IFS到ZFS的变换,IFS与Vague集的等价关系;证明了L-IFS到L-模糊集,区间值IFS到L-模糊集,区间值模糊集到IFS,IFS到区间值IFS之间变换的等价性。定义了直觉模糊语义算子,揭示了IFS时态逻辑算子及其扩展运算性质。揭示了直觉模糊关系的自反性、对称性及传递性,证明了直觉模糊合成运算也具有结合律,阐明了Atanassov算子对于直觉模糊关系性质的影响。
其次,针对直觉模糊逻辑(IFL)推理与命题演算,提出一种逻辑真值合成方法;基于均衡状态假设,导出作为特例的对称合成方法,从而使IFL与Zadeh模糊逻辑(ZFL)具有了相同的逻辑演算形式。针对直觉模糊条件推理,给出了蕴涵式、条件式、多重式、多维式及多重多维式推理等合成运算公式。针对带有可信度因子的IFL推理,分析了规则中的可信度因子传播对结论可信度的影响,给出了相关的计算结论真值的公式。针对直觉模糊近似推理,给出了推广的取式推理、拒式推理及假言推理等的合成运算公式。提出一种利用求传递闭包来构造直觉模糊等价矩阵的方法,证明了直觉模糊相似矩阵定理及传递闭包定理。提出一种利用真值限定的直觉模糊推理方法,给出了相关的推理合成运算公式。
第三,针对战场态势评估问题,提出一种基于直觉模糊决策的态势评估方法。首先,面向态势理解,将战场态势评估归结为一综合评价问题,建立了归一化的直觉模糊综合评判模型。接着,建立了战场态势评估指标体系,讨论了评判指标的效用值计算等度量问题和指标值的规范化方法。给出了利用德尔菲法与层次分析法相结合来确定和计算指标权重向量的方法。然后,通过电子战、防空反导、空防对抗等联合防空作战过程的战场态势评估实例,表明该方法对当前战场态势可给出有效的综合评价和理解,验证了方法的有效性。
第四,针对威胁评估问题,提出一种基于直觉模糊推理的威胁评估方法。首先,分析了联合防空作战中空天来袭目标影响威胁评估的主要因素及威胁评估的不确定性,建立了威胁评估功能模型及威胁程度量化等级。其次,建立了输入状态变量的属性函数及系统推理规则,设计了推理算法。分析了规则库中所包含规
Information in the upcoming operational environments is massive, complex, and highly distributed and redundant. Units of operations need to access fusion information of a battlefield, in order to form appropriate perception, timely and exactly to understand battlefield situation, to assess foe courses of action and capabilities, and to make decisions rapidly. The circumstances for decision making are usually quite complicated. Therefore, researches on situation and threat assessment (STA) of information fusion in high levels should be oriented to military decision and continuously seek new techniques and solutions. The aim of this dissertation is to perform the deep research on problems of STA by utilizing intuitionistic fuzzy sets (IFS) with the background of net-centric warfare (NCW).Firstly, intuitionistic fuzzy (IF) semantic match and operations of relations get into investigation. To the extensions of Zadeh's fuzzy sets (ZFS), transforms of IFS to ZFS and equivalent relations of IFS with Vague sets are expatiated. The equivalent properties of transforms of L-IFS to Z-fuzzy sets (FS), interval value IFS to L-FS, interval value (IV) FS to IFS, and IFS to IV IFS are proved by means of D-K operators. The semantic operators of IF are defined. The properties of temporal logic operators and extended operations over IFS are exposed. The properties of reflexive, symmetric, and transitive on IF relations (IFR) are explored with the proof of the theorem of combination law on IFR operations. The effects of Atanassov's operator on the IFR properties are described.Secondly, investigations of techniques for IF reasoning and confidence factors spreading proceed. To IF logic (IFL) reasoning and predicate calculus, a synthetic method for finding the truth of IFL propositions is proposed with a symmetric synthetic method derived on the basis of the hypothesis of an equilibrium status as a special instance, thus the forms of logic calculus on IFL are enabled to be the same as Zadeh fuzzy logic (ZFL). To conditional reasoning on IFL, mathematical formulas of inference compositional operations on implications, conditions, multiplications, and the multi-dimensions are derived. To issues of IFL reasoning with confidence factors, the effects of confidence factors spreading in rules on those of conclusions are analyzed. The related formulas for finding truth of conclusions are exposed. To approximate reasoning on IFL, mathematical formulas of inference compositional operations on generalized modus ponens, modus tollens, and hypothetical syllogism are derived. An approach to formation of IF equivalent matrixes by finding the transitive closure is presented with the proof of theorems of transitive closure and resembling matrix. A
