NDLI: Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis

Content Provider	IEEE Xplore Digital Library
Author	Wen-Ran Zhang
Copyright Year	1994
Description	Author affiliation: Dept. of Comput. Sci., Lamar Univ., Beaumont, TX, USA (Wen-Ran Zhang)
Abstract	A bipolar fuzzy set theory is presented for cognitive modeling and multiagent decision analysis. Firstly, notions of bipolar fuzziness are introduced. Secondly an interval-based bipolar fuzzy logic is defined which generalizes a real-valued bipolar fuzzy logic by allowing interval-based linguistic variables x and y to be substituted into (S, =, V, /spl otimes/) or (S, =, /spl cup/, /spl odot/) where S={/spl forall/(x,y)\|(x,y)/spl isin/([-1,0]/spl times/[0,+1])}. Thirdly, a fuzzy number-based bipolar logic is presented which. Further generalizes the interval-based model by allowing /spl alpha/-level fuzzy number-based linguistic variables x and y to be substituted into (S, =, V, /spl otimes/) or (S, =, /spl cup/, /spl odot/), S={/spl forall/(x,y)\|(x,y) maps ([-1,0]/spl times/[0,+1]) to [0,1]}. Bipolar fuzzy set operations of disjunction composition (V-/spl otimes/), union-composition (/spl cup/, /spl odot/), are proved commutative and associative; V respect to /spl otimes/ and /spl cup/ respect to /spl odot/ are proved distributive. It is shown that a interval-based bipolar variable is a nesting of a real-valued bipolar variable; a trapezoidal-fuzzy number-based bipolar variable is an 2-level nesting of an interval-based bipolar variable; and an /spl alpha/-level (/spl alpha/ is an integer) fuzzy number-based bipolar variable is an /spl alpha/+1 level nesting of an interval-based bipolar variable. Based on the nesting features, it is proved that /spl alpha/-level fuzzy number-based bipolar operations can be converted to interval-based and then real-valued bipolar operations. The conversions lead to significant computational simplification on bipolar fuzzy relations. Major advantages of the bipolar fuzzy set theory include: (1) it formalizes a unified approach to polarity and fuzziness; (2) it captures die bipolar or double-sided (negative and positive, or effect and side effect) nature of human perception and cognition; and (3) it provides a basis for bipolar cognitive modeling and multiagent decision analysis.<>
Starting Page	305
Ending Page	309
File Size	522376
Page Count	5
File Format	PDF
ISBN	0780321251
DOI	10.1109/IJCF.1994.375115
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-12-18
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy sets Fuzzy logic Fuzzy set theory Fuzzy systems Humans Computer science Cognition Decision making Negative feedback Linear algebra
Content Type	Text
Resource Type	Article

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