New Cognition to Multiplicative Consistency of Fuzzy Reciprocal Judgment Matrix

doi:10.12005/orms.2015.0076

Operations Research and Management Science ›› 2015, Vol. 24 ›› Issue (3): 1-5.DOI: 10.12005/orms.2015.0076

• Theory Analysis and Methodology Study • Next Articles

New Cognition to Multiplicative Consistency of Fuzzy Reciprocal Judgment Matrix

SHI Xi-jun¹, ZHANG Qiang¹, ZHU Ji-qiao²

1.School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China;
2.Beijing Building Materials Academy of Sciences Research, Beijing 100041, China

Received:2013-06-06 Online:2015-06-12

对模糊数互补判断矩阵乘性一致性的重新认识

石喜军¹, 张强¹, 朱吉乔²

1.北京理工大学管理与经济学院,北京 100081;
2.北京建筑材料科学研究总院,北京 100041

作者简介:石喜军(1966-),男,博士研究生,研究方向:模糊决策;张强(1955-),男,教授,博士生导师,研究方向:模糊对策与决策,不确定系统理论及应用;朱吉乔(1986-),男,硕士研究生,研究方向:管理决策理论与方法。
基金资助:
国家自然科学基金和高等学校博士学科点专项科研基金资助(70771010,71071018, 70801064,20111101110036)

Abstract

Abstract: To solve the problem that the relationship between addition and subtraction and that between multiplication and division in fuzzy numbers is no longer the inverse operation and make the operational laws more correspond to reality, this paper studies the multiplicative consistency of fuzzy reciprocal judgment matrix by introducing the concepts of independent variable, dependent variable, representative system and degree of freedom in classical mathematics. Then, the result reveals that it is unreasonable that if a fuzzy reciprocal judgment matrix satisfies the conditions of multiplicative consistency defined in some existing related literatures, then this matrix must be a precise reciprocal judgment matrix. Finally, based on the fuzzy cut set theory, using the relationships among elements of fuzzy reciprocal judgment matrix, the multiplicative consistency of fuzzy reciprocal judgment matrix is redefined.

Key words: management science and engineering, representative system, fuzzy theory, fuzzy number complement judgment matrix, independent fuzzy number, dependent fuzzy number

摘要： 为了解决模糊数间的加和减、乘和除已不再是逆运算的问题,并使得运算法则更加符合客观实际情况,而引入了经典数学中的自变量、因变量、代表系统及自由度等概念,进而对模糊数互补判断矩阵的乘性一致性进行了研究,结果发现若一个模糊数互补判断矩阵满足目前一些文献对其乘性一致性的定义则这个矩阵一定是精确数互补判断矩阵这一不合理之处。文章最后结合模糊集截集理论,利用模糊数互补判断矩阵元素间的关系,重新对乘性一致性模糊数互补判断矩阵进行了定义。

关键词: 管理科学与工程, 代表系统, 模糊集理论, 模糊数互补判断矩阵, 自变模糊数, 因变模糊数

CLC Number:

C934

SHI Xi-jun, ZHANG Qiang, ZHU Ji-qiao. New Cognition to Multiplicative Consistency of Fuzzy Reciprocal Judgment Matrix[J]. Operations Research and Management Science, 2015, 24(3): 1-5.

石喜军, 张强, 朱吉乔. 对模糊数互补判断矩阵乘性一致性的重新认识[J]. 运筹与管理, 2015, 24(3): 1-5.

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New Cognition to Multiplicative Consistency of Fuzzy Reciprocal Judgment Matrix

对模糊数互补判断矩阵乘性一致性的重新认识

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