This study shows that any raw data from input can be computed with variable fuzzy set. It provides a mathematical method for representing emotion quantitative, gradual qualitative, and mutated qualitative change. This framework improves calculation methods and mechanisms, closer to real emotional changes. Different psychological feelings. It paid attention to artificial emotion domains such as psychology, cognitive science, and informa- or affective computing.
In Japan, Kansei engineering from the s com- relatively simple model of the probability of showing emo- bines emotional and engineering. It adds emotional feelings tional changes. This mode of operation is helpful for quanti- to the product design and manufacturing and changes the tative emotional changes. However, it is difficult to consider mode of intuitive experience to guide the design.
For exam- or present qualitative emotional situations. In addition, ing artificial emotion framework. It provides an innovative they are also based on affective computing model in e-learn- approach to predict artificial emotions and feelings decision ing system [5]. In addition to retaining the original feeling of There are two kinds of ways to research the mental model: quantitative character, it also shows true feelings of gradual the basic emotions theory and dimension theory [6].
Theoretical Background 2. Emotion Modelling. In the field of artificial emotion, many studies have focused on intelligent computing systems 2. Artificial Emotion and Affective Computing. The artificial to create a perception, recognition, and understanding of emotion or affective computing is a new research direction human emotions. To achieve emotional fuzzy pattern recognition model, and variable fuzzy recog- intelligence system, we must first establish an appropriate nition model confrontation.
The base model with the core computational model to describe the emotion. Let in the blank spaces are the primary dyads—emotions that are mixtures of two of the primary emotions, as shown in Figure 1. Variable Fuzzy Sets when 3. Opposition Fuzzy Sets. The Relative Proportions of the Function. Figure 2: Tree-layer architecture.
Therefore, the relative proportions of quantitative and qualitative change gradient type, mutant the two functions a give complete description of the natural type judgment criteria are as follows: dialectic about a qualitative change in formation: gradient nonexplosive qualitative and mutant explosive qualitative. The architecture reference to the main field, and gradient-type and mutant type qualitative relevant research for emotion forecasting system is composed community sector.
The input data are dependent on the domain. This paper presents variable fuzzy set as a technique for emotion predicting. It provides an operational blueprint so that researcher can consult it for predicting emotions in the future, especially in game development.
Emotions predic- Positioning Verification tion in intelligent system can improve the interaction between and and humans and machines. It shows Figure 3: Four-layer architecture. VFS is mathematic method for representing emotion quantitative, gradual qualitative, and emotional states. Essentially, such a framework provides a natural way of dealing with problems in which the source of imprecision is the absence of sharply defined criteria of class membership rather than the presence of random variables.
We begin the discussion of fuzzy sets with several basic definitions. Thus, the nearer the value of fA x to unity, the higher the grade of membership of x in A. When there is a need to differentiate between such sets and fuzzy sets, the sets with two-valued characteristic functions will be referred to as ordinary sets or simply sets. Bellman, R.
Kalaba and L. Zadeh, October, For our purposes, it is convenient and sufficient to restrict the range of f to the unit interval. Then, one can give a precise, albeit subjective, characterization of A by specifying fA x as a function on R 1. It should be noted that, although the membership function of a fuzzy set has some resemblance to a probability function when X is a countable set or a probability density function when X is a continuum , there are essential differences between these concepts which will become clearer in the sequel once the rules of combination of membership functions and their basic properties have been established.
In fact, the notion of a fuzzy set is completely nonstatistical in nature. We begin with several definitions involving fuzzy sets which are obvious extensions of the corresponding definitions for ordinary sets. A fuzzy set is empty if and only if its membership function is identically zero on X.
This notion and the related notions of union and intersection are defined as follows. More precisely, if D is any fuzzy set which contains both A and B, then it also contains the union of A and B. To show that this definition is equivalent to 3 , we note, first, that C as defined by 3 contains both A and B, since Max Ira, f. Furthermore, if D is any fuzzy set containing both A and B, then f. The notion of an intersection of fuzzy sets can be defined in an analo- gous manner. Specifically: Intersection.
As in the case of ordinary sets, A and B are disjoint if A f l B is empty. Note that N, like U, has the associative property. The intersection and union of two fuzzy sets in R 1 are illustrated in Fig. The membership function of the union is comprised of curve seg- ments 1 and 2; that of the intersection is comprised of segments 3 and 4 heavy lines.
Illustration of the union and intersection of fuzzy sets in RI the case of fuzzy sets. Similarly, in the case of lo , the corresponding relation in terms of f. Essentially, fuzzy sets in X constitute a distributive lattice with a 0 and 1 Birkhoff, In the case of fuzzy sets, one can give an analogous interpretation in terms of sieves. Associate with.
More generally, a well-formed expression involving A s , -. Note t h a t the mesh sizes of the sieves in the network depend on x and t h a t the network as a whole is equivalent to a single sieve whose meshes are of size f c x.
Among the more important of these are the following. Algebraic product. The algebraic product of A and B is denoted by A B and is defined in terms of the membership functions of A and B by the relation fa. Absolute difference. This was pointed out by T. Note that for ordinary sets f'] and the alge- braic product are equivalent operations, as are O and.
This mode of combining f and g can be generalized to fuzzy sets in the following manner. Let A, B, and A be arbitrary fuzzy sets.
In the sequel, we shall merely de- fine the notion of a fuzzy relation and touch upon a few related concepts. Ordinarily, a relation is defined as a set of ordered pairs Halmos, ; e. For such relations, the membership function is of the form fA xl,. Fuzzy sets induced by mappings.
Let T be a mapping from X to a space Y. Consider now a converse problem in which A is a given fuzzy set in X, and T, as before, is a mapping from X to Y. The question is: What. If T is not one-one, then an ambiguity arises when two or more dis- tinct points in X, say xl and z2, with different grades of membership in A, are mapped into the same poirtt y in Y.
In this case, the question is: What grade of membership in B should be assigned to y? To resolve this ambiguity, we agree to assign the larger of the two grades of membership to y. More generally, the membership function for B will be defined by. CONVEXITY As will be seen in the sequel, the notion of convexity can readily be extended to fuzzy sets in such a way as to preserve many of the prop- erties which it has in the context of ordinary sets. This notion appears to be particularly useful in applications involving pattern classification, optimization and related problems.
An alternative and more direct definition of convexity is the fo! This is illustrated in Fig. I f A and B are convex, so is the intersection. This way of expressing convexity was suggested to the writer by his colleague, E. B y hypothesis, this set is contained in a sphere S of radius R e.
Let H be any hyper- plane supporting S. M will be referred to as the maximM grade in A. Note that 6 This proof was suggested by A. Let x. B y the Bolzano-Weierstrass theorem, this sequence m u s t have at least one limit point, say x0, in F i. Consequently, every spherical neighborhood of x0 will contain infinitely m a n y points from the sequence x l , x2, -.
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