method for IFL reasoning with truth qualifications is proposed, and the related sets of the compositional formulas of operations are derived.Thirdly, to the problems of battlefield situation assessment (BSA), a technique based on IF decision is proposed. First, BSA is concluded to an issue of synthetic judgement oriented to situation understanding, and an IF model for synthetic judgement is derived with a proof of the model normalized. Then, a system of evaluating goals for BSA is constructed, and approaches to effectiveness measures for evaluating goals and normalization of their values are described. Subsequently, methods of Delphi integrated with analytic hierarchy process (AHP) are utilized for finding weight vectors of goals. Finally, the efficient synthetic assessment and comprehension to current battlefield situation can be made out by using evaluating instances of electronic war, air-defense counter-missile and counterwork in the course of joint operations of air defense.Fourthly, to the questions of threat assessment (TA), a method based on IFL reasoning is proposed. First, the major factors of effects of attacking targets from space or air on TA in joint air defense operations and nondeterminacy to TA are analyzed. The functional model for TA is constructed and the measurement rank of threat degree is divided. Then, the membership and nonmembership functions for input state variables and inference rules are built with the algorithms for reasoning devised. Subsequently, completeness and interactivity and consistency of rules contained in the rulebase are checked with a verification method to the rulebase presented. The validity is checked by providing TA instances with 20 typical targets.Finally, to improve TA accuracy of synthetic value, a method of adaptive neuro-intuitionistic fuzzy inference system (ANIFIS) is proposed. A Takagi-Sugeno model for TA on the basis of ANIFIS is constructed. The global approaching property of the model is proven with the network learning algorithms devised. The validity is checked by providing TA instances with 20 typical targets. An analysis by comparison with simulated instances from the two methods is made. The results show that the latter is superior in performance.
首先,针对Zadeh模糊集(ZFS)的各种拓展,阐明了IFS到ZFS的变换,IFS与Vague集的等价关系;证明了L-IFS到L-模糊集,区间值IFS到L-模糊集,区间值模糊集到IFS,IFS到区间值IFS之间变换的等价性。定义了直觉模糊语义算子,揭示了IFS时态逻辑算子及其扩展运算性质。揭示了直觉模糊关系的自反性、对称性及传递性,证明了直觉模糊合成运算也具有结合律,阐明了Atanassov算子对于直觉模糊关系性质的影响。
其次,针对直觉模糊逻辑(IFL)推理与命题演算,提出一种逻辑真值合成方法;基于均衡状态假设,导出作为特例的对称合成方法,从而使IFL与Zadeh模糊逻辑(ZFL)具有了相同的逻辑演算形式。针对直觉模糊条件推理,给出了蕴涵式、条件式、多重式、多维式及多重多维式推理等合成运算公式。针对带有可信度因子的IFL推理,分析了规则中的可信度因子传播对结论可信度的影响,给出了相关的计算结论真值的公式。针对直觉模糊近似推理,给出了推广的取式推理、拒式推理及假言推理等的合成运算公式。提出一种利用求传递闭包来构造直觉模糊等价矩阵的方法,证明了直觉模糊相似矩阵定理及传递闭包定理。提出一种利用真值限定的直觉模糊推理方法,给出了相关的推理合成运算公式。
第三,针对战场态势评估问题,提出一种基于直觉模糊决策的态势评估方法。首先,面向态势理解,将战场态势评估归结为一综合评价问题,建立了归一化的直觉模糊综合评判模型。接着,建立了战场态势评估指标体系,讨论了评判指标的效用值计算等度量问题和指标值的规范化方法。给出了利用德尔菲法与层次分析法相结合来确定和计算指标权重向量的方法。然后,通过电子战、防空反导、空防对抗等联合防空作战过程的战场态势评估实例,表明该方法对当前战场态势可给出有效的综合评价和理解,验证了方法的有效性。
第四,针对威胁评估问题,提出一种基于直觉模糊推理的威胁评估方法。首先,分析了联合防空作战中空天来袭目标影响威胁评估的主要因素及威胁评估的不确定性,建立了威胁评估功能模型及威胁程度量化等级。其次,建立了输入状态变量的属性函数及系统推理规则,设计了推理算法。分析了规则库中所包含规
Information in the upcoming operational environments is massive, complex, and highly distributed and redundant. Units of operations need to access fusion information of a battlefield, in order to form appropriate perception, timely and exactly to understand battlefield situation, to assess foe courses of action and capabilities, and to make decisions rapidly. The circumstances for decision making are usually quite complicated. Therefore, researches on situation and threat assessment (STA) of information fusion in high levels should be oriented to military decision and continuously seek new techniques and solutions. The aim of this dissertation is to perform the deep research on problems of STA by utilizing intuitionistic fuzzy sets (IFS) with the background of net-centric warfare (NCW).Firstly, intuitionistic fuzzy (IF) semantic match and operations of relations get into investigation. To the extensions of Zadeh's fuzzy sets (ZFS), transforms of IFS to ZFS and equivalent relations of IFS with Vague sets are expatiated. The equivalent properties of transforms of L-IFS to Z-fuzzy sets (FS), interval