The Social Dimensions of Fuzzy Sets
Centre for Systemic Development
University of Western Sydney-Hawkesbury
Bourke St., Richmond 2753
This paper has been accepted for presentation at the IMACS/IEEE CSCC'99 Conference in Athens (Greece), July 4-8, 1999, dedicated to the founder of Fuzzy Sets theory - Prof. Lotfi Zadeh.
Abstract: Fuzzy set theory, as introduced by Zadeh, has its roots in the social nature of human understanding. Our abilities to understand up to a degree have been developed through our being-in-common, that is, through an inevitable process of fuzzification of meaning, so that to make it understandable, acceptable and operational for a multitude of people with different mental, emotional and spiritual world views. Although most of the fuzzy sets based work that has received praise and rewards has been in the field of engineering, fuzzy sets have a strong presence in social science and humanist research. (1) In group decision-making, fuzzy sets approach offers viable options for avoiding indecisiveness and confrontation, and this is of enormous significance for the social practice of negotiating and dealing with conflicts. (2) As far as each agent (human being or intelligent robot) acting in chaotic field of socio-economic complexity has limited data about other's behaviour, it is the mechanism of fuzziness that moves the whole system of interconnected agents from an initially chaotic field of operation towards a dynamically stable regime of order. (3) Virtual meaning generated by fuzzy concepts acts as a powerful catalysis of human creativity by activating, propelling and helping 'materialize' people's endeavor and search for understanding of their world. (4) Fuzzy sets approach directly relates to practical applications of such vital for organizational and social survival and evolution concepts as 'level of coherence in organization', 'creative misunderstanding', and 'integrity'.
Key Words: virtual meaning, level of coherence,
creative misunderstanding, edge of chaos, fuzzy granules, integrity.
Fuzzy set theory, as introduced by Zadeh , has its roots in the social nature of human understanding. Our abilities to understand up to a degree have been developed through our being-in-common, that is, through an inevitable process of fuzzification of meaning, so that to make it understandable, acceptable and operational for a multitude of people with different mental, emotional and spiritual world views.
According to fuzzy set theory, meaning of words can't be precisely defined - each linguistic construct in use can be described by a set of 'degrees of freedom', i.e. ways of understanding (interpretation, transformation into actions) by individuals or groups. The larger the power of this set and more diverse its elements, the richer in meaning is the linguistic construct related to it. Thus, thefuzziness of a linguistic construct, far from being meaningless, represents a significant source of meaning.
As far as the processes of creating,
interpreting and understanding meanings are crucial when dealing with
social complexity, fuzzy sets have a stable presence in this field
In group decision-making, fuzzy sets approach offers viable options for avoiding indecisiveness and confrontation. The Arrow Impossibility Theorem shows that there is no reasonable deterministic algorithm that can integrate choices made by individuals into an aggregate choice satisfactory for the entire group. The presence of fuzziness in individual preferences immediately 'softens' the conditions of choice, thus making possible the emergence of a socially satisfactory aggregation [2,3]. The implications of this result are indispensable for the social practice of negotiating and dealing with conflicts.
It is a challenge for those who
facilitate negotiation to gently 'nudge' the group towards such context
C of the discourse around the issue of consideration that maximizes
possibility for emergence of decision(s) satisfactory for all
participating agents. The harder the negotiation, the fuzzier could
be the context C, and the art of facilitation consists in keeping the
degree of fuzziness of C at levels that not only ensure its
meaningfulness for the agents but also incites and stimulates them to
joint action. Such fuzzy context can be characterized as
dynamically stable; the stability emerges as a result of agents'
According to complexity science, complex adaptive systems are constantly driven towards the edge between order and chaos where all the really interesting 'living' behaviour occurs in complex systems. Translated into language of organizational dynamics, the above proposition states that the most adaptable, the most 'alive' complex organizations operate (most of the time) at the edge of chaos, where some fuzzy ratio, a kind of internal compromise, manifests between the degrees of organization's malleability and stability. This fuzzy ratio ensures that the organization is flexible enough to respond even to slightest changes occurring both inside and outside it, and at the same time stable enough to keep its integrity not to dissolve in chaos. The higher the level of coherence (synchronization, resonance) between organization's agents, the easier is for the organization as a whole to balance at the edge of chaos.