value IFS to L-FS, interval value (IV) FS to IFS, and IFS to IV IFS are proved by means of D-K operators. The semantic operators of IF are defined. The properties of temporal logic operators and extended operations over IFS are exposed. The properties of reflexive, symmetric, and transitive on IF relations (IFR) are explored with the proof of the theorem of combination law on IFR operations. The effects of Atanassov's operator on the IFR properties are described.Secondly, investigations of techniques for IF reasoning and confidence factors spreading proceed. To IF logic (IFL) reasoning and predicate calculus, a synthetic method for finding the truth of IFL propositions is proposed with a symmetric synthetic method derived on the basis of the hypothesis of an equilibrium status as a special instance, thus the forms of logic calculus on IFL are enabled to be the same as Zadeh fuzzy logic (ZFL). To conditional reasoning on IFL, mathematical formulas of inference compositional operations on implications, conditions, multiplications, and the multi-dimensions are derived. To issues of IFL reasoning with confidence factors, the effects of confidence factors spreading in rules on those of conclusions are analyzed. The related formulas for finding truth of conclusions are exposed. To approximate reasoning on IFL, mathematical formulas of inference compositional operations on generalized modus ponens, modus tollens, and hypothetical syllogism are derived. An approach to formation of IF equivalent matrixes by finding the transitive closure is presented with the proof of theorems of transitive closure and resembling matrix. A
method for IFL reasoning with truth qualifications is proposed, and the related sets of the compositional formulas of operations are derived.Thirdly, to the problems of battlefield situation assessment (BSA), a technique based on IF decision is proposed. First, BSA is concluded to an issue of synthetic judgement oriented to situation understanding, and an IF model for synthetic judgement is derived with a proof of the model normalized. Then, a system of evaluating goals for BSA is constructed, and approaches to effectiveness measures for evaluating goals and normalization of their values are described. Subsequently, methods of Delphi integrated with analytic hierarchy process (AHP) are utilized for finding weight vectors of goals. Finally, the efficient synthetic assessment and comprehension to current battlefield situation can be made out by using evaluating instances of electronic war, air-defense counter-missile and counterwork in the course of joint operations of air defense.Fourthly, to the questions of threat assessment (TA), a method based on IFL reasoning is proposed. First, the major factors of effects of attacking targets from space or air on TA in joint air defense operations and nondeterminacy to TA are analyzed. The functional model for TA is constructed and the measurement rank of threat degree is divided. Then, the membership and nonmembership functions for input state variables and inference rules are built with the algorithms for reasoning devised. Subsequently, completeness and interactivity and consistency of rules contained in the rulebase are checked with a verification method to the rulebase presented. The validity is checked by providing TA instances with 20 typical targets.Finally, to improve TA accuracy of synthetic value, a method of adaptive neuro-intuitionistic fuzzy inference system (ANIFIS) is proposed. A Takagi-Sugeno model for TA on the basis of ANIFIS is constructed. The global approaching property of the model is proven with the network learning algorithms devised. The validity is checked by providing TA instances with 20 typical targets. An analysis by comparison with simulated instances from the two methods is made. The results show that the latter is superior in performance.
引文
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