Fuzzy set approach directly relates to the operational definition of level of coherence - a degree to which agents perceive their togetherness, interdependence and friendship within the organization. When the level of coherence in organization is low, its power differential (degrees of power concentration) immediately increases, and the organization can be easily transformed into dictatorial one - it loses its flexibility and capacity for adaptation and self-organization. The development of a dictatorial organization is imposed 'from above', and as a result of this the delicate compromise between organization's malleability and stability can not emerge - there is simply no enough 'space' for such an emergence. As a rule, the words used in commands lack fuzziness - every individual is forced to comprehend them in one and the same way.
In social studies there has been always a kind of tension between the unifying and differentiating ways of thinking. Unifying thinking tends to generalize and homogenize while neglecting diversity of the phenomena and processes under study; differentiating thinking tends to go into details while neglecting the ways they interconnect and unite. Fuzzy logic helps to transcend this duality as naturally as does the logic of life: the procession of life is always from the known to the unknown. Differentiating thinking is used to go deeper into the known phenomena so that to characterize them as precise as possible. Unifying thinking is used to approach processes in their integrity, keeping in mind that the knowledge available about the wholeness is inevitably fuzzy. However fuzzy the knowledge of the wholeness, it always conveys meaning to those who are able to zoom into the fuzzy granules of its description, releasing their intellectual, emotional or spiritual contents. "Microcosm reflects Macrocosm" - repeat the philosophers since time unmemorable. The theory of fractals developed by Mandelbrot allows us to see this reflection: "parts have the same form or structure as the whole, except that they are at different scales and may be slightly deformed" .
Through his curvy fractals Benoit
Mandelbrot reveals astonishing creativity of nature when 'computing'
with forms and structures. Through his fuzzy granules Lotfi
Zadeh reveals astonishing creativity of brain when 'computing' with
words and concepts . Fractals and granules enrich the ability of
social researchers to go deeper into the enigmas and paradoxes of
social complexity. At the source of these enigmas and paradoxes is the
bottomless complexity of human individuality. Society is only an
abstract word. What really exist are the individuals with their
physical, emotional, mental and spiritual fractality, granularity and
above all, integrity. With each other and with the universe.
Fuzzy Logic helps both human and
machine intelligence to link A with not A. All the
powerful apparatus of fuzzy mathematics has been created to explore how
this link manifests and works in natural systems, and how to make it
work efficiently in artificial systems. Once we know how to link
polarities like "yes" and "no", "chaos" and "order", "simplicity" and
"complexity", "words" and "numbers", "subjective" and "objective",
"attachment" and "detachment", "inner" and "outer", we are on the way
to find out how to transcend much more complex dualities of life, such
like "mine" and "yours", "ours" and "theirs", "we" and "they", "I" and
"the other". It is a hard task - unique for every one. Still there is
no fuzzy methodology explaining how to do it. Yet we must create it, if
we really want the life on Earth to continue.
 L. Zadeh, Fuzzy Sets, Information and Control, 8, 1965, pp. 338-359
 V. Dimitrov, Social Choice and Self-Organization under Fuzzy Management, Kybernetes, 6, 1976, pp. 153-156.
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 V. Dimitrov and B. Hodge, Virtual Meaning: Problems of Interpretation in the Social Sciences, in Computing with Words in Systems Analysis, Eds. L.Zadeh and J. Kacprzyk, Physica-Verlag, 1999
 G. Teubner, Autopoietic Law: A New Approach to Law and Society, de Gruyter, 1987
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